Resources

Read or watch:

Binary tree (note the first line: Not to be confused with B-tree.)
Data Structure and Algorithms - Tree
Tree Traversal
Binary Search Tree
Data structures: Binary Tree

Learning Objectives

At the end of this project, you are expected to be able to explain to anyone, without the help of Google:

General

What is a binary tree
What is the difference between a binary tree and a Binary Search Tree
What is the possible gain in terms of time complexity compared to linked lists
What are the depth, the height, the size of a binary tree
What are the different traversal methods to go through a binary tree
What is a complete, a full, a perfect, a balanced binary tree

Requirements

General

Allowed editors: vi, vim, emacs
All your files will be compiled on Ubuntu 20.04 LTS using gcc, using the options -Wall -Werror -Wextra -pedantic -std=gnu89
All your files should end with a new line
A README.md file, at the root of the folder of the project, is mandatory
Your code should use the Betty style. It will be checked using betty-style.pl and betty-doc.pl
You are not allowed to use global variables
No more than 5 functions per file
You are allowed to use the standard library
In the following examples, the main.c files are shown as examples. You can use them to test your functions, but you don’t have to push them to your repo (if you do we won’t take them into account). We will use our own main.c files at compilation. Our main.c files might be different from the one shown in the examples
The prototypes of all your functions should be included in your header file called binary_trees.h
Don’t forget to push your header file
All your header files should be include guarded

More Info

Data structures

Please use the following data structures and types for binary trees. Don’t forget to include them in your header file.

Basic Binary Tree

/**
 * struct binary_tree_s - Binary tree node
 *
 * @n: Integer stored in the node
 * @parent: Pointer to the parent node
 * @left: Pointer to the left child node
 * @right: Pointer to the right child node
 */
struct binary_tree_s
{
    int n;
    struct binary_tree_s *parent;
    struct binary_tree_s *left;
    struct binary_tree_s *right;
};

typedef struct binary_tree_s binary_tree_t;

Binary Search Tree

typedef struct binary_tree_s bst_t;

AVL Tree

typedef struct binary_tree_s avl_t;

Max Binary Heap

typedef struct binary_tree_s heap_t;

Note: For tasks 0 to 23 (included), you have to deal with simple binary trees. They are not BSTs, thus they don’t follow any kind of rule.

Print function

To match the examples in the tasks, you are given this function

This function is used only for visualization purposes. You don’t have to push it to your repo. It may not be used during the correction

Tasks

0. New node

Write a function that creates a binary tree node

Prototype: binary_tree_t *binary_tree_node(binary_tree_t *parent, int value);
Where parent is a pointer to the parent node of the node to create
And value is the value to put in the new node
When created, a node does not have any child
Your function must return a pointer to the new node, or NULL on failure

alex@/tmp/binary_trees$ cat 0-main.c
#include <stdlib.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);

    root->left = binary_tree_node(root, 12);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 16);

    root->right = binary_tree_node(root, 402);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 0-main.c 0-binary_tree_node.c -o 0-node
alex@/tmp/binary_trees$ ./0-node
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (016)     (256)     (512)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 0-binary_tree_node.c

1. Insert left

Write a function that inserts a node as the left-child of another node

Prototype: binary_tree_t *binary_tree_insert_left(binary_tree_t *parent, int value);
Where parent is a pointer to the node to insert the left-child in
And value is the value to store in the new node
Your function must return a pointer to the created node, or NULL on failure or if parent is NULL
If parent already has a left-child, the new node must take its place, and the old left-child must be set as the left-child of the new node.

alex@/tmp/binary_trees$ cat 1-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_print(root);
    printf("\n");
    binary_tree_insert_left(root->right, 128);
    binary_tree_insert_left(root, 54);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 1-main.c 1-binary_tree_insert_left.c 0-binary_tree_node.c -o 1-left
alex@/tmp/binary_trees$ ./1-left
  .--(098)--.
(012)     (402)

       .--(098)-------.
  .--(054)       .--(402)
(012)          (128)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 1-binary_tree_insert_left.c

2. Insert right

Write a function that inserts a node as the right-child of another node

Prototype: binary_tree_t *binary_tree_insert_right(binary_tree_t *parent, int value);
Where parent is a pointer to the node to insert the right-child in
And value is the value to store in the new node
Your function must return a pointer to the created node, or NULL on failure or if parent is NULL
If parent already has a right-child, the new node must take its place, and the old right-child must be set as the right-child of the new node.

alex@/tmp/binary_trees$ cat 2-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_print(root);
    printf("\n");
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 2-main.c 2-binary_tree_insert_right.c 0-binary_tree_node.c -o 2-right
alex@/tmp/binary_trees$ ./2-right
  .--(098)--.
(012)     (402)

  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 2-binary_tree_insert_right.c

3. Delete

Write a function that deletes an entire binary tree

Prototype: void binary_tree_delete(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to delete
If tree is NULL, do nothing

alex@/tmp/binary_trees$ cat 3-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);
    binary_tree_delete(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 3-main.c 3-binary_tree_delete.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 3-del
alex@/tmp/binary_trees$ valgrind ./3-del
==13264== Memcheck, a memory error detector
==13264== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==13264== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==13264== Command: ./3-del
==13264==
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
==13264==
==13264== HEAP SUMMARY:
==13264==     in use at exit: 0 bytes in 0 blocks
==13264==   total heap usage: 9 allocs, 9 frees, 949 bytes allocated
==13264==
==13264== All heap blocks were freed -- no leaks are possible
==13264==
==13264== For counts of detected and suppressed errors, rerun with: -v
==13264== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 3-binary_tree_delete.c

4. Is leaf

Write a function that checks if a node is a leaf

Prototype: int binary_tree_is_leaf(const binary_tree_t *node);
Where node is a pointer to the node to check
Your function must return 1 if node is a leaf, otherwise 0
If node is NULL, return 0

alex@/tmp/binary_trees$ cat 4-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int ret;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    ret = binary_tree_is_leaf(root);
    printf("Is %d a leaf: %d\n", root->n, ret);
    ret = binary_tree_is_leaf(root->right);
    printf("Is %d a leaf: %d\n", root->right->n, ret);
    ret = binary_tree_is_leaf(root->right->right);
    printf("Is %d a leaf: %d\n", root->right->right->n, ret);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 4-binary_tree_is_leaf.c 4-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 4-leaf
alex@/tmp/binary_trees$ ./4-leaf
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Is 98 a leaf: 0
Is 128 a leaf: 0
Is 402 a leaf: 1
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 4-binary_tree_is_leaf.c

