Given three positive integer n, x, y. The task is to print Greatest Common Divisor of numbers formed by n repeating x times and number formed by n repeating y times.
0 <= n, x, y <= 1000000000.
Examples :
Input : n = 123, x = 2, y = 3. Output : 123 Number formed are 123123 and 123123123. Greatest Common Divisor of 123123 and 123123123 is 123. Input : n = 4, x = 4, y = 6. Output : 44
The idea is based on Euclidean algorithm to compute GCD of two number.
Let f(n, x) be a function which gives a number n repeated x times. So, we need to find GCD(f(n, x), f(n, y)).
Let n = 123, x = 3, y = 2.
So, first number A is f(123, 3) = 123123123 and second number B is f(123, 2) = 123123. We know, GCD(A,B) = GCD(A – B, B), using this property we can subtract any multiple of B, say B’ from first A as long as B’ is smaller than A.
So, A = 123123123 and B’ can be 123123000. On subtracting A will became 123 and B remains same.
Therefore, A = A – B’ = f(n, x – y).
So, GCD(f(n, x), f(n, y)) = GCD(f(n, x – y), f(n, y))
We can conclude following,
GCD(f(n, x), f(n, y)) = f(n, GCD(x, y)).
Below is the implementation based on this approach:
CPP
// C++ program to print Greatest Common Divisor // of number formed by N repeating x times and // y times. #include<bits/stdc++.h> using namespace std; // Return the Greatest common Divisor of two numbers. int gcd(int a, int b) { if (a == 0) return b; return gcd(b%a, a); } // Prints Greatest Common Divisor of number formed // by n repeating x times and y times. void findgcd(int n, int x, int y) { // Finding GCD of x and y. int g = gcd(x,y); // Print n, g times. for (int i = 0; i < g; i++) cout << n; } // Driven Program int main() { int n = 123, x = 5, y = 2; findgcd(n, x, y); return 0; } |
Java
// Java program to print Greatest Common Divisor // of number formed by N repeating x times and // y times class GFG { // Return the Greatest common Divisor // of two numbers. static int gcd(int a, int b) { if (a == 0) return b; return gcd(b % a, a); } // Prints Greatest Common Divisor of // number formed by n repeating x // times and y times. static void findgcd(int n, int x, int y) { // Finding GCD of x and y. int g = gcd(x, y); // Print n, g times. for (int i = 0; i < g; i++) System.out.print(n); } // Driver code public static void main(String[] args) { int n = 123, x = 5, y = 2; findgcd(n, x, y); } } // This code is contributed by Anant Agarwal. |
Python3
# Python program to print Greatest # Common Divisor of number formed # by N repeating x times and y times # Return the Greatest common Divisor # of two numbers. def gcd(a, b): if (a == 0): return b return gcd(b % a, a) # Prints Greatest Common Divisor of # number formed by n repeating x times # and y times. def findgcd(n, x, y): # Finding GCD of x and y. g = gcd(x, y) # Print n, g times. for i in range(g): print(n) # Driver code n = 123x = 5y = 2 findgcd(n, x, y) # This code is contributed by Anant Agarwal. |
C#
// C# program to print Greatest Common // Divisor of number formed by N // repeating x times and y times using System; class GFG { // Return the Greatest common // Divisor of two numbers. static int gcd(int a, int b) { if (a == 0) return b; return gcd(b % a, a); } // Prints Greatest Common // Divisor of number formed // by n repeating x times // and y times. static void findgcd(int n, int x, int y) { // Finding GCD of x and y. int g = gcd(x, y); // Print n, g times. for (int i = 0; i < g; i++) Console.Write(n); } // Driver code public static void Main() { int n = 123, x = 5, y = 2; findgcd(n, x, y); } } // This code is contributed by // nitin mittal. |
PHP
<?php // PHP program to print // Greatest Common Divisor // of number formed by N // repeating x times and y times. // Return the Greatest common // Divisor of two numbers. function gcd($a, $b) { if ($a == 0) return $b; return gcd($b % $a, $a); } // Prints Greatest Common Divisor // of number formed by n repeating // x times and y times. function findgcd($n, $x, $y) { // Finding GCD of x and y. $g = gcd($x, $y); // Print n, g times. for ($i = 0; $i < $g; $i++) echo($n); } // Driver Code $n = 123; $x = 5; $y = 2; findgcd($n, $x, $y); // This code is contributed by Ajit. ?> |
Javascript
<script> // Javascript program to print Greatest Common Divisor // of number formed by N repeating x times and // y times. // Return the Greatest common Divisor of two numbers. function gcd(a, b) { if (a == 0) return b; return gcd(b%a, a); } // Prints Greatest Common Divisor of number formed // by n repeating x times and y times. function findgcd(n, x, y) { // Finding GCD of x and y. let g = gcd(x,y); // Print n, g times. for (let i = 0; i < g; i++) document.write(n); } // Driven Program let n = 123, x = 5, y = 2; findgcd(n, x, y); // This is code is contributed by Mayank Tyagi </script> |
Output :
123
Time Complexity: O(log(min(n)) )
Auxiliary Space: O(log(min(n))
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