Recursive program to print formula for GCD of n integers

Given a function gcd(a, b) to find GCD (Greatest Common Divisor) of two number. It is also known that GCD of three elements can be found by gcd(a, gcd(b, c)), similarly for four element it can find the GCD by gcd(a, gcd(b, gcd(c, d))). Given a positive integer n. The task is to print the formula to find the GCD of n integer using given gcd() function.

Examples:

Input : n = 3
Output : gcd(int, gcd(int, int))

Input : n = 5
Output : gcd(int, gcd(int, gcd(int, gcd(int, int))))

Approach: The idea is to use recursion to print the single line command. Now, to write a recursive function, say recursiveFun(n), the required string is composed of gcd(int, + recursiveFun(n – 1) + ). This means that the recursiveFun(n) should return a string that contains a call to itself and in order to evaluate that value, the recursive function will begin again for n – 1. This will, in turn, return another string with a call to n – 1 and so until n == 1 and the recursive function instead returns the string “int”.

Below is implementation of the above approach:

C++

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// CPP Program to print single line command
// to find the GCD of n integers
#include <bits/stdc++.h>
using namespace std;
  
// Function to print single line command
// to find GCD of n elements.
string recursiveFun(int n)
{
    // base case
    if (n == 1)
        return "int";
  
    // Recursive Step
    return "gcd(int, " + recursiveFun(n - 1) + ")";
}
  
// Driver Program
int main()
{
    int n = 5;
  
    cout << recursiveFun(n) << endl;
  
    return 0;
}

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Java

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// Java Program to print 
// single line command to
// find the GCD of n integers
class GFG
{
      
// Function to print single 
// line command to find GCD 
// of n elements.
static String recursiveFun(int n)
{
    // base case
    if (n == 1)
        return "int";
  
    // Recursive Step
    return "gcd(int, "
            recursiveFun(n - 1) + ")";
}
  
// Driver Code
public static void main(String [] arg)
{
    int n = 5;
  
    System.out.println(recursiveFun(n));
}
}
  
// This code is contributed 
// by Smitha

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Python3

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# Python 3 Program to print single line 
# command to find the GCD of n integers 
  
# Function to print single line command 
# to find GCD of n elements. 
def recursiveFun(n): 
      
    # base case 
    if (n == 1): 
        return "int"
  
    # Recursive Step 
    return "gcd(int, " + recursiveFun(n - 1) + ")"
  
# Driver Code
if __name__ == '__main__':
    n = 5
    print(recursiveFun(n)) 
  
# This code is contributed 
# by PrinciRaj1992

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C#

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// C# Program to print single
// line command to find the
// GCD of n integers
using System;
class GFG
{
      
// Function to print single 
// line command to find GCD 
// of n elements.
static String recursiveFun(int n)
{
    // base case
    if (n == 1)
        return "int";
  
    // Recursive Step
    return "gcd(int, " +
            recursiveFun(n - 1) + ")";
}
  
// Driver Code
public static void Main()
{
    int n = 5;
  
    Console.Write(recursiveFun(n));
}
}
  
// This code is contributed 
// by smitha

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Output:

gcd(int, gcd(int, gcd(int, gcd(int, int))))

Time Complexity: O(N), where N is the given number.



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