Given an array arr[] of N integers and a positive integer K, the task is to check if it is possible to split this array into distinct contiguous subarrays such that the Greatest Common Divisor of all elements of each subarray is greater than K.
Note: Each array element can be a part of exactly one subarray.
Examples:
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
Approach: This problem can be solved using the following observations:
- If any array element is found to be less than or equal to K, then the answer is always “No”. This is because the subarray that contains this number will always have GCD less than or equal to K.
- If no array element is found to be less than or equal to K, then it is always possible to divide the entire array into N subarrays each of size at least 1 whose GCD is always greater than K.
Therefore, from the above observations, the idea is to traverse the given array and check that if there exists any element in the array which is less than or equal to K. If found to be true, then print “No”. Otherwise print “Yes”.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <iostream>using namespace std;// Function to check if it is possible// to split an array into subarrays// having GCD at least Kstring 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 Codeint 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 approachimport java.io.*; class GFG{ // Function to check if it is possible// to split an array into subarrays// having GCD at least Kstatic 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 Kdef 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 Codeif __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 approachusing System;class GFG{ // Function to check if it is possible// to split an array into subarrays// having GCD at least Kstatic 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
<script>// JavaScript implementation of the above approach// Function to check if it is possible// to split an array into subarrays// having GCD at least Kfunction 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.</script> |
No
Time Complexity: O(N)
Auxiliary Space: O(1)
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