Smallest subarray with product divisible by k
Given an array of non-negative numbers, find length of smallest subarray whose product is a multiple of k.
Examples :
Input : arr[] = {1, 9, 16, 5, 4, 3, 2}
k = 720
Output: 3
The smallest subarray is {9, 16, 5} whose
product is 720.
Input : arr[] = {1, 2, 4, 5, 6}
K = 96
Output : No such subarray exists
The idea is simple. We traverse through all subarrays. For each subarray, we compute its product. If the product is multiple of k, we check if length of the subarray is smaller than current result.
C++
// C++ program to find smallest subarray // with product divisible by k. #include <bits/stdc++.h> using namespace std; // function to find the subarray of // minimum length and end of sub array int findsubArray(int arr[], int k) { // find the length of array int n = 7; // try of every sub array whether it // result in multiple of k or not if it // is store it in the result // and find for the minimum using // dynamic programming int res = n + 1; for (int i = 0; i < n; i++) { // Find minimum length product // beginning with arr[i]. int curr_prod = 1; for (int j = i; j < n; j++) { curr_prod = curr_prod * arr[j]; if (curr_prod % k == 0 && res > (j - i + 1)) { res = min(res, j - i + 1); break; } } } return (res == n + 1) ? 0 : res; } // driver Function int main(void) { int array[] = { 1, 9, 16, 5, 4, 3, 2 }; int k = 720; int answer = findsubArray(array, k); if (answer != 0) cout<<answer<<"\n"; else cout<<"No Such subarray exists."<<"\n"; return 0; } // This code is contributed by Nikita Tiwari. |
Java
// Java program to find smallest subarray // with product divisible by k. import java.util.*; // function to find the subarray of // minimum length and end of sub array public class findSubArray { public static int findsubArray(int arr[], int k) { // find the length of array int n = arr.length; // try of every sub array whether it result // in multiple of k or not if it // is store it in the result // and find for the minimum using // dynamic programming int res = n+1; for (int i = 0; i < n; i++) { // Find minimum length product beginning // with arr[i]. int curr_prod = 1; for (int j = i; j < n; j++) { curr_prod = curr_prod * arr[j]; if (curr_prod % k == 0 && res > (j-i+1)) { res = Math.min(res, j-i+1); break; } } } return (res == n+1)? 0 : res; } // driver Function public static void main(String[] args) { int array[] = { 1, 9, 16, 5, 4, 3, 2 }; int k = 720; int answer = findsubArray(array, k); if (answer != 0) System.out.println(answer); else System.out.println("No Such subarray exists."); } } |
Python3
# Python 3 program to find smallest # subarray with product divisible by k. # function to find the subarray of # minimum length and end of sub array def findsubArray(arr, k) : # find the length of array n= len(arr) # try of every sub array whether it # result in multiple of k or not if # it is store it in the result # and find for the minimum using # dynamic programming res = n+1 for i in range(0,n) : # Find minimum length product # beginning with arr[i]. curr_prod = 1 for j in range( i, n): curr_prod = curr_prod * arr[j] if (curr_prod % k == 0 and res > (j - i + 1)) : res = min(res, j - i + 1) break if(res == n + 1) : return 0 else : return res # driver Function array = [1, 9, 16, 5, 4, 3, 2 ] k = 720answer = findsubArray(array, k) if (answer != 0): print(answer) else : print("No Such subarray exists.") # This code is contributed by Nikita Tiwari. |
C#
// C# program to find smallest subarray // with product divisible by k. using System; public class GFG { // function to find the subarray of // minimum length and end of sub array public static int findsubArray(int []arr, int k) { // find the length of array int n = arr.Length; // try of every sub array whether it result // in multiple of k or not if it // is store it in the result // and find for the minimum using // dynamic programming int res = n+1; for (int i = 0; i < n; i++) { // Find minimum length product beginning // with arr[i]. int curr_prod = 1; for (int j = i; j < n; j++) { curr_prod = curr_prod * arr[j]; if (curr_prod % k == 0 && res > (j-i+1)) { res = Math.Min(res, j-i+1); break; } } } return (res == n+1) ? 0 : res; } // driver Function public static void Main() { int []array = { 1, 9, 16, 5, 4, 3, 2 }; int k = 720; int answer = findsubArray(array, k); if (answer != 0) Console.WriteLine(answer); else Console.WriteLine("No Such subarray" + " exists."); } } // This code is contributed by vt_m. |
PHP
<?php // PHP program to find smallest subarray // with product divisible by k. // function to find the subarray of // minimum length and end of sub array function findsubArray($arr, $k) { // find the length of array $n = 7; // try of every sub array // whether it result in // multiple of k or not if // it is store it in the // result and find for the // minimum using dynamic // programming $res = $n + 1; for ($i = 0; $i < $n; $i++) { // Find minimum length product // beginning with arr[i]. $curr_prod = 1; for ($j = $i; $j < $n; $j++) { $curr_prod = $curr_prod * $arr[$j]; if ($curr_prod % $k == 0 && $res > ($j - $i + 1)) { $res = min($res, $j - $i + 1); break; } } } return ($res == $n + 1) ? 0 : $res; } // Driver Code $arr = array(1, 9, 16, 5, 4, 3, 2); $k = 720; $answer = findsubArray($arr, $k); if ($answer != 0) echo $answer."\n"; else echo "No Such subarray exists."."\n"; // This code is contributed by Sam007 ?> |
Output:
3
Time Complexity = O(n^2)
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