5. Is root

Write a function that checks if a given node is a root

Prototype: int binary_tree_is_root(const binary_tree_t *node);
Where node is a pointer to the node to check
Your function must return 1 if node is a root, otherwise 0
If node is NULL, return 0

alex@/tmp/binary_trees$ cat 5-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int ret;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    ret = binary_tree_is_root(root);
    printf("Is %d a root: %d\n", root->n, ret);
    ret = binary_tree_is_root(root->right);
    printf("Is %d a root: %d\n", root->right->n, ret);
    ret = binary_tree_is_root(root->right->right);
    printf("Is %d a root: %d\n", root->right->right->n, ret);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 5-binary_tree_is_root.c 5-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 5-root
alex@/tmp/binary_trees$ ./5-root
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Is 98 a root: 1
Is 128 a root: 0
Is 402 a root: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 5-binary_tree_is_root.c

6. Pre-order traversal

Write a function that goes through a binary tree using pre-order traversal

Prototype: void binary_tree_preorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.
If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 6-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_preorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 6-main.c 6-binary_tree_preorder.c 0-binary_tree_node.c -o 6-pre
alex@/tmp/binary_trees$ ./6-pre
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
98
12
6
56
402
256
512
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 6-binary_tree_preorder.c

7. In-order traversal

Write a function that goes through a binary tree using in-order traversal

Prototype: void binary_tree_inorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.
If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 7-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_inorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 7-main.c 7-binary_tree_inorder.c 0-binary_tree_node.c -o 7-in
alex@/tmp/binary_trees$ ./7-in
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
6
12
56
98
256
402
512
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 7-binary_tree_inorder.c

8. Post-order traversal

Write a function that goes through a binary tree using post-order traversal

Prototype: void binary_tree_postorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.
If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 8-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_postorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 8-main.c 8-binary_tree_postorder.c 0-binary_tree_node.c -o 8-post
alex@/tmp/binary_trees$ ./8-post
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
6
56
12
256
512
402
98
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 8-binary_tree_postorder.c

9. Height

Write a function that measures the height of a binary tree

Prototype: size_t binary_tree_height(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the height.
If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 9-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t height;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    height = binary_tree_height(root);
    printf("Height from %d: %lu\n", root->n, height);
    height = binary_tree_height(root->right);
    printf("Height from %d: %lu\n", root->right->n, height);
    height = binary_tree_height(root->left->right);
    printf("Height from %d: %lu\n", root->left->right->n, height);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 9-binary_tree_height.c 9-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 9-height
alex@/tmp/binary_trees$ ./9-height
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Height from 98: 2
Height from 128: 1
Height from 54: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 9-binary_tree_height.c

10. Depth

Write a function that measures the depth of a node in a binary tree

Prototype: size_t binary_tree_depth(const binary_tree_t *tree);
Where tree is a pointer to the node to measure the depth
If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 10-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t depth;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    depth = binary_tree_depth(root);
    printf("Depth of %d: %lu\n", root->n, depth);
    depth = binary_tree_depth(root->right);
    printf("Depth of %d: %lu\n", root->right->n, depth);
    depth = binary_tree_depth(root->left->right);
    printf("Depth of %d: %lu\n", root->left->right->n, depth);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 10-binary_tree_depth.c 10-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 10-depth
alex@/tmp/binary_trees$ ./10-depth
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Depth of 98: 0
Depth of 128: 1
Depth of 54: 2
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 10-binary_tree_depth.c

11. Size

Write a function that measures the size of a binary tree

Prototype: size_t binary_tree_size(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the size
If tree is NULL, the function must return 0

alex@/tmp/binary_trees$ cat 11-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t size;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    size = binary_tree_size(root);
    printf("Size of %d: %lu\n", root->n, size);
    size = binary_tree_size(root->right);
    printf("Size of %d: %lu\n", root->right->n, size);
    size = binary_tree_size(root->left->right);
    printf("Size of %d: %lu\n", root->left->right->n, size);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 11-binary_tree_size.c 11-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 11-size
alex@/tmp/binary_trees$ ./11-size
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Size of 98: 5
Size of 128: 2
Size of 54: 1
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 11-binary_tree_size.c

12. Leaves

Write a function that counts the leaves in a binary tree

Prototype: size_t binary_tree_leaves(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to count the number of leaves
If tree is NULL, the function must return 0
A NULL pointer is not a leaf

alex@/tmp/binary_trees$ cat 12-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t leaves;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    leaves = binary_tree_leaves(root);
    printf("Leaves in %d: %lu\n", root->n, leaves);
    leaves = binary_tree_leaves(root->right);
    printf("Leaves in %d: %lu\n", root->right->n, leaves);
    leaves = binary_tree_leaves(root->left->right);
    printf("Leaves in %d: %lu\n", root->left->right->n, leaves);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 12-binary_tree_leaves.c 12-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 12-leaves
alex@/tmp/binary_trees$ ./12-leaves
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Leaves in 98: 2
Leaves in 128: 1
Leaves in 54: 1
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 12-binary_tree_leaves.c

13. Nodes

Write a function that counts the nodes with at least 1 child in a binary tree

Prototype: size_t binary_tree_nodes(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to count the number of nodes
If tree is NULL, the function must return 0
A NULL pointer is not a node

alex@/tmp/binary_trees$ cat 13-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t nodes;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    nodes = binary_tree_nodes(root);
    printf("Nodes in %d: %lu\n", root->n, nodes);
    nodes = binary_tree_nodes(root->right);
    printf("Nodes in %d: %lu\n", root->right->n, nodes);
    nodes = binary_tree_nodes(root->left->right);
    printf("Nodes in %d: %lu\n", root->left->right->n, nodes);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 13-binary_tree_nodes.c 13-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 13-nodes
alex@/tmp/binary_trees$ ./13-nodes
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Nodes in 98: 3
Nodes in 128: 1
Nodes in 54: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 13-binary_tree_nodes.c

14. Balance factor

Write a function that measures the balance factor of a binary tree

Prototype: int binary_tree_balance(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the balance factor
If tree is NULL, return 0

alex@/tmp/binary_trees$ cat 14-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int balance;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_insert_left(root, 45);
    binary_tree_insert_right(root->left, 50);
    binary_tree_insert_left(root->left->left, 10);
    binary_tree_insert_left(root->left->left->left, 8);
    binary_tree_print(root);

    balance = binary_tree_balance(root);
    printf("Balance of %d: %+d\n", root->n, balance);
    balance = binary_tree_balance(root->right);
    printf("Balance of %d: %+d\n", root->right->n, balance);
    balance = binary_tree_balance(root->left->left->right);
    printf("Balance of %d: %+d\n", root->left->left->right->n, balance);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 14-binary_tree_balance.c 14-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c 1-binary_tree_insert_left.c -o 14-balance
alex@/tmp/binary_trees$ ./14-balance
                      .-------(098)--.
            .-------(045)--.       (128)--.
       .--(012)--.       (050)          (402)
  .--(010)     (054)
(008)
Balance of 98: +2
Balance of 128: -1
Balance of 54: +0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 14-binary_tree_balance.c

