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Make Array Elements Equal to Zero

Difficulty: Easy

Problem Description

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. The process continues until all elements in nums become 0. Return the number of possible valid selections.

Key Insights

  • The selection of the initial position and movement direction must ensure that all elements in the array can be reduced to zero.
  • Movement can only occur from positions currently holding a zero, and the direction can change based on the values encountered.
  • Valid selections depend on the arrangement and values of elements adjacent to the zeros.

Space and Time Complexity

Time Complexity: O(n^2) - In the worst case, for each zero, we may need to simulate the process for all elements. Space Complexity: O(1) - We are using a constant amount of extra space.

Solution

To solve the problem, we iterate through each index of the array to find positions where nums[curr] == 0. For each of these positions, we simulate the process of reducing the array elements to zero in both left and right directions. If all elements can be reduced to zero starting from that position and direction, we count it as a valid selection.

Code Solutions

def make_array_elements_equal_to_zero(nums):
    n = len(nums)
    valid_count = 0

    for i in range(n):
        if nums[i] == 0:
            # Check left direction
            if can_reduce_to_zero(nums[:], i, -1):
                valid_count += 1
            # Check right direction
            if can_reduce_to_zero(nums[:], i, 1):
                valid_count += 1

    return valid_count

def can_reduce_to_zero(nums, start, direction):
    curr = start
    while 0 <= curr < len(nums):
        if nums[curr] == 0:
            curr += direction
        elif nums[curr] > 0:
            nums[curr] -= 1
            curr -= direction  # Reverse the direction
            curr += direction
        else:
            return False
    return all(x == 0 for x in nums)
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