C++ Recursion: Calculating product of two numbers without multiplication operator

Last update on April 14 2025 12:47:06 (UTC/GMT +8 hours)

13. Recursive Multiplication Without Using the Multiplication Operator

Write a C++ program to implement a recursive function to calculate the product of two numbers without using the multiplication operator.

Sample Solution:

C Code:

// Recursive function to calculate the product of two numbers without using the multiplication operator
#include <iostream>

// Recursive function to multiply two numbers without using the multiplication operator
int multiply(int x, int y) {
  // Base case: if either number is 0, the product is 0
  if (x == 0 || y == 0)
    return 0;

  // Recursive case: recursively add x to the product of (x, y - 1)
  // when y is positive, or recursively add (-x) to the product of (x, y + 1)
  // when y is negative
  if (y > 0)
    return x + multiply(x, y - 1); // Positive y: add x to the product
  else
    return -x + multiply(x, y + 1); // Negative y: add (-x) to the product
}

int main() {
  int n1, n2;
  std::cout << "Input the first number: ";
  std::cin >> n1;
  std::cout << "Input the second number: ";
  std::cin >> n2;

  // Calculate the product using recursion
  int result = multiply(n1, n2);

  std::cout << "Product of " << n1 << " and " << n2 << ": " << result << std::endl;

  return 0;
}

Sample Output:

Input the first number: 12
Input the second number: 34
Product of 12 and 34: 408

Explanation:

In the above exercise,

• The "multiply()" function takes two integers x and y as parameters and calculates their product without using the multiplication operator.
• The base case is when either x or y is 0, in which case the function returns 0.
• In the recursive case, if y is positive, the function recursively adds x to the product of x and y - 1. If y is negative, the function recursively adds -x to the product of x and y + 1.
• The recursive calls continue until the base case is reached, and the function returns the final product.
• The "main()" function prompts the user to enter two numbers, calls the "multiply()" function to calculate their product, and then displays the result.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a C++ program to recursively multiply two numbers using addition and subtraction only.
• Write a C++ program that implements a recursive function to compute the product of two integers without using the '*' operator.
• Write a C++ program to simulate multiplication recursively by adding one number repeatedly and handling negative values.
• Write a C++ program that calculates the product of two numbers using recursion and compares the result with standard multiplication.

CPP Code Editor:

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Next C++ Exercise: Calculating the sum of even and odd numbers in a range.