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12

Closest Distance Pair

Difficulty: EASY
Contributed By
Avg. time to solve
20 min

Problem Statement

You are given an array containing 'N' points in the plane. The task is to find out the distance of the closest points.

Note :
Where distance between two points (x1, y1) and (x2, y2) is calculated as [(x1 - x2) ^ 2] + [(y1 - y2) ^ 2].
Input Format :
The first line contains a single integer 'N' denoting the number of points.

The next 'N' lines contain two integers separated by a single space, where the first integer represents the x coordinate and the second integer represents the y coordinate.
Output Format :
The only line contains the minimum distance between the 'N' points.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints :
2 <= 'N' <= 10^5
-10^5 <= 'x' <= 10^5 
-10^5 <= 'y' <= 10^5

Time Limit: 1 sec
Sample Input 1:
5
1 2
2 3
3 4
5 6
2 1
Sample Output 1:
2
Explanation of Sample Output 1:
We have 2 pairs which are probable answers (1, 2) with (2, 3) and (2, 3) with (3, 4). The distance between both of them is equal to 2.
Sample Input 2 :
3
0 0
-3 -4
6 4
Sample Output 2 :
25
Explanation of Sample Output 1 :
If we choose the pairs (0, 0) and (-3, -4), the distance between them is 3^2 + 4^2 = 25. This is the optimal answer for this test case.
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