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
Solution1:
class Solution(object):
def kClosest(self, points, K):
return heapq.nsmallest(K, points, lambda (x, y): x * x + y * y)
Solution2:
Python sorting by distance
Hint:
Recall the definition of Euclidean distance.
Launch customized sorting to sort points by distance to origin.
Illustration and Visualization:
Implementation by sorting with distance:
class Solution:
def kClosest(self, points, K):
# sort by the distance to origin, in ascending order
points.sort( key = lambda point: (point[0]**2 + point[1]**2) )
return points[:K]
Implementation by heap sort with distance:
class Solution:
def kClosest(self, points, K):
# sort by the distance to origin, in ascending order
k_closet = heapq.nsmallest( K, points, key = lambda point: point[0]**2 + point[1]**2 )
return k_closet