Given an array arr[] and two integers X and Y. The task is to check whether it is possible to make all the elements equal by dividing them with X and Y any number of times including 0.
Examples:
Input: arr[] = {2, 4, 6, 8}, X = 2, Y = 3
Output: Yes
2 -> 2
4 -> (4 / X) = (4 / 2) = 2
6 -> (6 / Y) = (6 / 3) = 2
8 -> (8 / X) = (8 / 2) = 4 and 4 -> (4 / X) = (4 / 2) = 2Input: arr[] = {2, 4, 10}, X = 11, Y = 12
Output: No
Approach: Find the gcd of all the elements from the given array because this gcd is the value which can we get by dividing all the elements with some arbitrary constants say gcd = arr[0] / k1 or arr[1] / k2 or … or arr[n-1] / kn. Now the task is to find whether these constants k1, k2, k3, …, kn are of the form X * X * X * … * Y Y Y * ….. If yes then it is possible to make all the elements equal with the given operation else it isn’t.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function that returns true if num // is of the form x*x*x*...*y*y*... bool isDivisible( int num, int x, int y) { // While num is divisible // by either x or y, keep dividing while (num % x == 0 || num % y == 0) { if (num % x == 0) num /= x; if (num % y == 0) num /= y; } // If num > 1, it means it cannot be // further divided by either x or y if (num > 1) return false ; return true ; } // Function that returns true if all // the array elements can be made // equal with the given operation bool isPossible( int arr[], int n, int x, int y) { // To store the gcd of the array elements int gcd = arr[0]; for ( int i = 1; i < n; i++) gcd = __gcd(gcd, arr[i]); // For every element of the array for ( int i = 0; i < n; i++) { // Check if k is of the form x*x*..*y*y*... // where (gcd * k = arr[i]) if (!isDivisible(arr[i] / gcd, x, y)) return false ; } return true ; } // Driver code int main() { int arr[] = { 2, 4, 6, 8 }; int n = sizeof (arr) / sizeof (arr[0]); int x = 2, y = 3; if (isPossible(arr, n, x, y)) cout << "Yes" ; else cout << "No" ; return 0; } |
Java
// Java implementation of the approach class GFG { // Function that returns true if num // is of the form x*x*x*...*y*y*... public static boolean isDivisible( int num, int x, int y) { // While num is divisible // by either x or y, keep dividing while (num % x == 0 || num % y == 0 ) { if (num % x == 0 ) num /= x; if (num % y == 0 ) num /= y; } // If num > 1, it means it cannot be // further divided by either x or y if (num > 1 ) return false ; return true ; } // Function to calculate gcd of two numbers // using Euclid's algorithm public static int _gcd( int a, int b) { while (a != b) { if (a > b) a = a - b; else b = b - a; } return a; } // Function that returns true if all // the array elements can be made // equal with the given operation public static boolean isPossible( int [] arr, int n, int x, int y) { // To store the gcd of the array elements int gcd = arr[ 0 ]; for ( int i = 1 ; i < n; i++) gcd = _gcd(gcd, arr[i]); // For every element of the array for ( int i = 0 ; i < n; i++) { // Check if k is of the form x*x*..*y*y*... // where (gcd * k = arr[i]) if (!isDivisible(arr[i] / gcd, x, y)) return false ; } return true ; } // Driver code public static void main(String[] args) { int [] arr = { 2 , 4 , 6 , 8 }; int n = arr.length; int x = 2 , y = 3 ; if (isPossible(arr, n, x, y)) System.out.println( "Yes" ); else System.out.println( "No" ); } } // This code is contributed by // sanjeev2552 |
Python3
# Python3 implementation of the approach from math import gcd as __gcd # Function that returns True if num # is of the form x*x*x*...*y*y*... def isDivisible(num, x, y): # While num is divisible # by either x or y, keep dividing while (num % x = = 0 or num % y = = 0 ): if (num % x = = 0 ): num / / = x if (num % y = = 0 ): num / / = y # If num > 1, it means it cannot be # further divided by either x or y if (num > 1 ): return False return True # Function that returns True if all # the array elements can be made # equal with the given operation def isPossible(arr, n, x, y): # To store the gcd of the array elements gcd = arr[ 0 ] for i in range ( 1 ,n): gcd = __gcd(gcd, arr[i]) # For every element of the array for i in range (n): # Check if k is of the form x*x*..*y*y*... # where (gcd * k = arr[i]) if (isDivisible(arr[i] / / gcd, x, y) = = False ): return False return True # Driver code arr = [ 2 , 4 , 6 , 8 ] n = len (arr) x = 2 y = 3 if (isPossible(arr, n, x, y) = = True ): print ( "Yes" ) else : print ( "No" ) # This code is contributed by mohit kumar 29 |
C#
// C# implementation of the approach using System; class GFG { // Function that returns true if num // is of the form x*x*x*...*y*y*... public static bool isDivisible( int num, int x, int y) { // While num is divisible // by either x or y, keep dividing while (num % x == 0 || num % y == 0) { if (num % x == 0) num /= x; if (num % y == 0) num /= y; } // If num > 1, it means it cannot be // further divided by either x or y if (num > 1) return false ; return true ; } // Function to calculate gcd of two numbers // using Euclid's algorithm public static int _gcd( int a, int b) { while (a != b) { if (a > b) a = a - b; else b = b - a; } return a; } // Function that returns true if all // the array elements can be made // equal with the given operation public static bool isPossible( int [] arr, int n, int x, int y) { // To store the gcd of the array elements int gcd = arr[0]; for ( int i = 1; i < n; i++) gcd = _gcd(gcd, arr[i]); // For every element of the array for ( int i = 0; i < n; i++) { // Check if k is of the form x*x*..*y*y*... // where (gcd * k = arr[i]) if (!isDivisible(arr[i] / gcd, x, y)) return false ; } return true ; } // Driver code public static void Main() { int [] arr = { 2, 4, 6, 8 }; int n = arr.Length; int x = 2, y = 3; if (isPossible(arr, n, x, y)) Console.Write( "Yes" ); else Console.Write( "No" ); } } // This code is contributed by // anuj_67.. |
Javascript
<script> // Javascript implementation of the approach // Function that returns true if num // is of the form x*x*x*...*y*y*... function isDivisible(num, x, y) { // While num is divisible // by either x or y, keep dividing while (num % x == 0 || num % y == 0) { if (num % x == 0) num /= x; if (num % y == 0) num /= y; } // If num > 1, it means it cannot be // further divided by either x or y if (num > 1) return false ; return true ; } // Function to calculate gcd of two numbers // using Euclid's algorithm function __gcd(a, b) { while (a != b) { if (a > b) a = a - b; else b = b - a; } return a; } // Function that returns true if all // the array elements can be made // equal with the given operation function isPossible(arr, n, x, y) { // To store the gcd of the array elements var gcd = arr[0]; for ( var i = 1; i < n; i++) gcd = __gcd(gcd, arr[i]); // For every element of the array for ( var i = 0; i < n; i++) { // Check if k is of the form x*x*..*y*y*... // where (gcd * k = arr[i]) if (!isDivisible(arr[i] / gcd, x, y)) return false ; } return true ; } // Driver code var arr = [ 2, 4, 6, 8 ]; var n = arr.length; var x = 2, y = 3; if (isPossible(arr, n, x, y)) document.write( "Yes" ); else document.write( "No" ); </script> |
Yes
Time Complexity: O(n*log(max(x,y))), where n , x , y are given by the user
Auxiliary Space: O(1), as no extra space is used
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