15. Is full

Write a function that checks if a binary tree is full

Prototype: int binary_tree_is_full(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 15-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int full;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    root->left->left = binary_tree_node(root->left, 10);
    binary_tree_print(root);

    full = binary_tree_is_full(root);
    printf("Is %d full: %d\n", root->n, full);
    full = binary_tree_is_full(root->left);
    printf("Is %d full: %d\n", root->left->n, full);
    full = binary_tree_is_full(root->right);
    printf("Is %d full: %d\n", root->right->n, full);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 15-binary_tree_is_full.c 15-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 15-full
alex@/tmp/binary_trees$ ./15-full
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)
Is 98 full: 0
Is 12 full: 1
Is 128 full: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 15-binary_tree_is_full.c

16. Is perfect

Write a function that checks if a binary tree is perfect

Prototype: int binary_tree_is_perfect(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 16-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int perfect;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 10);

    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n\n", perfect);

    root->right->right->left = binary_tree_node(root->right->right, 10);
    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n\n", perfect);

    root->right->right->right = binary_tree_node(root->right->right, 10);
    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n", perfect);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 16-binary_tree_is_perfect.c 16-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 16-perfect
alex@/tmp/binary_trees$ ./16-perfect
       .-------(098)-------.
  .--(012)--.         .--(128)--.
(010)     (054)     (010)     (402)
Perfect: 1

       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (010)       .--(402)
                              (010)
Perfect: 0

       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (010)       .--(402)--.
                              (010)     (010)
Perfect: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 16-binary_tree_is_perfect.c

17. Sibling

Write a function that finds the sibling of a node

Prototype: binary_tree_t *binary_tree_sibling(binary_tree_t *node);
Where node is a pointer to the node to find the sibling
Your function must return a pointer to the sibling node
If node is NULL or the parent is NULL, return NULL
If node has no sibling, return NULL

alex@/tmp/binary_trees$ cat 17-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    binary_tree_t *sibling;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 402);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 110);
    root->right->right->left = binary_tree_node(root->right->right, 200);
    root->right->right->right = binary_tree_node(root->right->right, 512);

    binary_tree_print(root);
    sibling = binary_tree_sibling(root->left);
    printf("Sibling of %d: %d\n", root->left->n, sibling->n);
    sibling = binary_tree_sibling(root->right->left);
    printf("Sibling of %d: %d\n", root->right->left->n, sibling->n);
    sibling = binary_tree_sibling(root->left->right);
    printf("Sibling of %d: %d\n", root->left->right->n, sibling->n);
    sibling = binary_tree_sibling(root);
    printf("Sibling of %d: %p\n", root->n, (void *)sibling);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 17-main.c 17-binary_tree_sibling.c 0-binary_tree_node.c -o 17-sibling
alex@/tmp/binary_trees$ ./17-sibling
       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (110)       .--(402)--.
                              (200)     (512)
Sibling of 12: 128
Sibling of 110: 402
Sibling of 54: 10
Sibling of 98: (nil)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 17-binary_tree_sibling.c

18. Uncle

Write a function that finds the uncle of a node

Prototype: binary_tree_t *binary_tree_uncle(binary_tree_t *node);
Where node is a pointer to the node to find the uncle
Your function must return a pointer to the uncle node
If node is NULL, return NULL
If node has no uncle, return NULL

alex@/tmp/binary_trees$ cat 18-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    binary_tree_t *uncle;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 402);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 110);
    root->right->right->left = binary_tree_node(root->right->right, 200);
    root->right->right->right = binary_tree_node(root->right->right, 512);

    binary_tree_print(root);
    uncle = binary_tree_uncle(root->right->left);
    printf("Uncle of %d: %d\n", root->right->left->n, uncle->n);
    uncle = binary_tree_uncle(root->left->right);
    printf("Uncle of %d: %d\n", root->left->right->n, uncle->n);
    uncle = binary_tree_uncle(root->left);
    printf("Uncle of %d: %p\n", root->left->n, (void *)uncle);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 18-main.c 18-binary_tree_uncle.c 0-binary_tree_node.c -o 18-uncle
alex@/tmp/binary_trees$ ./18-uncle
       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (110)       .--(402)--.
                              (200)     (512)
Uncle of 110: 12
Uncle of 54: 128
Uncle of 12: (nil)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 18-binary_tree_uncle.c

19. Lowest common ancestor

Write a function that finds the lowest common ancestor of two nodes

Prototype: binary_tree_t *binary_trees_ancestor(const binary_tree_t *first, const binary_tree_t *second);
Where first is a pointer to the first node -And second is a pointer to the second node
Your function must return a pointer to the lowest common ancestor node of the two given nodes
If no common ancestor was found, your function must return NULL

alex@/tmp/binary_trees$ cat 100-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * launch_test - Test ancestor function and print informations
 *
 * @n1: First node
 * @n2: Second node
 */
void launch_test(binary_tree_t *n1, binary_tree_t *n2)
{
    binary_tree_t *ancestor;

    ancestor = binary_trees_ancestor(n1, n2);
    printf("Ancestor of [%d] & [%d]: ", n1->n, n2->n);
    if (!ancestor)
        printf("(nil)\n");
    else
        printf("%d\n", ancestor->n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 128);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 45);
    root->right->right->left = binary_tree_node(root->right->right, 92);
    root->right->right->right = binary_tree_node(root->right->right, 65);
    binary_tree_print(root);

    launch_test(root->left, root->right);
    launch_test(root->right->left, root->right->right->right);
    launch_test(root->right->right, root->right->right->right);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 100-main.c 100-binary_trees_ancestor.c 0-binary_tree_node.c -o 100-ancestor
alex@/tmp/binary_trees$ ./100-ancestor
       .-------(098)-------.
  .--(012)--.         .--(402)-------.
(010)     (054)     (045)       .--(128)--.
                              (092)     (065)
Ancestor of [12] & [402]: 98
Ancestor of [45] & [65]: 402
Ancestor of [128] & [65]: 128
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 100-binary_trees_ancestor.c

20. Level-order traversal

Write a function that goes through a binary tree using level-order traversal

Prototype: void binary_tree_levelorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.
If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 101-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_levelorder(root, &print_num);
    binary_tree_delete(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 101-main.c 101-binary_tree_levelorder.c 0-binary_tree_node.c 3-binary_tree_delete.c -o 101-lvl
alex@/tmp/binary_trees$ valgrind ./101-lvl
==23445== Memcheck, a memory error detector
==23445== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==23445== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==23445== Command: ./101-lvl
==23445==
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
98
12
402
6
56
256
512
==23445==
==23445== HEAP SUMMARY:
==23445==     in use at exit: 0 bytes in 0 blocks
==23445==   total heap usage: 19 allocs, 19 frees, 1,197 bytes allocated
==23445==
==23445== All heap blocks were freed -- no leaks are possible
==23445==
==23445== For counts of detected and suppressed errors, rerun with: -v
==23445== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 101-binary_tree_levelorder.c

