Smallest subarray with product divisible by k

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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.

Implementation:

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 = 720
answer = 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
?>

Javascript

<script>
    // Javascript 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
        let 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
        let res = n+1;
        for (let i = 0; i < n; i++) {
   
            // Find minimum length product beginning
            // with arr[i]. 
            let curr_prod = 1; 
            for (let 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;
    }
     
    let array = [ 1, 9, 16, 5, 4, 3, 2 ];
    let k = 720;
    let answer = findsubArray(array, k);
    if (answer != 0)
      document.write(answer);
    else
      document.write("No Such subarray"
                        + " exists.");
     
</script>

Output:

Time Complexity: O(n^2)

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