make-array-elements-equal-to-zero

You are given 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.

Return the number of possible valid selections.

Example 1:

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

Output: 2

Explanation:

The only possible 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 possible valid selections.

Constraints:

• 1 <= nums.length <= 100


• 0 <= nums[i] <= 100


• There is at least one element i where nums[i] == 0.