Square Difference of Two large Consecutive Numbers

Given two positive consecutive numbers M and N, the task is to find the square difference of the two numbers without computing the square of those numbers.

Examples:

Input: N = 4, M = 5
Output: 9
Explanation:
52 – 42 = 25 – 16 = 9.

Input: N = 999999999, M = 1000000000
Output: 1999999999

Approach: The idea is to use the algebraic expression to solve this problem. It is given in the question that M = N + 1. Therefore:



  • The value to be computed is M2 – N2.
  • On replacing M with N + 1, the above equation becomes:
    (N + 1)2 - N2
    
  • (N + 1)2 can be expanded to:
    N2 + 12 + 2 * N - N2
  • On simplifying, the above equation becomes:
    1 + 2 * N
    1 + N + N
    (1 + N) + N
    M + N
    
  • Therefore, we simply need to compute and return the value of M + N.

Below is the implementation of the above approach:

CPP

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// C++ program to find the square
// difference of two large
// consecutive numbers
  
#include <bits/stdc++.h>
using namespace std;
typedef long long l;
  
// Function to find the square
// difference of two large
// consecutive numbers
l difference(l M, l N)
{
    return M + N;
}
  
// Driver code
int main()
{
    l M = 999999999;
    l N = 1000000000;
  
    cout << difference(M, N) << endl;
}

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Java

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// Java program to find the square
// difference of two large
// consecutive numbers
  
  
class GFG{
   
// Function to find the square
// difference of two large
// consecutive numbers
static long difference(long M, long N)
{
    return M + N;
}
   
// Driver code
public static void main(String[] args)
{
    long M = 999999999;
    long N = 1000000000;
   
    System.out.print(difference(M, N) +"\n");
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 program to find the square
# difference of two large
# consecutive numbers
  
# Function to find the square
# difference of two large
# consecutive numbers
def difference(M, N):
    return M + N
  
# Driver code
if __name__ == '__main__':
    M = 999999999
    N = 1000000000
  
    print(difference(M, N))
  
# This code is contributed by mohit kumar 29    

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C#

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// C# program to find the square
// difference of two large
// consecutive numbers
using System;
  
public class GFG{
    
// Function to find the square
// difference of two large
// consecutive numbers
static long difference(long M, long N)
{
    return M + N;
}
    
// Driver code
public static void Main(String[] args)
{
    long M = 999999999;
    long N = 1000000000;
    
    Console.Write(difference(M, N) +"\n");
}
}
  
// This code is contributed by 29AjayKumar

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Output:

1999999999

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