coin_change_2.py

"""

518. Coin Change 2
Medium

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return the number of combinations that make up that amount. If that amount of money cannot be made up by any combination of the coins, return 0.

You may assume that you have an infinite number of each kind of coin.

The answer is guaranteed to fit into a signed 32-bit integer.

 

Example 1:

Input: amount = 5, coins = [1,2,5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1
Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.
Example 3:

Input: amount = 10, coins = [10]
Output: 1
 

Constraints:

1 <= coins.length <= 300
1 <= coins[i] <= 5000
All the values of coins are unique.
0 <= amount <= 5000

"""

# V0 
# IDEA : DP
# DP EQUATION : dp[i] += dp[i - coin]
class Solution(object):
    def change(self, amount, coins):
        """
        :type amount: int
        :type coins: List[int]
        :rtype: int
        """
        # beware of it : e.g.  dp[3] needs to have [0,1,2,3], so length needs to be (amount + 1) 
        dp = [0] * (amount + 1)
        dp[0] = 1
        for coin in coins:
            for i in range(1, amount + 1):
                # beware of it 
                if coin <= i:
                    # beware of it 
                    dp[i] += dp[i - coin]
        return dp[amount]

# V1
# https://blog.csdn.net/fuxuemingzhu/article/details/82845212
# IDEA : DP
# DP EQUATION : dp[i] += dp[i - coin], when coin <= i 
class Solution(object):
    def change(self, amount, coins):
        """
        :type amount: int
        :type coins: List[int]
        :rtype: int
        """
        dp = [0] * (amount + 1)
        dp[0] = 1
        for coin in coins:
            for i in range(1, amount + 1):
                if coin <= i:
                    dp[i] += dp[i - coin]
        return dp[amount]

# V1'
# IDEA : DP
# https://leetcode.com/problems/coin-change-2/solution/
class Solution:
    def change(self, amount: int, coins: List[int]) -> int:
        dp = [0] * (amount + 1)
        dp[0] = 1
        
        for coin in coins:
            for x in range(coin, amount + 1):
                dp[x] += dp[x - coin]
        return dp[amount]

# V1'
# https://www.jiuzhang.com/solution/coin-change-ii/#tag-highlight-lang-python
class Solution:
    """
    @param amount: a total amount of money amount
    @param coins: the denomination of each coin
    @return: the number of combinations that make up the amount
    """
    def change(self, amount, coins):
        # write your code here
        dp = [0] * (amount + 1)
        dp[0] = 1
        for i in range(len(coins)):
            for j in range(coins[i], amount + 1):
                dp[j] += dp[j - coins[i]]
        return dp[amount]

# V2