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Calculate the sum of sum of numbers in range L to R

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  • Last Updated : 13 Jul, 2022
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Given two numbers L and R. The task is to find the sum of numbers in the range L to R.

Examples:

Input: L = 3, R = 6
Output: 40
Explanation: 3 + 3+4 + 3+4+5 + 3+4+5+6 = 40

Input: L = 5, R = 6
Output: 16

 

Approach: This problem is formula-based. For the illustration given below, observe the number of times each number is repeating in the sum, and depending upon that the final sum is calculated. 

Illustration: L = 3, R = 6

Sum = 3 + 3+4 + 3+4+5 + 3+4+5+6 = 3+3+3+3 + 4+4+4 + 5+5 + 6 (Upon Grouping)
That is equals to 3*4 + 4*3 + 5*2 + 6*1

Therefore for any range L to R, the sum can be calculated as:

L*D + (L+1)*(D-1) + (L+2)*(D-2) + … + (R-1)*(2) + R*1

Below is the implementation of above approach.

C++




// C++ program for above approach
#include <iostream>
using namespace std;
 
// Function to return sum
int findSum(int L, int R)
{
    // Initializing the variables
    int sum = 0, d = R - L + 1;
 
    for (int i = L; i <= R; i++) {
        sum += (i * d);
        d--;
    }
 
    // Return Sum as the final result.
    return sum;
}
 
// Driver Code
int main()
{
    int L = 3, R = 6;
 
    // Function call
    cout << findSum(L, R);
 
    return 0;
}


Java




// Java code to implement above approach
import java.util.*;
public class GFG {
 
// Function to return sum
static int findSum(int L, int R)
{
   
    // Initializing the variables
    int sum = 0, d = R - L + 1;
 
    for (int i = L; i <= R; i++) {
        sum += (i * d);
        d--;
    }
 
    // Return Sum as the final result.
    return sum;
}
 
// Driver code
public static void main(String args[])
{
    int L = 3, R = 6;
 
    // Function call
    System.out.println(findSum(L, R));
 
}
}
 
// This code is contributed by Samim Hossain Mondal.


Python




# Pyhton program for above approach
 
# Function to return sum
def findSum(L, R):
     
    # Initializing the variables
    sum = 0
    d = R - L + 1
 
    for i in range(L, R + 1):
        sum += (i * d)
        d = d - 1
 
    # Return Sum as the final result.
    return sum
 
# Driver Code
L = 3
R = 6
 
# Function call
print(findSum(L, R))
 
# This code is contributed by Samim Hossain Mondal.


C#




// C# code to implement above approach
using System;
public class GFG {
 
  // Function to return sum
  static int findSum(int L, int R)
  {
 
    // Initializing the variables
    int sum = 0, d = R - L + 1;
 
    for (int i = L; i <= R; i++) {
      sum += (i * d);
      d--;
    }
 
    // Return Sum as the final result.
    return sum;
  }
 
  // Driver code
  public static void Main()
  {
    int L = 3, R = 6;
 
    // Function call
    Console.WriteLine(findSum(L, R));
  }
}
 
// This code is contributed by ukasp.


Javascript




<script>
   // JavaScript code for the above approach
 
 
   // Function to return sum
   function findSum(L, R) {
     // Initializing the variables
     let sum = 0, d = R - L + 1;
 
     for (let i = L; i <= R; i++) {
       sum += (i * d);
       d--;
     }
 
     // Return Sum as the final result.
     return sum;
   }
 
   // Driver Code
 
   let L = 3, R = 6;
 
   // Function call
   document.write(findSum(L, R));
 // This code is contributed by Potta Lokesh
 </script>


 
 

Output

40

 Time Complexity: O(R-L+1)

Auxiliary Space: O(1), since no extra space has been taken.

 


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