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 |
1999999999
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