检查是否可以将数组拆分为 GCD 超过 K 的子数组

给定一个由N 个整数组成的数组arr[]和一个正整数K ，任务是检查是否可以将此数组拆分为不同的连续子数组，使得每个子数组的所有元素的最大公约数大于K 。

注意：每个数组元素可以恰好是一个子数组的一部分。

例子：

Input: arr[] = {3, 2, 4, 4, 8}, K = 1
Output: Yes
Explanation:
One valid split is [3], [2, 4], [4, 8] with GCD 3, 2 and 4 respectively. 
Another Valid Split is [3], [2, 4], [4], [8] with GCD 3, 2, 4 and 8 respectively.
Therefore, the given array can be split into subarrays having GCD > K.

Input: arr[] = {2, 4, 6, 1, 8, 16}, K = 3
Output: No

方法：这个问题可以通过以下观察来解决：

• 如果发现任何数组元素小于或等于 K ，则答案始终为“否”。这是因为包含此数字的子数组将始终具有小于或等于K 的GCD。
• 如果没有发现数组元素小于或等于K ，那么总是可以将整个数组划分为N个子数组，每个子数组的大小至少为1，其 GCD 总是大于K 。

因此，从上面的观察来看，想法是遍历给定的数组并检查数组中是否存在任何小于或等于K 的元素。如果发现是真的，则打印“否” 。否则打印“是” 。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to check if it is possible
// to split an array into subarrays
// having GCD at least K
string canSplitArray(int arr[], int n,
                     int k)
{
 
    // Iterate over the array arr[]
    for (int i = 0; i < n; i++) {
 
        // If the current element
        // is less than or equal to k
        if (arr[i] <= k) {
            return "No";
        }
    }
 
    // If no array element is found
    // to be less than or equal to k
    return "Yes";
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 2, 4, 6, 1, 8, 16 };
 
    int N = sizeof arr / sizeof arr[0];
 
    // Given K
    int K = 3;
 
    // Function Call
    cout << canSplitArray(arr, N, K);
}

Java

// Java program for the above approach
import java.io.*;
 
class GFG{
     
// Function to check if it is possible
// to split an array into subarrays
// having GCD at least K
static String canSplitArray(int arr[],
                            int n, int k)
{
     
    // Iterate over the array arr[]
    for(int i = 0; i < n; i++)
    {
         
        // If the current element
        // is less than or equal to k
        if (arr[i] <= k)
        {
            return "No";
        }
    }
     
    // If no array element is found
    // to be less than or equal to k
    return "Yes";
}
 
// Driver code
public static void main (String[] args)
{
     
    // Given array arr[]
    int arr[] = { 2, 4, 6, 1, 8, 16 };
     
    // Length of the array
    int N = arr.length;
     
    // Given K
    int K = 3;
     
    // Function call
    System.out.println(canSplitArray(arr, N, K));
}
}
 
// This code is contributed by jana_sayantan

Python3

# Python3 program for the above approach
 
# Function to check if it is possible
# to split an array into subarrays
# having GCD at least K
def canSplitArray(arr, n, k):
 
    # Iterate over the array arr[]
    for i in range(n):
 
        # If the current element
        # is less than or equal to k
        if (arr[i] <= k):
            return "No"
 
    # If no array element is found
    # to be less than or equal to k
    return "Yes"
 
# Driver Code
if __name__ == '__main__':
 
    # Given array arr[]
    arr = [ 2, 4, 6, 1, 8, 16 ]
 
    N = len(arr)
 
    # Given K
    K = 3
 
    # Function call
    print(canSplitArray(arr, N, K))
 
# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to check if it is possible
// to split an array into subarrays
// having GCD at least K
static String canSplitArray(int []arr,
                            int n, int k)
{
     
    // Iterate over the array []arr
    for(int i = 0; i < n; i++)
    {
         
        // If the current element
        // is less than or equal to k
        if (arr[i] <= k)
        {
            return "No";
        }
    }
     
    // If no array element is found
    // to be less than or equal to k
    return "Yes";
}
 
// Driver code
public static void Main(String[] args)
{
     
    // Given array []arr
    int []arr = { 2, 4, 6, 1, 8, 16 };
     
    // Length of the array
    int N = arr.Length;
     
    // Given K
    int K = 3;
     
    // Function call
    Console.WriteLine(canSplitArray(arr, N, K));
}
}
 
// This code is contributed by Amit Katiyar

Javascript

 
// JavaScript implementation of the above approach
 
// Function to check if it is possible
// to split an array into subarrays
// having GCD at least K
function canSplitArray(arr, n, k)
{
       
    // Iterate over the array arr[]
    for(let i = 0; i < n; i++)
    {
           
        // If the current element
        // is less than or equal to k
        if (arr[i] <= k)
        {
            return "No";
        }
    }
       
    // If no array element is found
    // to be less than or equal to k
    return "Yes";
}
 
// Driver code
         
    // Given array arr[]
    let arr = [ 2, 4, 6, 1, 8, 16 ];
       
    // Length of the array
    let N = arr.length;
       
    // Given K
    let K = 3;
       
    // Function call
    document.write(canSplitArray(arr, N, K));
       
    // This code is contributed by code_hunt.

输出：

No

时间复杂度： O(N)
辅助空间： O(1)

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