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# Count Triplets such that one of the numbers can be written as sum of the other two in C++

We are given an array Arr[] of integers with length n. The goal is to find the number of triplets (Arr[i],Arr[j],Arr[k]) such that the sum of any two numbers is equal to the third number.

a+b=c, where a,b,c are elements of Arr[] with indexes i,j,k such that 0<=i<j<k<n We will do this by using three for loops. Increment count if arr[x]+arr[y]=arr[z] and x!=y!=z. Let’s understand with examples.

## Input

arr[]= { 1,2,2,3,4 }, N=5

## Output

Number of triplets: 4

## Explanation

Triplets with arr[x]+arr[y]=arr[z].

Arr{}=[ 1,2,2,3,4 ] =(1,2,3) → 1+2=3 Arr{}=[ 1,2,2,3,4 ] =(1,2,3) → 1+2=3 Arr{}=[ 1,2,2,3,4 ] =(1,3,4) → 1+3=4 Arr{}=[ 1,2,2,3,4 ] =(2,2,4) → 2+2=4

Total triplets: 4

## Input

arr[]= {2,2,2,2,2}, N=5

## Output

Number of triplets: 0

## Explanation

Every two numbers have sum=4 which is not equal to third=2.

Total triplets: 0

## Approach used in the below program is as follows

We take an integer array Arr[] initialized with random numbers.

Variable N stores the length of Arr[].

Function countTriplets(int arr[],int n) takes an array, its length returns the triplets in which one of the numbers can be written as sum of the other two

Take the initial variable count as 0 for the number of triplets.

Traverse array using three for loops for each element of the triplet.

Outermost loop from 0<=i<n-2, inner loop i<j<n-1, innermost j<k<n.

Check if arr[i]+arr[j]==arr[k] or arr[i]+arr[k]==arr[j] or arr[k]+arr[j]==arr[i] If true then increment count.

At the end of all loops count will have a total number of triplets that meet the condition.

Return the count as result.

## Example

#include <bits/stdc++.h> using namespace std; int countTriplets(int arr[], int n){ int count = 0; for (int i = 0; i < n-2; i++){ for (int j = i+1; j < n-1; j++){ for (int k = j+1; k < n; k++){ if(arr[i]+arr[j]==arr[k] || arr[j]+arr[k]==arr[i] || arr[k]+arr[i]==arr[j]){ count++; } } } } return count; } int main(){ int Arr[]={ 1,2,2,3,4 }; int N=5; //length of array cout <<endl<< "Number of triplets : "<<countTriplets(Arr,N); return 0; }

## Output

Number of triplets : 4

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