Number of Zero-Filled Subarrays

 ven an integer array nums, return the number of subarrays filled with 0.


A subarray is a contiguous non-empty sequence of elements within an array.


 


Example 1:


Input: nums = [1,3,0,0,2,0,0,4]

Output: 6

Explanation: 

There are 4 occurrences of [0] as a subarray.

There are 2 occurrences of [0,0] as a subarray.

There is no occurrence of a subarray with a size more than 2 filled with 0. Therefore, we return 6.

Example 2:


Input: nums = [0,0,0,2,0,0]

Output: 9

Explanation:

There are 5 occurrences of [0] as a subarray.

There are 3 occurrences of [0,0] as a subarray.

There is 1 occurrence of [0,0,0] as a subarray.

There is no occurrence of a subarray with a size more than 3 filled with 0. Therefore, we return 9.

Example 3:


Input: nums = [2,10,2019]

Output: 0

Explanation: There is no subarray filled with 0. Therefore, we return 0.

 

🔍 Problem Recap

We need to count how many subarrays consist entirely of zeros.

  • Example: nums = [0,0,0]
    Subarrays: [0], [0], [0], [0,0], [0,0], [0,0,0] → 6

The formula you used is correct:

count of zero-filled subarrays in a run of length len=len⋅(len+1)2\text{count of zero-filled subarrays in a run of length len} = \frac{len \cdot (len+1)}{2}

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