检查是否可以通过双倍或三倍
使数组相等
给定 n 个元素的数组。您可以将数组中的元素增加两倍或三倍任意次数。完成所有操作后，检查是否有可能使数组中的所有元素相等。
例:
Input : A[] = {75, 150, 75, 50}
Output : Yes
Explanation : Here, 75 should be doubled twice and
150 should be doubled once and 50 should be doubled
once and tripled once.Then, all the elements will
be equal to 300.
Input : A[] = {100, 151, 200}
Output : No
Explanation : No matter what we do all elements in
the array could not be equal.
这个想法是重复地将每个元素除以 2 和 3，直到这个元素可以被整除。在这一步之后，如果所有元素都变得相同，那么答案是肯定的。
这是如何工作的？我们知道每一个整数都可以表示为质数2a. 3b. 5c. 7d…..。所以，在我们的问题中，我们可以通过加倍(2)或三倍(3)来增加 a 和 b。我们可以通过乘以 2 或 3 使数组中所有元素的 a 和 b 相等。但是这些数在它们的乘积表示中也有其他质数，我们不能改变它们的幂。所以为了使所有的数相等，它们应该从一开始就对其他质数具有相等的幂。我们可以通过将所有的数字尽可能多地除以二或三来检查它。那么他们都应该是平等的。
c++
// C++ program to check if all numbers can
// be made equal by repeated division of 2
// and 3
#include <bits/stdc++.h>
using namespace std;
bool canMakeEqual(int a[], int n)
{
for (int i = 0; i < n; i++) {
// continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
int main()
{
int A[] = { 75, 150, 75, 50 };
int n = sizeof(A) / sizeof(A[0]);
if (canMakeEqual(A, n))
cout << "Yes";
else
cout << "No";
return 0;
}
Java
// Java program to check if all numbers can
// be made equal by repeated division of 2
// and 3
import java.util.*;
class GFG {
static Boolean canMakeEqual(int a[], int n)
{
for (int i = 0; i < n; i++) {
// Continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// Continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
public static void main(String[] args)
{
int A[] = { 75, 150, 75, 50 };
int n = A.length;
if (canMakeEqual(A, n))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by 'Gitanjali'.
python 3
T2
c
T31
// C# program to check if all numbers can
// be made equal by repeated division of 2
// and 3
using System;
class GFG {
static Boolean canMakeEqual(int []a, int n)
{
for (int i = 0; i < n; i++) {
// Continuously divide every number by 2
while (a[i] % 2 == 0)
a[i] = a[i] / 2;
// Continuously divide every number by 3
while (a[i] % 3 == 0)
a[i] = a[i] / 3;
}
// Check if all numbers same
for (int i = 1; i < n; i++)
if (a[i] != a[0])
return false;
return true;
}
// Driver Code
public static void Main()
{
int []A = { 75, 150, 75, 50 };
int n = A.Length;
if (canMakeEqual(A, n))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code is contributed by 'vt_m'.
PHPT4T37】JavascriptT40
输出:
Yes
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