Write a program in C++ to find the kth smallest difference between all pairs of elements in an array

Suppose we have a list containing multiple integers. We have to find the difference between each pair of values ​​in the array and find the kth smallest number of differences. The index starts from 0 and the value k is given to us as input.

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

The difference between the two pairs is -

(2, 6) = 4

(2, 4) = 2

(2, 8 ) = 6

(6, 4) = 2

(6, 8) = 2

(4, 8) = 4

If we Sorting the values, it becomes 2, 2, 2, 4, 4, 6. The second minimum value is 2. (indexed from 0).

To solve this problem, we will follow the following steps-

• Increase k by 1
• Sort the array input
• le: = 0
• ri := The last element of the input - The first item of the input
• while le
• mid := (le ri) / 2
• tmp := 0
• lp := 0
• is used to initialize i := 1, when i
• while input[i] - input[lp] > mid, execute −
  • lp := lp 1
• tmp := tmp i - lp

If tmp >= k, then -

• ri := mid

##otherwise

le := mid 1

Return le

Example

Let us look at the following implementation to understand better -

#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

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