leetcode - 1658. Minimum Operations to Reduce X to Zero

Description

You are given an integer array nums and an integer x. In one operation, you can either remove the leftmost or the rightmost element from the array nums and subtract its value from x. Note that this modifies the array for future operations.

Return the minimum number of operations to reduce x to exactly 0 if it is possible, otherwise, return -1.

Example 1:

Input: nums = [1,1,4,2,3], x = 5
Output: 2
Explanation: The optimal solution is to remove the last two elements to reduce x to zero.

Example 2:

Input: nums = [5,6,7,8,9], x = 4
Output: -1

Example 3:

Input: nums = [3,2,20,1,1,3], x = 10
Output: 5
Explanation: The optimal solution is to remove the last three elements and the first two elements (5 operations in total) to reduce x to zero.

Constraints:

1 <= nums.length <= 10^5
1 <= nums[i] <= 10^4
1 <= x <= 10^9

Solution

Queue

Every time try with leftest and rightest items, use BFS.

Time complexity: $o(2^n)$
Space complexity: $o(n)$

Code

Queue

class Solution:
    def minOperations(self, nums: List[int], x: int) -> int:
        queue = collections.deque([(0, len(nums) - 1, x, 0)])
        visited = set()
        while queue:
            left, right, r, res = queue.popleft()
            if (left, right, r) in visited:
                continue
            visited.add((left, right, r))
            if r == 0:
                return res
            elif r < 0:
                continue
            if left > right:
                continue
            queue.append((left + 1, right, r - nums[left], res + 1))
            queue.append((left, right - 1, r - nums[right], res + 1))
        return -1