21. Is complete

Write a function that checks if a binary tree is complete

Prototype: int binary_tree_is_complete(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 102-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int complete;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 10);

    binary_tree_print(root);
    complete = binary_tree_is_complete(root);
    printf("Is %d complete: %d\n", root->n, complete);
    complete = binary_tree_is_complete(root->left);
    printf("Is %d complete: %d\n", root->left->n, complete);

    root->right->left = binary_tree_node(root->right, 112);
    binary_tree_print(root);
    complete = binary_tree_is_complete(root);
    printf("Is %d complete: %d\n", root->n, complete);

    root->left->left->left = binary_tree_node(root->left->left, 8);
    binary_tree_print(root);
    complete = binary_tree_is_complete(root);
    printf("Is %d complete: %d\n", root->n, complete);

    root->left->right->left = binary_tree_node(root->left->right, 23);
    binary_tree_print(root);
    complete = binary_tree_is_complete(root);
    printf("Is %d complete: %d\n", root->n, complete);

    binary_tree_delete(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 102-main.c 102-binary_tree_is_complete.c 0-binary_tree_node.c 3-binary_tree_delete.c -o 102-complete
alex@/tmp/binary_trees$ ./102-complete
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)
Is 98 complete: 0
Is 12 complete: 1
       .-------(098)-------.
  .--(012)--.         .--(128)--.
(010)     (054)     (112)     (402)
Is 98 complete: 1
            .-------(098)-------.
       .--(012)--.         .--(128)--.
  .--(010)     (054)     (112)     (402)
(008)
Is 98 complete: 1
            .------------(098)-------.
       .--(012)-------.         .--(128)--.
  .--(010)       .--(054)     (112)     (402)
(008)          (023)
Is 98 complete: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 102-binary_tree_is_complete.c

22. Rotate left

Write a function that performs a left-rotation on a binary tree

Prototype: binary_tree_t *binary_tree_rotate_left(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to rotate
Your function must return a pointer to the new root node of the tree once rotated

alex@/tmp/binary_trees$ cat 103-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->right = binary_tree_node(root, 128);
    root->right->right = binary_tree_node(root->right, 402);
    binary_tree_print(root);
    printf("Rotate-left %d\n", root->n);
    root = binary_tree_rotate_left(root);
    binary_tree_print(root);
    printf("\n");

    root->right->right = binary_tree_node(root->right, 450);
    root->right->left = binary_tree_node(root->right, 420);
    binary_tree_print(root);
    printf("Rotate-left %d\n", root->n);
    root = binary_tree_rotate_left(root);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 103-binary_tree_rotate_left.c 103-main.c 0-binary_tree_node.c -o 103-rotl
alex@/tmp/binary_trees$ ./103-rotl
(098)--.
     (128)--.
          (402)
Rotate-left 98
  .--(128)--.
(098)     (402)

  .--(128)-------.
(098)       .--(402)--.
          (420)     (450)
Rotate-left 128
       .-------(402)--.
  .--(128)--.       (450)
(098)     (420)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 103-binary_tree_rotate_left.c

23. Rotate right

Write a function that performs a right-rotation on a binary tree

Prototype: binary_tree_t *binary_tree_rotate_right(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to rotate
Your function must return a pointer to the new root node of the tree once rotated

alex@/tmp/binary_trees$ cat 104-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 64);
    root->left->left = binary_tree_node(root->left, 32);
    binary_tree_print(root);
    printf("Rotate-right %d\n", root->n);
    root = binary_tree_rotate_right(root);
    binary_tree_print(root);
    printf("\n");

    root->left->left = binary_tree_node(root->left, 20);
    root->left->right = binary_tree_node(root->left, 56);
    binary_tree_print(root);
    printf("Rotate-right %d\n", root->n);
    root = binary_tree_rotate_right(root);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 104-binary_tree_rotate_right.c 104-main.c 0-binary_tree_node.c -o 104-rotr
alex@/tmp/binary_trees$ ./104-rotr
       .--(098)
  .--(064)
(032)
Rotate-right 98
  .--(064)--.
(032)     (098)

       .-------(064)--.
  .--(032)--.       (098)
(020)     (056)
Rotate-right 64
  .--(032)-------.
(020)       .--(064)--.
          (056)     (098)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 104-binary_tree_rotate_right.c

24. Is BST

Write a function that checks if a binary tree is a valid Binary Search Tree

Prototype: int binary_tree_is_bst(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid BST, and 0 otherwise
If tree is NULL, return 0

Properties of a Binary Search Tree:

The left subtree of a node contains only nodes with values less than the node’s value
The right subtree of a node contains only nodes with values greater than the node’s value
The left and right subtree each must also be a binary search tree
There must be no duplicate values

alex@/tmp/binary_trees$ cat 110-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int bst;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 10);

    binary_tree_print(root);
    bst = binary_tree_is_bst(root);
    printf("Is %d bst: %d\n", root->n, bst);
    bst = binary_tree_is_bst(root->left);
    printf("Is %d bst: %d\n", root->left->n, bst);

    root->right->left = binary_tree_node(root->right, 97);
    binary_tree_print(root);
    bst = binary_tree_is_bst(root);
    printf("Is %d bst: %d\n", root->n, bst);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 110-main.c 110-binary_tree_is_bst.c 0-binary_tree_node.c -o 110-is_bst
alex@/tmp/binary_trees$ ./110-is_bst
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)
Is 98 bst: 1
Is 12 bst: 1
       .-------(098)-------.
  .--(012)--.         .--(128)--.
(010)     (054)     (097)     (402)
Is 98 bst: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 110-binary_tree_is_bst.c

25. BST - Insert

Write a function that inserts a value in a Binary Search Tree

Prototype: bst_t *bst_insert(bst_t **tree, int value);
Where tree is a double pointer to the root node of the BST to insert the value
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in tree is NULL, the created node must become the root node.
If the value is already present in the tree, it must be ignored

Your file 0-binary_tree_node.c will be compile during the correction

alex@/tmp/binary_trees$ cat 111-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    bst_t *root;
    bst_t *node;

    root = NULL;
    node = bst_insert(&root, 98);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 402);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 12);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 46);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 128);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 256);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 512);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 1);
    printf("Inserted: %d\n", node->n);
    node = bst_insert(&root, 128);
    printf("Node should be nil -> %p\n", (void *)node);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 111-bst_insert.c 111-main.c 0-binary_tree_node.c -o 111-bst_insert
alex@/tmp/binary_trees$ ./111-bst_insert
Inserted: 98
Inserted: 402
Inserted: 12
Inserted: 46
Inserted: 128
Inserted: 256
Inserted: 512
Inserted: 1
Node should be nil -> (nil)
       .-------(098)------------.
  .--(012)--.         .-------(402)--.
(001)     (046)     (128)--.       (512)
                         (256)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 111-bst_insert.c, 0-binary_tree_node.c

