Solution for Minimum Number of Operations to Move All Balls to Each Box

This problem asks us to find out the minimum number of operations required to move all balls to each box. The operation is defined as moving one ball from one box to another.

Approach

We can use a two-pointer approach here, where we will maintain the left pointer (i) and the right pointer (j). We will also maintain two list left and right where left[i] will contain the total number of operations required to move all the balls from boxes 0 to i and right[j] will contain the total number of operations required to move all the balls from boxes j to n-1 where n is the total number of boxes.

After that, we can loop through the boxes and calculate the total number of operations for each box as left[i] + right[i].

Time Complexity

The time complexity of the above approach is O(n^2) as we are iterating through the array twice.

Space Complexity

The space complexity of the above approach is O(n) as we are using two lists of length n.

Code

class Solution(object): 

    def minOperations(self, boxes):
        n = len(boxes)
        left, right = [0] * n, [0] * n
        count = left_op, right_op = boxes[0], boxes[-1]
        for i in range(1, n):
            left_op += count
            count += boxes[i]
            left[i] = left_op
            right_op += boxes[n-1-i]
            right[n-1-i] = right_op
            
        return [left[i] + right[i] for i in range(n)]