973. K Closest Points to Origin

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https://leetcode.com/problems/k-closest-points-to-origin/

We have a list of points on the plane.  Find the K closest points to the origin (0, 0).
(Here, the distance between two points on a plane is the Euclidean distance.)
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]]
(The answer [[-2,4],[3,3]] would also be accepted.)

Note:
  1. 1 <= K <= points.length <= 10000
  2. -10000 < points[i][0] < 10000
  3. -10000 < points[i][1] < 10000

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Intuition

 We need a data structure of size K, we also need to consider each array element as candidate 

 Initialize data structure with first K elements from array

 Iterate array K through the end
  If array element is larger than max element in data structure
    Current element is not candidate for answer => Do nothing
  If array element is less than max element
    Current element is candidate for answer => Add current element, trash the max element from collection 

At the end of array traversal, we will have popped out larger elements and K smallest elements remain

Data structure should support
  Quick lookup of largest element
  Low cost of adding one element, removing one element

 Max Heap is appropriate

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Time - O(n * log(K))
Space - O(K)
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