Make Array Elements Equal to Zero

Easy

You receive an integer array nums.

Start by selecting a starting position curr such that nums[curr] == 0, and choose a movement direction of either left or right.

After that, you repeat the following process:

If curr is out of the range [0, n - 1], this process ends.
If nums[curr] == 0, move in the current direction by incrementing curr if you are moving right, or decrementing curr if you are moving left.
Else if nums[curr] > 0:
- Decrement nums[curr] by 1.
- Reverse your movement direction (left becomes right and vice versa).
- Take a step in your new direction.

A selection of the initial position curr and movement direction is considered valid if every element in nums becomes 0 by the end of the process.

Find and provide the count of valid valid selections.

Example 1

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

Output: 2

Explanation: The only valid valid selections are the following:

Choose curr = 3, and a movement direction to the left.
- [1,0,2,0,3] -> [1,0,2,0,3] -> [1,0,1,0,3] -> [1,0,1,0,3] -> [1,0,1,0,2] -> [1,0,1,0,2] -> [1,0,0,0,2] -> [1,0,0,0,2] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,0].
Choose curr = 3, and a movement direction to the right.
- [1,0,2,0,3] -> [1,0,2,0,3] -> [1,0,2,0,2] -> [1,0,2,0,2] -> [1,0,1,0,2] -> [1,0,1,0,2] -> [1,0,1,0,1] -> [1,0,1,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [0,0,0,0,0].

Example 2

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

Output: 0

Explanation: There are no valid valid selections.

Constraints

Responses stay private.