Dada una array arr[] y dos enteros X e Y. La tarea es verificar si es posible hacer que todos los elementos sean iguales dividiéndolos con X e Y cualquier número de veces, incluido 0.
Ejemplos:
Entrada: arr[] = {2, 4, 6, 8}, X = 2, Y = 3
Salida: Sí
2 -> 2
4 -> (4 / X) = (4 / 2) = 2
6 -> ( 6/Y) = (6/3) = 2
8 -> (8/X) = (8/2) = 4 y 4 -> (4/X) = (4/2) = 2Entrada: arr[] = {2, 4, 10}, X = 11, Y = 12
Salida: No
Enfoque: Encuentre el gcd de todos los elementos de la array dada porque este gcd es el valor que podemos obtener al dividir todos los elementos con algunas constantes arbitrarias, digamos gcd = arr[0] / k1 o arr[1] / k2 o… o arr[n-1] / kn . Ahora la tarea es encontrar si estas constantes k1, k2, k3, …, kn son de la forma X * X * X * … * YYY * …. . Si es así, entonces es posible hacer que todos los elementos sean iguales a la operación dada, de lo contrario no lo es.
A continuación se muestra la implementación del enfoque anterior:
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>
Producción:
Yes
Complejidad de tiempo: O(n*log(max(x,y))), donde n , x , y son proporcionados por el usuario
Espacio auxiliar: O(1), ya que no se utiliza espacio adicional