# Find K-th Smallest Pair Distance in C++

C++Server Side ProgrammingProgramming

Suppose we have an integer array; we have to find the kth smallest distance among all the pairs. The distance of a pair (A, B) is actually the absolute difference between A and B. So if the input is like [1,3,8], then all possible pairs are [1,3], [3, 8], [1, 8], then when k = 2, the second smallest distance is 5 (8 - 3).

To solve this, we will follow these steps −

• n := size of nums, x := 0
• for initialize i := 0, when i < n, update (increase i by 1), do −
• x := maximum of x and nums[i]
• Define an array cnt of size x + 1
• for initialize i := 0, when i < n, update (increase i by 1), do −
• for initialize j := i + 1, when j < n, update (increase j by 1), do −
• increase cnt[|nums[j] - nums[i]|] by 1
• for initialize i := 0, when i <= x, update (increase i by 1), do −
• if cnt[i] >= k, then −
• return i
• k := k - cnt[i]
• return x

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int smallestDistancePair(vector<int>& nums, int k) {
int n = nums.size();
int x = 0;
for(int i = 0; i < n; i++)x = max(x, nums[i]);
vector <int> cnt(x + 1);
for(int i = 0 ; i < n; i++){
for(int j = i + 1; j < n; j++){
cnt[abs(nums[j] - nums[i])]++;
}
}
for(int i = 0; i <= x; i++){
if(cnt[i] >= k)return i;
k -= cnt[i];
}
return x;
}
};
main(){
Solution ob;
vector<int> v = {1,3,8};
cout << (ob.smallestDistancePair(v, 2));
}

## Input

{1,3,8}

## Output

5