26. BST - Array to BST

Write a function that builds a Binary Search Tree from an array

Prototype: bst_t *array_to_bst(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created BST, or NULL on failure
If a value of the array is already present in the tree, this value must be ignored

Your files 111-bst_insert.c and 0-binary_tree_node.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 112-main.c
#include <stdlib.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    bst_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);

    tree = array_to_bst(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 112-array_to_bst.c 112-main.c 111-bst_insert.c 0-binary_tree_node.c -o 112-bst_array
alex@/tmp/binary_trees$ ./112-bst_array
                                     .------------(079)-------.
                 .-----------------(047)-------.         .--(087)--.
       .-------(021)-------.              .--(068)     (084)     (091)-------.
  .--(002)--.         .--(032)--.       (062)                           .--(098)
(001)     (020)     (022)     (034)                                   (095)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 112-array_to_bst.c, 111-bst_insert.c, 0-binary_tree_node.c

27. BST - Search

Write a function that searches for a value in a Binary Search Tree

Prototype: bst_t *bst_search(const bst_t *tree, int value);
Where tree is a pointer to the root node of the BST to search
And value is the value to search in the tree
Your function must return a pointer to the node containing a value equals to value
If tree is NULL or if nothing is found, your function must return NULL

alex@/tmp/binary_trees$ cat 113-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    bst_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);
    bst_t *node;

    tree = array_to_bst(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);
    node = bst_search(tree, 32);
    printf("Found: %d\n", node->n);
    binary_tree_print(node);
    node = bst_search(tree, 512);
    printf("Node should be nil -> %p\n", (void *)node);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 113-bst_search.c 113-main.c 112-array_to_bst.c 111-bst_insert.c 0-binary_tree_node.c -o 113-bst_search
alex@/tmp/binary_trees$ ./113-bst_search
                                     .------------(079)-------.
                 .-----------------(047)-------.         .--(087)--.
       .-------(021)-------.              .--(068)     (084)     (091)-------.
  .--(002)--.         .--(032)--.       (062)                           .--(098)
(001)     (020)     (022)     (034)                                   (095)
Found: 32
  .--(032)--.
(022)     (034)
Node should be nil -> (nil)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 113-bst_search.c

28. BST - Remove

Write a function that removes a node from a Binary Search Tree

Prototype: bst_t *bst_remove(bst_t *root, int value);
Where root is a pointer to the root node of the tree where you will remove a node
And value is the value to remove in the tree
Once located, the node containing a value equals to value must be removed and freed
If the node to be deleted has two children, it must be replaced with its first in-order successor (not predecessor)
Your function must return a pointer to the new root node of the tree after removing the desired value

alex@/tmp/binary_trees$ cat 114-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    bst_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);

    tree = array_to_bst(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);

    tree = bst_remove(tree, 79);
    printf("Removed 79...\n");
    binary_tree_print(tree);

    tree = bst_remove(tree, 21);
    printf("Removed 21...\n");
    binary_tree_print(tree);

    tree = bst_remove(tree, 68);
    printf("Removed 68...\n");
    binary_tree_print(tree);
    binary_tree_delete(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 114-bst_remove.c 114-main.c 112-array_to_bst.c 111-bst_insert.c 0-binary_tree_node.c 3-binary_tree_delete.c -o 114-bst_rm
alex@/tmp/binary_trees$ valgrind ./114-bst_rm
==14720== Memcheck, a memory error detector
==14720== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==14720== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==14720== Command: ./114-bst_rm
==14720==
                                     .------------(079)-------.
                 .-----------------(047)-------.         .--(087)--.
       .-------(021)-------.              .--(068)     (084)     (091)-------.
  .--(002)--.         .--(032)--.       (062)                           .--(098)
(001)     (020)     (022)     (034)                                   (095)
Removed 79...
                                     .------------(084)--.
                 .-----------------(047)-------.       (087)--.
       .-------(021)-------.              .--(068)          (091)-------.
  .--(002)--.         .--(032)--.       (062)                      .--(098)
(001)     (020)     (022)     (034)                              (095)
Removed 21...
                                .------------(084)--.
                 .------------(047)-------.       (087)--.
       .-------(022)--.              .--(068)          (091)-------.
  .--(002)--.       (032)--.       (062)                      .--(098)
(001)     (020)          (034)                              (095)
Removed 68...
                                .-------(084)--.
                 .------------(047)--.       (087)--.
       .-------(022)--.            (062)          (091)-------.
  .--(002)--.       (032)--.                             .--(098)
(001)     (020)          (034)                         (095)
==14720==
==14720== HEAP SUMMARY:
==14720==     in use at exit: 0 bytes in 0 blocks
==14720==   total heap usage: 40 allocs, 40 frees, 5,772 bytes allocated
==14720==
==14720== All heap blocks were freed -- no leaks are possible
==14720==
==14720== For counts of detected and suppressed errors, rerun with: -v
==14720== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 114-bst_remove.c

29. Big O #BST

What are the average time complexities of those operations on a Binary Search Tree (one answer per line):

Inserting the value n
Removing the node with the value n
Searching for a node in a BST of size n

Repo:

GitHub repository: binary_trees
File: 115-O

30. Is AVL

Write a function that checks if a binary tree is a valid AVL Tree

Prototype: int binary_tree_is_avl(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid AVL Tree, and 0 otherwise
If tree is NULL, return 0

Properties of an AVL Tree:

An AVL Tree is a BST
The difference between heights of left and right subtrees cannot be more than one
The left and right subtrees must also be AVL trees

alex@/tmp/binary_trees$ cat 120-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * basic_tree - Build a basic binary tree
 *
 * Return: A pointer to the created tree
 */
binary_tree_t *basic_tree(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 10);
    return (root);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int avl;

    root = basic_tree();

    binary_tree_print(root);
    avl = binary_tree_is_avl(root);
    printf("Is %d avl: %d\n", root->n, avl);
    avl = binary_tree_is_avl(root->left);
    printf("Is %d avl: %d\n", root->left->n, avl);

    root->right->left = binary_tree_node(root->right, 97);
    binary_tree_print(root);
    avl = binary_tree_is_avl(root);
    printf("Is %d avl: %d\n", root->n, avl);

    root = basic_tree();
    root->right->right->right = binary_tree_node(root->right->right, 430);
    binary_tree_print(root);
    avl = binary_tree_is_avl(root);
    printf("Is %d avl: %d\n", root->n, avl);

    root->right->right->right->left = binary_tree_node(root->right->right->right, 420);
    binary_tree_print(root);
    avl = binary_tree_is_avl(root);
    printf("Is %d avl: %d\n", root->n, avl);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 120-main.c 120-binary_tree_is_avl.c 0-binary_tree_node.c -o 120-is_avl
alex@/tmp/binary_trees$ ./120-is_avl
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)
Is 98 avl: 1
Is 12 avl: 1
       .-------(098)-------.
  .--(012)--.         .--(128)--.
(010)     (054)     (097)     (402)
Is 98 avl: 0
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)--.
                              (430)
Is 98 avl: 0
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)-------.
                                .--(430)
                              (420)
Is 98 avl: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 120-binary_tree_is_avl.c

