Find GCD of an Array of Numeric Strings

In this article, we'll delve into an intriguing problem related to arrays and string manipulation. The problem we're examining today is "Find the GCD (Greatest Common Divisor) of an array made up of numeric strings". This problem is a great way to hone your skills in string manipulation, arrays, and number theory.

Problem Statement

Given an array of strings where each string represents a positive integer, our task is to find the Greatest Common Divisor (GCD) of all these integers.

Approach

We'll convert each string to an integer and calculate the GCD of all these integers. To calculate the GCD, we can use Euclid's algorithm, which is an efficient way to find the GCD of two numbers.

Example

Here're the programs that solves the problem

#include <stdio.h>
#include <stdlib.h>

// Function to calculate the greatest common divisor (GCD) using Euclidean algorithm
int gcd(int a, int b) {
   if (b == 0) {
      return a;
   }
   return gcd(b, a % b);
}

// Function to find the GCD of an array of integers
int findGCD(int arr[], int size) {
   int result = arr[0];
    
   // Loop through the array and update the GCD with each element
   for (int i = 1; i < size; i++) {
      result = gcd(result, arr[i]);
   }
    
   return result;
}

int main() {
   int arr[] = {42, 84, 126, 168};
   int size = sizeof(arr) / sizeof(arr[0]);
   int result = findGCD(arr, size);
   printf("The GCD of the array is: %d\n", result);
   return 0;
}

The GCD of the array is: 42

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
using namespace std;

int gcd(int a, int b) {
   if (b == 0) {
      return a;
   }
   return gcd(b, a % b);
}

int findGCD(vector<string>& arr) {
   int result = stoi(arr[0]);
   
   for(int i = 1; i < arr.size(); i++) {
      result = gcd(result, stoi(arr[i]));
   }
   
   return result;
}

int main() {
   vector<string> arr = {"42", "84", "126", "168"};
   int result = findGCD(arr);
   cout << "The GCD of the array is: " << result << endl;
   return 0;
}

The GCD of the array is: 42

import java.util.Arrays;

public class GCDProgram {
   // Function to calculate the greatest common divisor (GCD) using Euclidean algorithm
   public static int gcd(int a, int b) {
      if (b == 0) {
         return a;
      }
      return gcd(b, a % b);
   }
   // Function to find the GCD of an array of integers
   public static int findGCD(int[] arr) {
      int result = arr[0];

      // Loop through the array and update the GCD with each element
      for (int i = 1; i < arr.length; i++) {
         result = gcd(result, arr[i]);
      }

      return result;
   }

   public static void main(String[] args) {
      int[] arr = {42, 84, 126, 168};
      int result = findGCD(arr);
      System.out.println("The GCD of the array is: " + result);
   }
}

The GCD of the array is: 42

# Function to calculate the greatest common divisor (GCD) using Euclidean algorithm
def gcd(a, b):
   if b == 0:
      return a
   return gcd(b, a % b)

# Function to find the GCD of a list of integers
def find_gcd(arr):
   result = int(arr[0])
    
   # Loop through the list and update the GCD with each element
   for i in range(1, len(arr)):
      result = gcd(result, int(arr[i]))
    
   return result

if __name__ == "__main__":
   arr = ["42", "84", "126", "168"]
   result = find_gcd(arr)
   print("The GCD of the array is:", result)

The GCD of the array is: 42

Explanation with a Test Case

Let's take the array of strings {"42", "84", "126", "168"}.

When we pass this array to the findGCD function, it first converts the first string to an integer and stores it in the variable result.

Then it iterates over the rest of the array, converting each string to an integer and updating result to be the GCD of result and the current integer.

For the given array, the GCD of all the integers is 42. So, the function will return 42.

Conclusion

This problem demonstrates how we can manipulate strings and use number theory to solve complex problems in C++. It's an excellent problem to practice your C++ coding skills and to understand Euclid's algorithm for finding the GCD of two numbers.