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C++ Program to find out the minimum difference value in n integer pairs
Suppose, we are given two arrays a and b that have a total of n and m values in them respectively. We have to make n or m number of pairs (whichever is minimum) using values from the two arrays. A pair must contain a value from array a and another one from array b. We have to make the pairs in such a way so that the difference of the value in the pairs is minimum and the same. We print the value as output.
So, if the input is like n = 4, m = 4, a = {2, 3, 4, 7}, b = {3, 4, 6, 5}, then the output will be 1.
The pairs that can be made are −
(3, 4), (4, 5), (7, 6), (2, 3).
The difference in the value in all pairs is 1.
Steps
To solve this, we will follow these steps −
sort the array a Define an array s1 initialized with 0 Define an array s2 initialized with 0 for initialize i := 1, when i < n, update i := i + 2, do: insert last element of s1 + a[i] - a[i - 1] at the end of s1 for initialize i := 2, when i < n, update i := i + 2, do: insert last element of s2 + a[i] - a[i - 1] at the end of s2 ans := infinity for each value w in b, do: diff := first element in the array a not less than w - first value of a sub := last element of s1[diff / 2] + s2 ans := minimum of ans and sub print(ans)
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
void solve(int n, int m, vector<int> a, vector<int> b){
sort(a.begin(), a.end());
vector<int> s1 = {0};
vector<int> s2 = {0};
for (int i = 1; i < n; i += 2)
s1.push_back(a[i] - a[i - 1] + s1.back());
for (int i = 2; i < n; i += 2)
s2.push_back(a[i] - a[i - 1] + s2.back());
int ans = INF;
for (const auto & w : b) {
int diff = lower_bound(a.begin(), a.end(), w) - a.begin();
int sub = s1[diff / 2] + s2.back() - s2[diff / 2] + abs(a[diff / 2 * 2] - w);
ans = min(ans, sub);
}
cout << ans << endl;
}
int main() {
int n = 4, m = 4;
vector<int> a = {2, 3, 4, 7}, b = {3, 4, 6, 5};
solve(n, m, a, b);
return 0;
}Input
4, 4, {2, 3, 4, 7}, {3, 4, 6, 5}Output
1
Updated on: 02-Mar-2022
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