Maximum Product Difference Between Two Pairs.cpp

/* 
    Solution by Rahul Surana
    
    ***********************************************************

The product difference between two pairs (a, b) and (c, d) is defined as (a * b) - (c * d).

For example, the product difference between (5, 6) and (2, 7) is (5 * 6) - (2 * 7) = 16.
Given an integer array nums, choose four distinct indices w, x, y, and z such that the product difference between pairs (nums[w], nums[x]) and (nums[y], nums[z]) is maximized.

Return the maximum such product difference.



    ***********************************************************
*/


#include <bits/stdc++.h>
#define ll          long long
#define vl          vector<ll>
#define vi          vector<int>
#define pi          pair<int,int>
#define pl          pair<ll,ll>
#define all(a)      a.begin(),a.end()
#define mem(a,x)    memset(a,x,sizeof(a))
#define pb          push_back
#define mp          make_pair
#define F           first
#define S           second
#define FOR(i,a)     for(int i = 0; i < a; i++)
#define trace(x)    cerr<<#x<<" : "<<x<<endl;
#define trace2(x,y) cerr<<#x<<" : "<<x<<" | "<<#y<<" : "<<y<<endl;
#define trace3(x,y,z) cerr<<#x<<" : "<<x<<" | "<<#y<<" : "<<y<<" | "<<#z<<" : "<<z<<endl;
#define fast_io         std::ios::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL)
 
using namespace std;


vector<int> ar;

int main()
{
    fast_io;
    int n;
    FOR(i,n) { int a; cin >> a; ar.pb(a); }
    cout << maxProductDifference(ar);
}

int maxProductDifference(vector<int>& nums) {
    sort(nums.begin(),nums.end());
    return(nums[nums.size()-1] *nums[nums.size()-2]) - (nums[0] *nums[1]);
}