31. AVL - Insert

Write a function that inserts a value in an AVL Tree

Prototype: avl_t *avl_insert(avl_t **tree, int value);
Where tree is a double pointer to the root node of the AVL tree for inserting the value
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in tree is NULL, the created node must become the root node.
The resulting tree after insertion, must be a balanced AVL Tree

Your files 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c, 104-binary_tree_rotate_right.c and 0-binary_tree_node.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 121-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    avl_t *root;
    avl_t *node;

    root = NULL;
    node = avl_insert(&root, 98);
    printf("Inserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 402);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 12);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 46);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 128);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 256);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 512);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = avl_insert(&root, 50);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 121-avl_insert.c 121-main.c 14-binary_tree_balance.c 103-binary_tree_rotate_left.c 104-binary_tree_rotate_right.c 0-binary_tree_node.c -o 121-avl_insert
alex@/tmp/binary_trees$ ./121-avl_insert
Inserted: 98
(098)

Inserted: 402
(098)--.
     (402)

Inserted: 12
  .--(098)--.
(012)     (402)

Inserted: 46
  .-------(098)--.
(012)--.       (402)
     (046)

Inserted: 128
  .-------(098)-------.
(012)--.         .--(402)
     (046)     (128)

Inserted: 256
  .-------(098)-------.
(012)--.         .--(256)--.
     (046)     (128)     (402)

Inserted: 512
  .-------(098)-------.
(012)--.         .--(256)--.
     (046)     (128)     (402)--.
                              (512)

Inserted: 50
       .-------(098)-------.
  .--(046)--.         .--(256)--.
(012)     (050)     (128)     (402)--.
                                   (512)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 121-avl_insert.c, 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c, 104-binary_tree_rotate_right.c, 0-binary_tree_node.c

32. AVL - Array to AVL

Write a function that builds an AVL tree from an array

Prototype: avl_t *array_to_avl(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created AVL tree, or NULL on failure
If a value of the array is already present in the tree, this value must be ignored

Your files 121-avl_insert.c, 0-binary_tree_node.c, 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c and 104-binary_tree_rotate_right.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 122-main.c
#include <stdlib.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    avl_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);

    tree = array_to_avl(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 122-array_to_avl.c 122-main.c 121-avl_insert.c 0-binary_tree_node.c 14-binary_tree_balance.c 103-binary_tree_rotate_left.c 104-binary_tree_rotate_right.c -o 122-avl_array
alex@/tmp/binary_trees$ ./122-avl_array
                 .-----------------(047)-----------------.
       .-------(021)-------.                   .-------(084)-------.
  .--(002)--.         .--(032)--.         .--(068)--.         .--(091)-------.
(001)     (020)     (022)     (034)     (062)     (079)     (087)       .--(098)
                                                                      (095)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 122-array_to_avl.c, 121-avl_insert.c, 0-binary_tree_node.c, 103-binary_tree_rotate_left.c, 104-binary_tree_rotate_right.c, 14-binary_tree_balance.c

33. AVL - Remove

Write a function that removes a node from an AVL tree

Prototype: avl_t *avl_remove(avl_t *root, int value);
Where root is a pointer to the root node of the tree for removing a node
And value is the value to remove in the tree
Once located, the node containing a value equals to value must be removed and freed
If the node to be deleted has two children, it must be replaced with its first in-order successor (not predecessor)
After deletion of the desired node, the tree must be rebalanced if necessary
Your function must return a pointer to the new root node of the tree after removing the desired value, and after rebalancing

Your files 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c and 104-binary_tree_rotate_right.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 123-main.c
#include <stdio.h>
#include <stdlib.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    avl_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);

    tree = array_to_avl(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);

    tree = avl_remove(tree, 47);
    printf("Removed 47...\n");
    binary_tree_print(tree);

    tree = avl_remove(tree, 79);
    printf("Removed 79...\n");
    binary_tree_print(tree);

    tree = avl_remove(tree, 32);
    printf("Removed 32...\n");
    binary_tree_print(tree);

    tree = avl_remove(tree, 34);
    printf("Removed 34...\n");
    binary_tree_print(tree);

    tree = avl_remove(tree, 22);
    printf("Removed 22...\n");
    binary_tree_print(tree);
    binary_tree_delete(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 123-avl_remove.c 123-main.c 103-binary_tree_rotate_left.c 104-binary_tree_rotate_right.c 122-array_to_avl.c 121-avl_insert.c 14-binary_tree_balance.c 3-binary_tree_delete.c 0-binary_tree_node.c -o 123-avl_rm
alex@/tmp/binary_trees$ valgrind ./123-avl_rm
==15646== Memcheck, a memory error detector
==15646== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==15646== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==15646== Command: ./123-avl_rm
==15646==
                 .-----------------(047)-----------------.
       .-------(021)-------.                   .-------(084)-------.
  .--(002)--.         .--(032)--.         .--(068)--.         .--(091)-------.
(001)     (020)     (022)     (034)     (062)     (079)     (087)       .--(098)
                                                                      (095)
Removed 47...
                 .-----------------(062)------------.
       .-------(021)-------.              .-------(084)-------.
  .--(002)--.         .--(032)--.       (068)--.         .--(091)-------.
(001)     (020)     (022)     (034)          (079)     (087)       .--(098)
                                                                 (095)
Removed 79...
                 .-----------------(062)-----------------.
       .-------(021)-------.                   .-------(091)-------.
  .--(002)--.         .--(032)--.         .--(084)--.         .--(098)
(001)     (020)     (022)     (034)     (068)     (087)     (095)
Removed 32...
                 .------------(062)-----------------.
       .-------(021)-------.              .-------(091)-------.
  .--(002)--.         .--(034)       .--(084)--.         .--(098)
(001)     (020)     (022)          (068)     (087)     (095)
Removed 34...
                 .-------(062)-----------------.
       .-------(021)--.              .-------(091)-------.
  .--(002)--.       (022)       .--(084)--.         .--(098)
(001)     (020)               (068)     (087)     (095)
Removed 22...
       .------------(062)-----------------.
  .--(002)-------.              .-------(091)-------.
(001)       .--(021)       .--(084)--.         .--(098)
          (020)          (068)     (087)     (095)
==15646==
==15646== HEAP SUMMARY:
==15646==     in use at exit: 0 bytes in 0 blocks
==15646==   total heap usage: 48 allocs, 48 frees, 7,350 bytes allocated
==15646==
==15646== All heap blocks were freed -- no leaks are possible
==15646==
==15646== For counts of detected and suppressed errors, rerun with: -v
==15646== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 123-avl_remove.c, 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c, 104-binary_tree_rotate_right.c

