K Divisible Elements Subarrays LeetCode Solution

Problem – K Divisible Elements Subarrays LeetCode Solution

Given an integer array nums and two integers k and p, return the number of distinct subarrays which have at most k elements divisible by p.

Two arrays nums1 and nums2 are said to be distinct if:

  • They are of different lengths, or
  • There exists at least one index i where nums1[i] != nums2[i].

subarray is defined as a non-empty contiguous sequence of elements in an array.

Example 1:

Input: nums = [2,3,3,2,2], k = 2, p = 2
Output: 11
Explanation:
The elements at indices 0, 3, and 4 are divisible by p = 2.
The 11 distinct subarrays which have at most k = 2 elements divisible by 2 are:
[2], [2,3], [2,3,3], [2,3,3,2], [3], [3,3], [3,3,2], [3,3,2,2], [3,2], [3,2,2], and [2,2].
Note that the subarrays [2] and [3] occur more than once in nums, but they should each be counted only once.
The subarray [2,3,3,2,2] should not be counted because it has 3 elements that are divisible by 2.

Example 2:

Input: nums = [1,2,3,4], k = 4, p = 1
Output: 10
Explanation:
All element of nums are divisible by p = 1.
Also, every subarray of nums will have at most 4 elements that are divisible by 1.
Since all subarrays are distinct, the total number of subarrays satisfying all the constraints is 10.

Constraints:

  • 1 <= nums.length <= 200
  • 1 <= nums[i], p <= 200
  • 1 <= k <= nums.length

K Divisible Elements Subarrays LeetCode Solution in C++

class Solution {
public:

    int countDistinct(vector<int>& nums, int k, int p) {
        
        int n=nums.size();
        set<vector<int>>ans;
        
        int i,j;
        for(i=0;i<n;i++)
        {
            vector<int>tt;
            int ct=0;
            for(j=i;j<n;j++)
            {
                tt.push_back(nums[j]);
                if(nums[j]%p==0)
                    ++ct;
                if(ct>k)
                    break;
                ans.insert(tt);
                    
            }
        }
        return ans.size();
    }
    
};

K Divisible Elements Subarrays LeetCode Solution in Python

class Solution:
    def countDistinct(self, nums: List[int], k: int, p: int) -> int:
        n = len(nums)                        
        sub_arrays = set()
        
		# generate all combinations of subarray
        for start in range(n):
            cnt = 0
            temp = ''
            for i in range(start, n):
                if nums[i]%p == 0:
                    cnt+=1                 
                temp+=str(nums[i]) + ',' # build the sequence subarray in CSV format          
                if cnt>k: # check for termination 
                    break
                sub_arrays.add(temp)                                    
                
        return len(sub_arrays)

K Divisible Elements Subarrays LeetCode Solution in Java

class Solution {
    public int countDistinct(int[] nums, int k, int p) {
        int n = nums.length;
		// we are storing hashcode for all the substrings so that we can compare them faster.
		// main goal is to avoid entire sub array comparision using hashcode.
        Set<Long> ways = new HashSet<>(); 
        for(int i = 0; i < n; i++) {
            int cnt = 0;
            long hc = 1; // this is the running hashcode for sub array [i...j]
            for(int j = i; j < n; j++) {
                hc = 199L * hc + nums[j]; // updating running hashcode, since we nums are <=200, we shall consider a prime near 200 to avoid collision
                if(nums[j] % p == 0)
                    cnt++;
                if(cnt <= k) { // if current subarray [i...j] is valid, add its hashcode in our storage.
                    ways.add(hc);
                }
            }
        }
        return ways.size();
    }
}
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