给定长度为N的数组arr [] ,任务是找到将数组中元素的最大数量除以最大的数字。
例子:
Input: arr[] = {2, 12, 6}
Output: 2
1 and 2 are the only integers which divide the
maximum number of elements from the array
(i.e. all the elements) and 2 is
the maximum among them.
Input: arr[] = {1, 7, 9}
Output: 1
方法:解决此问题的直接方法是采用所有要素的GCD。为什么这种方法行得通? 1是将数组的所有元素相除的数字。现在,任何其他大于1的数字都将除以数组的所有元素(在这种情况下,数字本身就是答案)或它将除以数组的一个子集,即1为答案,因为它从中除以更多元素数组。因此,最直接的方法是获取数组所有元素的GCD。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the largest number
// that divides the maximum elements
// from the given array
int findLargest(int* arr, int n)
{
// Finding gcd of all the numbers
// in the array
int gcd = 0;
for (int i = 0; i < n; i++)
gcd = __gcd(arr[i], gcd);
return gcd;
}
// Driver code
int main()
{
int arr[] = { 3, 6, 9 };
int n = sizeof(arr) / sizeof(int);
cout << findLargest(arr, n);
return 0;
}
Java
// Java implementation of the approach
class GFG {
// Function to return the largest number
// that divides the maximum elements
// fom the given array
static int findLargest(int[] arr, int n)
{
// Finding gcd of all the numbers
// in the array
int gcd = 0;
for (int i = 0; i < n; i++)
gcd = __gcd(arr[i], gcd);
return gcd;
}
static int __gcd(int a, int b)
{
return b == 0 ? a : __gcd(b, a % b);
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 3, 6, 9 };
int n = arr.length;
System.out.print(findLargest(arr, n));
}
}
// This code is contributed by PrinciRaj1992
Python3
# Python3 implementation of the approach
from math import gcd as __gcd
# Function to return the largest number
# that divides the maximum elements
# fom the given array
def findLargest(arr, n):
# Finding gcd of all the numbers
# in the array
gcd = 0
for i in range(n):
gcd = __gcd(arr[i], gcd)
return gcd
# Driver code
if __name__ == '__main__':
arr = [3, 6, 9]
n = len(arr)
print(findLargest(arr, n))
# This code is contributed by Mohit Kumar
C#
// C# implementation of the approach
using System;
class GFG {
// Function to return the largest number
// that divides the maximum elements
// fom the given array
static int findLargest(int[] arr, int n)
{
// Finding gcd of all the numbers
// in the array
int gcd = 0;
for (int i = 0; i < n; i++)
gcd = __gcd(arr[i], gcd);
return gcd;
}
static int __gcd(int a, int b)
{
return b == 0 ? a : __gcd(b, a % b);
}
// Driver code
public static void Main(String[] args)
{
int[] arr = { 3, 6, 9 };
int n = arr.Length;
Console.Write(findLargest(arr, n));
}
}
// This code is contributed by PrinciRaj1992
输出
3
时间复杂度: O(N * log(N))
辅助空间: O(N)