Consecutive Number Square Difference Calculation using Simple Arithmetic

Take two input parameters, M and N, representing two consecutive numbers where M = N + 1.
Calculate the value of (M + N) * (M – N).
Return the result as the output of the function.
Call the function with the test case inputs and print the output.

C++

#include <iostream>
 
using namespace std;
 
int square_difference(int M, int N) {
    return (M + N) * (M - N);
}
 
int main() {
    int N = 4;
    int M = 5;
 
    cout << "Input: N = " << N << ", M = " << M << endl;
    cout << "Output: " << square_difference(M, N) << endl;
 
    N = 999999999;
    M = 1000000000;
 
    cout << "Input: N = " << N << ", M = " << M << endl;
    cout << "Output: " << square_difference(M, N) << endl;
 
    return 0;
}

Java

public class Main {
    public static int squareDifference(int M, int N) {
        return (M + N) * (M - N);
    }
 
    public static void main(String[] args) {
        int N = 4;
        int M = 5;
 
        System.out.println("Input: N = " + N + ", M = " + M);
        System.out.println("Output: " + squareDifference(M, N));
 
        N = 999999999;
        M = 1000000000;
 
        System.out.println("Input: N = " + N + ", M = " + M);
        System.out.println("Output: " + squareDifference(M, N));
    }
}

Python3

def square_difference(M, N):
    return (M + N) * (M - N)
 
# Driver code
if __name__ == '__main__':
    N = 4
    M = 5
 
    print("Input: N =", N, ", M =", M)
    print("Output:", square_difference(M, N))
     
    N = 999999999
    M = 1000000000
 
    print("Input: N =", N, ", M =", M)
    print("Output:", square_difference(M, N))

C#

using System;
 
namespace CSharpConversion {
class Program {
    // A function that calculates the square of the
    // difference between M and N
    static int SquareDifference(int M, int N)
    {
        return (M + N) * (M - N);
    }
    static void Main(string[] args)
    {
        int N = 4;
        int M = 5;
 
        // Print the input values
        Console.WriteLine("Input: N = " + N + ", M = " + M);
 
        // Call the SquareDifference function and print the
        // output
        Console.WriteLine("Output: "
                          + SquareDifference(M, N));
 
        N = 999999999;
        M = 1000000000;
 
        // Print the input values
        Console.WriteLine("Input: N = " + N + ", M = " + M);
 
        // Call the SquareDifference function and print the
        // output
        Console.WriteLine("Output: "
                          + SquareDifference(M, N));
 
        Console.ReadLine();
    }
}
}
// This code is contributed by sarojmcy2e

Javascript

function square_difference(M, N)
{
 
    // Calculate and return the result of the expression (M + N) * (M - N)
    return (M + N) * (M - N);
}
 
// Example usage
let N = 4;
let M = 5;
 
console.log("Input: N =", N, ", M =", M);
console.log("Output:", square_difference(M, N));
 
N = 999999999;
M = 1000000000;
 
console.log("Input: N =", N, ", M =", M);
console.log("Output:", square_difference(M, N));

Output

Input: N = 4 , M = 5
Output: 9
Input: N = 999999999 , M = 1000000000
Output: 1999999999

Time complexity: O(1)
Auxiliary space: O(1)

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

// 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;
}

Java

// 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

Python3

# 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    

C#

// 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

Javascript

<script>
 
// JavaScript program to find the square
// difference of two large
// consecutive numbers
 
// Function to find the square
// difference of two large
// consecutive numbers
function difference(M, N)
{
    return M + N;
}
 
// Driver code
let M = 999999999;
let N = 1000000000;
 
document.write(difference(M, N));
 
</script>

Output

1999999999

Time Complexity: O(1)

Auxiliary Space: O(1)

Tags:

#Algorithms #Aptitude #DSA #Algorithms

Approach: Mathematical Calculation

Consecutive Number Square Difference Calculation using Simple Arithmetic

C++

Java

Python3

C#

Javascript

Square Difference of Two large Consecutive Numbers

CPP

Java

Python3

C#

Javascript

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