34. AVL - From sorted array

Write a function that builds an AVL tree from an array

Prototype: avl_t *sorted_array_to_avl(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created AVL tree, or NULL on failure
You can assume there will be no duplicate value in the array
You are not allowed to rotate
You can only have 2 functions in your file

Your file 0-binary_tree_node.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 124-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_array - Prints an array of integers
 *
 * @array: The array to be printed
 * @size: Size of the array
 */
void print_array(const int *array, size_t size)
{
    size_t i;

    for (i = 0; i < size; ++i)
        printf("(%03d)", array[i]);
    printf("\n");
}

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    avl_t *tree;
    int array[] = {
        1, 2, 20, 21, 22, 32, 34, 47, 62, 68,
        79, 84, 87, 91, 95, 98
    };
    size_t n = sizeof(array) / sizeof(array[0]);

    tree = sorted_array_to_avl(array, n);
    if (!tree)
        return (1);
    print_array(array, n);
    binary_tree_print(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 124-main.c 124-sorted_array_to_avl.c 0-binary_tree_node.c -o 124-avl_sorted
alex@/tmp/binary_trees$ ./124-avl_sorted
(001)(002)(020)(021)(022)(032)(034)(047)(062)(068)(079)(084)(087)(091)(095)(098)
                 .-----------------(047)-----------------.
       .-------(021)-------.                   .-------(084)-------.
  .--(002)--.         .--(032)--.         .--(068)--.         .--(091)--.
(001)     (020)     (022)     (034)     (062)     (079)     (087)     (095)--.
                                                                           (098)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 124-sorted_array_to_avl.c, 0-binary_tree_node.c

35. Big O #AVL Tree

What are the average time complexities of those operations on an AVL Tree (one answer per line):

Inserting the value n
Removing the node with the value n
Searching for a node in an AVL tree of size n

Repo:

GitHub repository: binary_trees
File: 125-O

36. Is Binary heap

Write a function that checks if a binary tree is a valid Max Binary Heap

Prototype: int binary_tree_is_heap(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid Max Binary Heap, and 0 otherwise
If tree is NULL, return 0

Properties of a Max Binary Heap:

It’s a complete tree
In a Max Binary Heap, the value at root must be maximum among all values present in Binary Heap
The last property must be recursively true for all nodes in Binary Tree

alex@/tmp/binary_trees$ cat 130-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * basic_tree - Build a basic binary tree
 *
 * Return: A pointer to the created tree
 */
binary_tree_t *basic_tree(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 90);
    root->right = binary_tree_node(root, 85);
    root->left->right = binary_tree_node(root->left, 80);
    root->left->left = binary_tree_node(root->left, 79);
    return (root);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int heap;

    root = basic_tree();

    binary_tree_print(root);
    heap = binary_tree_is_heap(root);
    printf("Is %d heap: %d\n", root->n, heap);
    heap = binary_tree_is_heap(root->left);
    printf("Is %d heap: %d\n", root->left->n, heap);

    root->right->left = binary_tree_node(root->right, 97);
    binary_tree_print(root);
    heap = binary_tree_is_heap(root);
    printf("Is %d heap: %d\n", root->n, heap);

    root = basic_tree();
    root->right->right = binary_tree_node(root->right, 79);
    binary_tree_print(root);
    heap = binary_tree_is_heap(root);
    printf("Is %d heap: %d\n", root->n, heap);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 130-main.c 130-binary_tree_is_heap.c 0-binary_tree_node.c -o 130-is_heap
alex@/tmp/binary_trees$ ./130-is_heap
       .-------(098)--.
  .--(090)--.       (085)
(079)     (080)
Is 98 heap: 1
Is 90 heap: 1
       .-------(098)-------.
  .--(090)--.         .--(085)
(079)     (080)     (097)
Is 98 heap: 0
       .-------(098)--.
  .--(090)--.       (085)--.
(079)     (080)          (079)
Is 98 heap: 0
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 130-binary_tree_is_heap.c

37. Heap - Insert

Write a function that inserts a value in Max Binary Heap

Prototype: heap_t *heap_insert(heap_t **root, int value)
Where root is a double pointer to the root node of the Heap to insert the value
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in root is NULL, the created node must become the root node.
You have to respect a Max Heap ordering
You are allowed to have up to 6 functions in your file

Your file 0-binary_tree_node.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 131-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    heap_t *root;
    heap_t *node;

    root = NULL;
    node = heap_insert(&root, 98);
    printf("Inserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 402);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 12);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 46);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 128);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 256);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 512);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    node = heap_insert(&root, 50);
    printf("\nInserted: %d\n", node->n);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 131-main.c 131-heap_insert.c 0-binary_tree_node.c -o 131-heap_insert
alex@/tmp/binary_trees$ ./131-heap_insert
Inserted: 98
(098)

Inserted: 402
  .--(402)
(098)

Inserted: 12
  .--(402)--.
(098)     (012)

Inserted: 46
       .--(402)--.
  .--(098)     (012)
(046)

Inserted: 128
       .-------(402)--.
  .--(128)--.       (012)
(046)     (098)

Inserted: 256
       .-------(402)-------.
  .--(128)--.         .--(256)
(046)     (098)     (012)

Inserted: 512
       .-------(512)-------.
  .--(128)--.         .--(402)--.
(046)     (098)     (012)     (256)

Inserted: 50
            .-------(512)-------.
       .--(128)--.         .--(402)--.
  .--(050)     (098)     (012)     (256)
(046)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 131-heap_insert.c, 0-binary_tree_node.c

38. Heap - Array to Binary Heap

Write a function that builds a Max Binary Heap tree from an array

Prototype: heap_t *array_to_heap(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created Binary Heap, or NULL on failure

Your files 131-heap_insert.c and 0-binary_tree_node.c will be compiled during the correction

alex@/tmp/binary_trees$ cat 132-main.c #include <stdlib.h> #include "binary_trees.h"

/**

main - Entry point
Return: 0 on success, error code on failure */ int main(void) { heap_t *tree; int array[] = { 79, 47, 68, 87, 84, 91, 21, 32, 34, 2, 20, 22, 98, 1, 62, 95 }; size_t n = sizeof(array) / sizeof(array[0]);

tree = array_to_heap(array, n); if (!tree) return (1); binary_tree_print(tree); return (0); } alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 132-main.c 132-array_to_heap.c 131-heap_insert.c 0-binary_tree_node.c -o 132-heap_array alex@/tmp/binary_trees$ ./132-heap_array .-----------------(098)-----------------. .-------(095)-------. .-------(091)-------. .--(084)--. .--(079)--. .--(087)--. .--(062)--. .--(047) (034) (002) (020) (022) (068) (001) (021) (032) alex@/tmp/binary_trees$


