1769. Minimum Number of Operations to Move All Balls to Each Box - Explanation

class Solution:
    def minOperations(self, boxes: str) -> List[int]:
        n = len(boxes)
        res = [0] * n

        for pos in range(n):
            for i in range(n):
                if boxes[i] == '1':
                    res[pos] += abs(pos - i)

        return res

class Solution:
    def minOperations(self, boxes: str) -> List[int]:
        n = len(boxes)
        res = [0] * n

        prefix_count = [0] * (n + 1)
        index_sum = [0] * (n + 1)
        for i in range(n):
            prefix_count[i + 1] = prefix_count[i] + (boxes[i] == '1')
            index_sum[i + 1] = index_sum[i] + (i if boxes[i] == '1' else 0)

        for i in range(n):
            left = prefix_count[i]
            left_sum = index_sum[i]

            right = prefix_count[n] - prefix_count[i + 1]
            right_sum = index_sum[n] - index_sum[i + 1]

            res[i] = (i * left - left_sum) + (right_sum - i * right)

        return res

class Solution:
    def minOperations(self, boxes: str) -> List[int]:
        n = len(boxes)
        res = [0] * n

        balls = moves = 0
        for i in range(n):
            res[i] = balls + moves
            moves += balls
            balls += int(boxes[i])

        balls = moves = 0
        for i in range(n - 1, -1, -1):
            res[i] += balls + moves
            moves += balls
            balls += int(boxes[i])

        return res