# 973. K Closest Points to Origin

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**2 + point**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**2 + point**2  )

return k_closet``````
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