Count quadruples from four sorted arrays whose sum is equal to a given value x in C++

We are given four arrays A[], B[], C[] and D[]. The goal is to find all quadruples of elements of these arrays such that A[i]+B[j]+C[k]+D[l] =x. All four arrays have the same number of elements N.

We will do this by traversing each array once and compare if A[i]+B[j]+C[j]+D[l]==x. If true increment count.

Let’s understand with examples.


A[]={ 1,2,3}; B[]={ 2,3,2}; C[]={ 4,3,1}; D[]={ 3,1,1 }; X=12


Count of Quadruples: 4


Quadruples such as ( A[i] B[j] C[k] D[l] ) are:
(2 3 4 3) , (3 2 4 3), (3 3 3 3), (3 2 4 3)
Number of quadruples : 4


A[]={ 1,1,1}; B[]={ 2,2,2}; C[]={ 3,3,3}; D[]={ 4,4,4 }; X=15


Count of Quadruples: 0


No such elements could be paired.

Approach used in the below program is as follows

  • We take integer arrays A[],B[], C[] and D[] of equal length initialized with random numbers.

  • Take variable N to store their length.

  • Function countQuad(int a[],int b[],int c[],d[],int x, int n) takes all arrays as input with their same length n and returns count.

  • Traverse using four loops for each array.

  • Outermost loop 0<=i<n for a[], inner 0<=j<n for b[], other 0<=k<n for c[] and innermost 0<=l

  • Compare if a[i]+b[j]+c[k]+d[l]==x. If true increment count.

  • At the end of all loops count will have quadruples with sum x.

  • Return count as result.


 Live Demo

#include <bits/stdc++.h>
using namespace std;
int countQuads(int a[],int b[],int c[],int d[],int x, int n){
   int count = 0;
   for (int i = 0; i < n; i++){
      for (int j = 0; j < n; j++){
         for (int k = 0; k < n; k++){
            for (int l = 0; l < n; l++){
               int sum=a[i]+b[j]+c[k]+d[l];
                  cout<<endl<<a[i]<<" "<<b[j]<<" "<<c[k]<<" "<<d[l];}
   return count;
int main(){
   int A[]={ 1,1,1}; int B[]={ 2,2,2}; int C[]={ 3,3,3}; int D[]={ 4,4,4 };
   int X=15;
   int N=3; //length of each array
   cout <<endl<< "Number of quadruples : "<<countQuads(A,B,C,D,X,N);
   return 0;


If we run the above code it will generate the following output −

Number of quadruples : 0

Updated on: 31-Oct-2020


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