Problem: Minimum Number of Operations to Move All Balls to Each Box

You have n boxes represented as a binary string boxes, where:

• '0' means the box is empty.
• '1' means the box contains one ball.

You can move a ball from one box to an adjacent box in one operation. A box is adjacent if the difference in their indices is 1.

You need to calculate an array answer of size n where:

• answer[i] is the minimum number of operations required to move all balls to the ith box, considering the initial positions of the balls.

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Examples

Example 1:

Input:
boxes = "110"
Output:
[1, 1, 3]

The number of operations required to move all balls to the 0th index box from the initial state = 1.

The number of operations required to move all balls to the 1st index box from the initial state = 1.

The number of operations required to move all balls to the 3rd index box from the initial state = 2.

The total number of operations required to move all balls to each index box from the initial state is given by the array:

ans = [1, 1, 3]

Explanation:

1. For the first box: Move one ball from the second box → 1 operation.
2. For the second box: Move one ball from the first box → 1 operation.
3. For the third box:
   • Move one ball from the first box → 2 operations.
   • Move one ball from the second box → 1 operation.
     Total = 3 operations.

Example 2:

Input:
boxes = "001011"
Output:
[11, 8, 5, 4, 3, 4]

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Constraints

$$n = \text{boxes.length}$$ $$1 \leq n \leq 2000$$ $$\text{boxes}[i] \in \{ 0 , 1 \}$$