O(n^2) solution with explanation

  • 2

    The height of the base of each box is the highest top of any other box already dropped that overlaps along the x-axis.

    So for each box, we iterate over all previously dropped boxes to find the base_height of the new box. The default is zero (ground level) if no overlaps are found.
    If there is no overlap between a box and a previous box, then they are separate and will not stick, so the new box will not go on top of the previous box.
    If there is overlap then the base_height of the new box will be the max of the previous base_height and height of the top of the previous box.

    Store the height of the new box as being base_height + side_length. Then append to the result the higher of the previous maximum height and this new box height.

    class Solution(object):
        def fallingSquares(self, positions):
            :type positions: List[List[int]]
            :rtype: List[int]
            heights, result = [], []    # heights is the top edge height for each box dropped
            highest = 0                 # greatest height so far
            for i, position in enumerate(positions):
                left, side_length = position[0], position[1]
                base_height = 0         # default if no overlap with any boxes
                for j in range(i):      # loop over all previously dropped boxes
                    prev_left, prev_side = positions[j][0], positions[j][1]  
                    if (left + side_length <= prev_left) or (left >= prev_left + prev_side):
                        continue        # no overlap between this box and previous box
                    base_height = max(base_height, heights[j])
                heights.append(base_height + side_length)
                highest = max(highest, heights[-1])
            return result

  • 1

    @yorkshire shouldn't heights.append(height + side_length) be heights.append(base_height + side_length)

  • 0

    @chaitanyaphalak Yes, thanks for pointing that out, I just changed the name for clarity but missed that. Corrected now

Log in to reply

Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect.