Given three positive integers X, Y, and Z. The task is to find two numbers A and B of X and Y digits respectively with their GCD having Z digits. where Z ≤ min(X, Y). If there are multiple possible answers print any of them.
Examples:
Input: X = 2, Y = 3, Z = 1
Output: A = 11, B = 100
Explanation: A and B contains 2 and 3 digits respectively and GCD(A, B) is 1 which has 1 digit.Input: X = 2, Y = 2, Z = 2
Output: A = 13, B = 26
Approach: The task can be solved using some observations. Calculate A equals 10x-1, B as 10y-1, and C as 10z-1. Increment A with C to achieve GCD with Z digits. Follow the below steps to solve the problem:
- Initialize 3 variables A, B, C with 1.
- Append Z -1 zeroes with C.
- Append X – 1 zeroes in last of A.
- Append Y – 1 zero in last of B.
- Increment A by the value of C.
- Print A and B as the answer.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the desired numbersvoid findTwoNumbers(int X, int Y, int Z){ int A, B, C; A = B = C = 1; for (int i = 1; i <= X - 1; i++) { A = A * 10; } for (int i = 1; i <= Y - 1; i++) { B = B * 10; } for (int i = 1; i <= Z - 1; i++) { C = C * 10; } A = A + C; cout << "A = " << A << " B = " << B;}// Driver Codeint main(){ int X = 2, Y = 3, Z = 1; findTwoNumbers(X, Y, Z); return 0;} |
Java
// Java program for the above approachimport java.io.*;public class GFG { // Function to find the desired numbers static void findTwoNumbers(int X, int Y, int Z) { int A, B, C; A = B = C = 1; for (int i = 1; i <= X - 1; i++) { A = A * 10; } for (int i = 1; i <= Y - 1; i++) { B = B * 10; } for (int i = 1; i <= Z - 1; i++) { C = C * 10; } A = A + C; System.out.println("A = " + A + " B = " + B); } // Driver Code public static void main(String args[]) { int X = 2, Y = 3, Z = 1; findTwoNumbers(X, Y, Z); }}// This code is contributed by Saurabh Jaiswal |
Python3
# python3 program for the above approach# Function to find the desired numbersdef findTwoNumbers(X, Y, Z): A = B = C = 1 for i in range(1, X): A = A * 10 for i in range(1, Y): B = B * 10 for i in range(1, Z): C = C * 10 A = A + C print(f"A = {A} B = {B}")# Driver Codeif __name__ == "__main__": X, Y, Z = 2, 3, 1 findTwoNumbers(X, Y, Z) # This code is contributed by rakeshsahni |
C#
// C# program for the above approachusing System;public class GFG{ // Function to find the desired numbersstatic void findTwoNumbers(int X, int Y, int Z){ int A, B, C; A = B = C = 1; for (int i = 1; i <= X - 1; i++) { A = A * 10; } for (int i = 1; i <= Y - 1; i++) { B = B * 10; } for (int i = 1; i <= Z - 1; i++) { C = C * 10; } A = A + C; Console.Write("A = " + A + " B = " + B);}// Driver Codepublic static void Main(){ int X = 2, Y = 3, Z = 1; findTwoNumbers(X, Y, Z);}}// This code is contributed by Samim Hossain Mondal. |
Javascript
<script> // JavaScript code for the above approach // Function to find the desired numbers function findTwoNumbers(X, Y, Z) { let A, B, C; A = B = C = 1; for (let i = 1; i <= X - 1; i++) { A = A * 10; } for (let i = 1; i <= Y - 1; i++) { B = B * 10; } for (let i = 1; i <= Z - 1; i++) { C = C * 10; } A = A + C; document.write("A = " + A + " B = " + B); } // Driver Code let X = 2, Y = 3, Z = 1; findTwoNumbers(X, Y, Z); // This code is contributed by Potta Lokesh</script> |
Output
A = 11 B = 100
Time Complexity: O(max(X, Y))
Auxiliary Space: O(1)
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