Mathematical Calculation

Approach: Consecutive Number Square Difference Calculation using Simple Arithmetic

In this approach, we will use mathematical calculation to find the square difference of two large consecutive numbers. We know that the square of a number is equal to the sum of the first n odd numbers, where n is the number itself. Using this, we can calculate the squares of the two consecutive numbers and subtract them to find the square difference.

Steps:

Calculate the square of the larger number.
Calculate the square of the smaller number.
Subtract the smaller square from the larger square to get the square difference.

C++

#include <bits/stdc++.h>
using namespace std;
 
int square_difference(int n, int m) {
    int larger = max(n, m);
    int smaller = min(n, m);
    int larger_square = larger * larger;
    int smaller_square = smaller * smaller;
    return larger_square - smaller_square;
}
 
int main() {
    cout << square_difference(4, 5) << endl;
    cout << square_difference(999999999, 1000000000) << endl;
    return 0;
}

Java

import java.util.*;
 
public class Main {
 
    public static int square_difference(int n, int m) {
        int larger = Math.max(n, m);
        int smaller = Math.min(n, m);
        int larger_square = larger * larger;
        int smaller_square = smaller * smaller;
        return larger_square - smaller_square;
    }
 
    public static void main(String[] args) {
        System.out.println(square_difference(4, 5));
        System.out.println(square_difference(999999999, 1000000000));
    }
}

Python3

def square_difference(n, m):
    larger = max(n, m)
    smaller = min(n, m)
    larger_square = larger ** 2
    smaller_square = smaller ** 2
    return larger_square - smaller_square
print(square_difference(4, 5))
print(square_difference(999999999, 1000000000))

C#

using System;
 
public class Program
{
    public static int SquareDifference(int n, int m)
    {
        int larger = Math.Max(n, m);
        int smaller = Math.Min(n, m);
        int larger_square = larger * larger;
        int smaller_square = smaller * smaller;
        return larger_square - smaller_square;
    }
 
    public static void Main()
    {
        Console.WriteLine(SquareDifference(4, 5));
        Console.WriteLine(SquareDifference(999999999, 1000000000));
    }
}

Javascript

function square_difference(n, m) {
    // Find the larger and smaller numbers
    let larger = Math.max(n, m);
    let smaller = Math.min(n, m);
 
    // Calculate the squares of the numbers
    let larger_square = larger * larger;
    let smaller_square = smaller * smaller;
 
    // Calculate the difference between the squares
    return larger_square - smaller_square;
}
 
console.log(square_difference(4, 5));
console.log(square_difference(999999999, 1000000000));

Output

9
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: Consecutive Number Square Difference Calculation using Simple Arithmetic

Mathematical Calculation

C++

Java

Python3

C#

Javascript

Square Difference of Two large Consecutive Numbers

CPP

Java

Python3

C#

Javascript

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