用有 Z 位的 GCD 分别求 X 位和 Y 位的两个数 A 和 B

给定三个正整数X 、 Y和Z 。任务是找到两个分别为X和Y位的数字A和B ，它们的 GCD 有Z位。其中Z ≤ min(X, Y) 。如果有多个可能的答案，请打印其中任何一个。

例子：

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

方法：可以使用一些观察来解决该任务。计算A等于10 ^x-1 ， B等于10 ^y-1 ， C等于10 ^z-1 。用C增加A以实现Z位的 GCD。请按照以下步骤解决问题：

• 用 1 初始化 3 个变量 A、B、C。
• 用 C 附加 Z -1 个零。
• 在 A 的最后一个附加 X – 1 个零。
• 在 B 的最后一个附加 Y - 1 个零。
• 将 A 增加 C 的值。
• 打印 A 和 B 作为答案。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find the desired numbers
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;
 
    cout << "A = " << A << " B = " << B;
}
 
// Driver Code
int main()
{
    int X = 2, Y = 3, Z = 1;
    findTwoNumbers(X, Y, Z);
    return 0;
}

Java

// Java program for the above approach
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 numbers
def 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 Code
if __name__ == "__main__":
 
    X, Y, Z = 2, 3, 1
    findTwoNumbers(X, Y, Z)
 
    # This code is contributed by rakeshsahni

C#

// C# program for the above approach
using System;
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;
 
    Console.Write("A = " + A + " B = " + B);
}
 
// Driver Code
public static void Main()
{
    int X = 2, Y = 3, Z = 1;
    findTwoNumbers(X, Y, Z);
}
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript

    // 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

输出

A = 11 B = 100

时间复杂度：O(max(X, Y))
辅助空间：O(1)