What is the time complexity of LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box?

The Python solution on this page runs in O(n).

What is the space complexity of LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box?

The Python solution on this page uses O(n) auxiliary space.

Minimum Number of Operations to Move All Balls to Each Box — LeetCode 1769 Python Solution

MediumArrayStringPrefix Sum

Problem: #1769
Pattern: Prefix Sum
Reading time: 3 min
Source: leetcode.com

The problem

You have n boxes. You are given a binary string boxes of length n, where boxes[i] is '0' if the ith box is empty, and '1' if it contains one ball.

Example

Input: boxes = "110"
Output: [1,1,3]
Explanation: The answer for each box is as follows:

Python solution

Python

class Solution:
    def minOperations(self, boxes: str) -> List[int]:
        n = len(boxes)
        left = [0] * n
        right = [0] * n
        cnt = 0
        for i in range(1, n):
            if boxes[i - 1] == '1':
                cnt += 1
            left[i] = left[i - 1] + cnt
        cnt = 0
        for i in range(n - 2, -1, -1):
            if boxes[i + 1] == '1':
                cnt += 1
            right[i] = right[i + 1] + cnt
        return [a + b for a, b in zip(left, right)]

Complexity

Measure	Complexity
Time	O(n)
Space	O(n) auxiliary

Pattern: Prefix Sum

Precompute running totals once so any range query becomes a single subtraction. LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Prefix Sum.

The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box?: LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box is rated Medium on LeetCode.
What is the time complexity of LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box?: The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box?: The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box cover?: LeetCode 1769. Minimum Number of Operations to Move All Balls to Each Box is tagged Array, String and Prefix Sum on LeetCode.