**Repo:**
- GitHub repository: `binary_trees`
- File: `132-array_to_heap.c, 131-heap_insert.c, 0-binary_tree_node.c`

### 39. Heap - Extract

Write a function that extracts the root node of a Max Binary Heap

- Prototype: `int heap_extract(heap_t **root);`
- Where `root` is a double pointer to the root node of heap
- Your function must return the value stored in the root node
- The root node must be freed and replace with the last `level-order` node of the heap
- Once replaced, the heap must be rebuilt if necessary
- If your function fails, return `0`

```shell
alex@/tmp/binary_trees$ cat 133-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    heap_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);
    int extract;

    tree = array_to_heap(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);

    extract = heap_extract(&tree);
    printf("Extracted: %d\n", extract);
    binary_tree_print(tree);

    extract = heap_extract(&tree);
    printf("Extracted: %d\n", extract);
    binary_tree_print(tree);

    extract = heap_extract(&tree);
    printf("Extracted: %d\n", extract);
    binary_tree_print(tree);
    binary_tree_delete(tree);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 133-main.c 133-heap_extract.c 132-array_to_heap.c 131-heap_insert.c 3-binary_tree_delete.c -o 133-heap_extract
alex@/tmp/binary_trees$ valgrind ./133-heap_extract
==29133== Memcheck, a memory error detector
==29133== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==29133== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==29133== Command: ./133-heap_extract
==29133==
                      .-----------------(098)-----------------.
            .-------(095)-------.                   .-------(091)-------.
       .--(084)--.         .--(079)--.         .--(087)--.         .--(062)--.
  .--(047)     (034)     (002)     (020)     (022)     (068)     (001)     (021)
(032)
Extracted: 98
                 .-----------------(095)-----------------.
       .-------(084)-------.                   .-------(091)-------.
  .--(047)--.         .--(079)--.         .--(087)--.         .--(062)--.
(032)     (034)     (002)     (020)     (022)     (068)     (001)     (021)
Extracted: 95
                 .-----------------(091)-----------------.
       .-------(084)-------.                   .-------(087)-------.
  .--(047)--.         .--(079)--.         .--(068)--.         .--(062)
(032)     (034)     (002)     (020)     (022)     (021)     (001)
Extracted: 91
                 .-----------------(087)-----------------.
       .-------(084)-------.                   .-------(068)--.
  .--(047)--.         .--(079)--.         .--(022)--.       (062)
(032)     (034)     (002)     (020)     (001)     (021)
==29133==
==29133== HEAP SUMMARY:
==29133==     in use at exit: 0 bytes in 0 blocks
==29133==   total heap usage: 213 allocs, 213 frees, 9,063 bytes allocated
==29133==
==29133== All heap blocks were freed -- no leaks are possible
==29133==
==29133== For counts of detected and suppressed errors, rerun with: -v
==29133== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 133-heap_extract.c

40. Heap - Sort

Write a function that converts a Binary Max Heap to a sorted array of integers

Prototype: int *heap_to_sorted_array(heap_t *heap, size_t *size);
Where heap is a pointer to the root node of the heap to convert
And size is an address to store the size of the array
You can assume size is a valid address
Since we are using Max Heap, the returned array must be sorted in descending order

Your file 133-heap_extract.c will be compile during the correction

alex@/tmp/binary_trees$ cat 134-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_array - Prints an array of integers
 *
 * @array: The array to be printed
 * @size: Number of elements in @array
 */
void print_array(const int *array, size_t size)
{
    size_t i;

    i = 0;
    while (array && i < size)
    {
        if (i > 0)
            printf(", ");
        printf("%d", array[i]);
        ++i;
    }
    printf("\n");
}

/**
 * main - Entry point
 *
 * Return: 0 on success, error code on failure
 */
int main(void)
{
    heap_t *tree;
    int array[] = {
        79, 47, 68, 87, 84, 91, 21, 32, 34, 2,
        20, 22, 98, 1, 62, 95
    };
    size_t n = sizeof(array) / sizeof(array[0]);
    int *sorted;
    size_t sorted_size;

    print_array(array, n);
    tree = array_to_heap(array, n);
    if (!tree)
        return (1);
    binary_tree_print(tree);
    sorted = heap_to_sorted_array(tree, &sorted_size);
    print_array(sorted, sorted_size);
    free(sorted);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 134-main.c 134-heap_to_sorted_array.c 133-heap_extract.c 132-array_to_heap.c 131-heap_insert.c -o 134-heap_sort
alex@/tmp/binary_trees$ valgrind ./134-heap_sort
==46529== Memcheck, a memory error detector
==46529== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==46529== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==46529== Command: ./134-heap_sort
==46529==
79, 47, 68, 87, 84, 91, 21, 32, 34, 2, 20, 22, 98, 1, 62, 95
                      .-----------------(098)-----------------.
            .-------(095)-------.                   .-------(091)-------.
       .--(084)--.         .--(079)--.         .--(087)--.         .--(062)--.
  .--(047)     (034)     (002)     (020)     (022)     (068)     (001)     (021)
(032)
98, 95, 91, 87, 84, 79, 68, 62, 47, 34, 32, 22, 21, 20, 2, 1
==46529==
==46529== HEAP SUMMARY:
==46529==     in use at exit: 0 bytes in 0 blocks
==46529==   total heap usage: 301 allocs, 301 frees, 8,323 bytes allocated
==46529==
==46529== All heap blocks were freed -- no leaks are possible
==46529==
==46529== For counts of detected and suppressed errors, rerun with: -v
==46529== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

Repo:

GitHub repository: binary_trees
File: 134-heap_to_sorted_array.c, 133-heap_extract.c

41. Big O #Binary Heap

What are the average time complexities of those operations on a Binary Heap (one answer per line):

Inserting the value n
Extracting the root node
Searching for a node in a binary heap of size n

Repo:

GitHub repository: binary_trees
File: 135-O

Files

README.md

Latest commit

History

README.md

File metadata and controls

Resources

Learning Objectives

General

Requirements

General

More Info

Data structures

Basic Binary Tree

Binary Search Tree

AVL Tree

Max Binary Heap

Print function

Tasks

0. New node

1. Insert left

2. Insert right

3. Delete

4. Is leaf

5. Is root

6. Pre-order traversal

7. In-order traversal

8. Post-order traversal

9. Height

10. Depth

11. Size

12. Leaves

13. Nodes

14. Balance factor

15. Is full

16. Is perfect

17. Sibling

18. Uncle

19. Lowest common ancestor

20. Level-order traversal

21. Is complete

22. Rotate left

23. Rotate right

24. Is BST

25. BST - Insert

26. BST - Array to BST

27. BST - Search

28. BST - Remove

29. Big O #BST

30. Is AVL

31. AVL - Insert

32. AVL - Array to AVL

33. AVL - Remove

34. AVL - From sorted array

35. Big O #AVL Tree

36. Is Binary heap

37. Heap - Insert

38. Heap - Array to Binary Heap

40. Heap - Sort

41. Big O #Binary Heap