Given an array of integers, Check if there exist four elements at different indexes in the array whose sum is equal to a given value k.

For example, if the given array is {1 5 1 0 6 0} and k = 7, then your function should print “YES” as (1+5+1+0=7).

Examples:

Input : arr[] = {1 5 1 0 6 0} k = 7 Output : YES Input : arr[] = {38 7 44 42 28 16 10 37 33 2 38 29 26 8 25} k = 22 Output : NO

We have discussed different solutions in below two sets.

Find four elements that sum to a given value | Set 1 (n^3 solution)

Find four elements that sum to a given value | Set 2 ( O(n^2Logn) Solution)

In this post, an optimized solution is discussed that works in O(n^{2}) on average.

The idea is to create a hashmap to store pair sums.

Loop i = 0 to n-1 : Loop j = i + 1 to n-1 calculate sum = arr[i] + arr[j]If(k-sum) exist in hash a) Check in hash table for all pairs of indexes which form (k-sum). b) If there is any pair with no no common indexes. return trueElseupdate hash table EndLoop; EndLoop;

`// C++ program to find if there exist 4 elements ` `// with given sum ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function to check if there exist four ` `// elements whose sum is equal to k ` `bool` `findfour(` `int` `arr[], ` `int` `n, ` `int` `k) ` `{ ` ` ` `// map to store sum and indexes for ` ` ` `// a pair sum ` ` ` `unordered_map<` `int` `, vector<pair<` `int` `, ` `int` `> > > hash; ` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` `for` `(` `int` `j = i + 1; j < n; j++) { ` ` ` ` ` `// calculate the sum of each pair ` ` ` `int` `sum = arr[i] + arr[j]; ` ` ` ` ` `// if k-sum exist in map ` ` ` `if` `(hash.find(k - sum) != hash.end()) { ` ` ` `auto` `num = hash.find(k - sum); ` ` ` `vector<pair<` `int` `, ` `int` `> > v = num->second; ` ` ` ` ` `// check for index coincidence as if ` ` ` `// there is a common that means all ` ` ` `// the four numbers are not from ` ` ` `// different indexes and one of the ` ` ` `// index is repeated ` ` ` `for` `(` `int` `k = 0; k < num->second.size(); k++) { ` ` ` ` ` `pair<` `int` `, ` `int` `> it = v[k]; ` ` ` ` ` `// if all indexes are different then ` ` ` `// it means four number exist ` ` ` `// set the flag and break the loop ` ` ` `if` `(it.first != i && it.first != j && ` ` ` `it.second != i && it.second != j) ` ` ` `return` `true` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// store the sum and index pair in hashmap ` ` ` `hash[sum].push_back(make_pair(i, j)); ` ` ` `} ` ` ` `} ` ` ` `hash.clear(); ` ` ` `return` `false` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `k = 7; ` ` ` `int` `arr[] = { 1, 5, 1, 0, 6, 0 }; ` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` ` ` `if` `(findfour(arr, n, k)) ` ` ` `cout ` ` ` `<< ` `"YES"` `<< endl; ` ` ` `else` ` ` `cout << ` `"NO"` `<< endl; ` ` ` `return` `0; ` `} ` |

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Output:

YES

This article is contributed by **Niteesh Kumar**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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