Find K-th Smallest Difference Between Element Pairs in C++

Suppose we are given a list containing several integer numbers. We have to find out the difference between each pair of values in the array and find out the k-th smallest difference number. The index starts at 0 and the value k is given to us as input.

So, if the input is like numbers = {2, 6, 4, 8}, k = 2, then the output will be 2.

The differences between the pairs are −

(2, 6) = 4

(2, 4) = 2

(2, 8) = 6

(6, 4) = 2

(6, 8) = 2

(4, 8) = 4

If we sort the values, it becomes 2, 2, 2, 4, 4, 6. The 2-nd smallest value is 2. (Index starts from 0).

To solve this, we will follow these steps −

• increase k by 1
• sort the array input
• le := 0
• ri := last element of input - first item of input
• while le < ri, do −
  • mid := (le + ri) / 2
  • tmp := 0
  • lp := 0
  • for initialize i := 1, when i < size of input, update (increase i by 1), do −
    • while input[i] - input[lp] > mid, do −
      • lp := lp + 1
    • tmp := tmp + i - lp
  • if tmp >= k, then −
    • ri := mid
  • Otherwise
    • le := mid + 1
• return le

Example

Let us see the following implementation to get better understanding −

#include<bits/stdc++.h>

using namespace std;

int solve(vector<int>& input, int k) {
k++;
sort(input.begin(), input.end());
int le = 0;
int ri = input.back() - input[0];
while (le < ri) {
int mid = (le + ri) / 2;
long long tmp = 0;
int lp = 0;
for (int i = 1; i < input.size(); i++) {
while (input[i] - input[lp] > mid) lp++;
tmp += i - lp;
}
if (tmp >= k)
ri = mid;
else
le = mid + 1;
}
return le;
}
int main() {
vector<int> numbers = {2, 6, 4, 8};
cout<< solve(numbers, 2) <<endl;
return 0;
}

Input

vector<int> numbers = {2, 6, 4, 8};
cout<< solve(numbers, 2) <<endl;

Output

2