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Count number of triplets in an array having sum in the range [a,b] in C++
We are given an array of integers, Arr[] and two variables a and b to define a range [a,b]. The goal is to find the number of triplets whose sum lies in between this range [a,b].
We will do this by using three for loops. Increment count if arr[i]+arr[j]+arr[k]>=a and arr[i]+arr[j]+arr[k]<=b. Where 0<=i<=n-2, i<j<n-1, j<k<n. Where n is no. of elements in Arr[].
Let’s understand with examples.
Input − arr[]= { 1,2,3,4,5 }, N=5, L=2, R=8
Output − Number of triplets − 4
Explanation −
Triplets with sum>=2 and sum<=8 (1,2,3) → 6 (1,2,4) → 7 (1,2,5) → 8 (1,3,4) → 8 Total triplets: 4
Input − arr[]= {2,2,2,2,2}, N=5, L=2, R=5
Output − Number of triplets − 0
Explanation −
Every triplet will have the sum 6. Which is not in the range [2,5]
Total triplets: 0
Approach used in the below program is as follows
We take an integer array Arr[] initialized with random numbers.
Take variables L and R for defining a range [L,R]. N stores the length of Arr[].
Function countTriplets(int arr[],int n,int a,int b) takes an array, its length and range variables as input and returns the triplets whose sum lies in this range.
Take the initial variable count as 0 for the number of triplets.
Take the initial variable sum as the sum of each triplet. Initially 0.
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.
Calculate sum=arr[i]+arr[j]+arr[k]. If a<=sum<=b 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 desired result.
Example
#include <bits/stdc++.h>
using namespace std;
int countTriplets(int arr[],int n,int a,int b){
int count = 0;
int sum=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++){
sum=arr[i]+arr[j]+arr[k];
if ( sum>=a && sum<=b) //check{
count++;
// cout<<endl<<"a :"<<arr[i]<<" b :"<<arr[j]<<" c :"<<arr[k]; //to print
}
}
}
}
return count;
}
int main(){
int Arr[]={ 5,4,3,6,8,2 };
int L=9;
int R=15;
int N=6; //length of array
cout <<endl<< "Number of triplets : "<<countTriplets(Arr,N,L,R);
return 0;
}Output
If we run the above code it will generate the following output −
Number of triplets : 14
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