k-closest-points-to-origin.py

"""

973. K Closest Points to Origin
Medium

Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer k, return the k closest points to the origin (0, 0).

The distance between two points on the X-Y plane is the Euclidean distance (i.e., √(x1 - x2)2 + (y1 - y2)2).

You may return the answer in any order. The answer is guaranteed to be unique (except for the order that it is in).

 

Example 1:


Input: points = [[1,3],[-2,2]], k = 1
Output: [[-2,2]]
Explanation:
The distance between (1, 3) and the origin is sqrt(10).
The distance between (-2, 2) and the origin is sqrt(8).
Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin.
We only want the closest k = 1 points from the origin, so the answer is just [[-2,2]].
Example 2:

Input: points = [[3,3],[5,-1],[-2,4]], k = 2
Output: [[3,3],[-2,4]]
Explanation: The answer [[-2,4],[3,3]] would also be accepted.
 

Constraints:

1 <= k <= points.length <= 104
-104 < xi, yi < 104


"""

# V0
# IDEA : sort + lambda
class Solution(object):
    def kClosest(self, points, K):
        points.sort(key = lambda x : x[0]**2 +  x[1]**2)
        return points[:K]

# V0'
# IDEA : sort + lambda
class Solution(object):
    def kClosest(self, points, k):
        def my_func(x, y):
            return x**2 + y**2
        # edge case
        if not points:
            return
        points.sort(key= lambda (x, y) : my_func(x, y))
        #print ("points = " + str(points))
        return points[:k]

# V1 
class Solution(object):
    def kClosest(self, points, K):
        # python sort list on lmabda func
        # https://stackoverflow.com/questions/3216398/sorting-by-arbitrary-lambda
        points.sort(key = lambda x : x[0]**2 +  x[1]**2)
        return points[:K]


# V2
# Time:  O(n) on average
# Space: O(1)

# quick select solution
from random import randint
class Solution(object):
    def kClosest(self, points, K):
        """
        :type points: List[List[int]]
        :type K: int
        :rtype: List[List[int]]
        """
        def dist(point):
            return point[0]**2 + point[1]**2
        
        def kthElement(nums, k, compare):
            def PartitionAroundPivot(left, right, pivot_idx, nums, compare):
                new_pivot_idx = left
                nums[pivot_idx], nums[right] = nums[right], nums[pivot_idx]
                for i in range(left, right):
                    if compare(nums[i], nums[right]):
                        nums[i], nums[new_pivot_idx] = nums[new_pivot_idx], nums[i]
                        new_pivot_idx += 1

                nums[right], nums[new_pivot_idx] = nums[new_pivot_idx], nums[right]
                return new_pivot_idx

            left, right = 0, len(nums) - 1
            while left <= right:
                pivot_idx = randint(left, right)
                new_pivot_idx = PartitionAroundPivot(left, right, pivot_idx, nums, compare)
                if new_pivot_idx == k - 1:
                    return
                elif new_pivot_idx > k - 1:
                    right = new_pivot_idx - 1
                else:  # new_pivot_idx < k - 1.
                    left = new_pivot_idx + 1
                    
        kthElement(points, K, lambda a, b: dist(a) < dist(b))
        return points[:K]

# V3  
# Time:  O(nlogk)
# Space: O(k)
import heapq
class Solution2(object):
    def kClosest(self, points, K):
        """
        :type points: List[List[int]]
        :type K: int
        :rtype: List[List[int]]
        """
        def dist(point):
            return point[0]**2 + point[1]**2
        
        max_heap = []
        for point in points:
            heapq.heappush(max_heap, (-dist(point), point))
            if len(max_heap) > K:
                heapq.heappop(max_heap)
        return [heapq.heappop(max_heap)[1] for _ in range(len(max_heap))]