first try

Author: ndsvw

main.py

@@ -0,0 +1,66 @@
+def maxHeight(d1, d2, d3):
+ """
+ A method that calculates largest possible tower height of given boxes (bad approach 1/2).
+ Problem description: https://practice.geeksforgeeks.org/problems/box-stacking/1
+ time complexity: O(n*max(max_d1, max_d2, max_d3)^2)
+ space complexity: O(n*max(max_d1, max_d2, max_d3)^2)
+
+ Parameters
+ ----------
+ d1 : int[]
+ a list of int values representing the 1st dimension of a / multiple 3d-box(es)
+ d2 : int[]
+ a list of int values representing the 2nd dimension of a / multiple 3d-box(es)
+ d3 : int[]
+ a list of int values representing the 3rd dimension of a / multiple 3d-box(es)
+
+ Returns
+ -------
+ x : int
+ the largest possible tower height
+ """
+
+ assert(len(d1) >= 1)
+ assert(len(d1) == len(d2) == len(d3))
+
+ max_dimension = max([
+ max(d1),
+ max(d2),
+ max(d3)
+ ])
+
+ boxes = zip(d1, d2, d3)
+ boxes = map(sorted, boxes)
+ boxes = sorted(boxes, key=lambda e: e[2])
+ boxes = sorted(boxes, key=lambda e: e[1])
+ boxes = sorted(boxes, key=lambda e: e[0])
+ boxes = boxes + list(map(lambda e: [e[1], e[2], e[0]], boxes))
+ boxes = sorted(boxes, key=lambda e: e[2])
+ boxes = sorted(boxes, key=lambda e: e[1])
+ boxes = sorted(boxes, key=lambda e: e[0])
+
+ n = len(boxes)
+
+ # dimension 1: i.th box
+ # dimension 2: x-coordinate left
+ # dimension 3: y-coordinate left
+ max_height = {i: [[0 for _ in range(max_dimension + 1)]
+ for _ in range(max_dimension + 1)] for i in range(-1, n)}
+
+ for i in range(n):
+ box_x, box_y, box_z = boxes[i][0], boxes[i][1], boxes[i][2]
+ for x in range(max_dimension + 1):
+ for y in range(max_dimension + 1):
+ max_tmp = max_height[i-1][x][y]
+ if box_x <= x and box_y <= y:
+ max_tmp = max(
+ max_tmp, max_height[i-1][box_x-1][box_y-1] + box_z)
+ if box_x <= x and box_z <= y:
+ max_tmp = max(
+ max_tmp, max_height[i-1][box_x-1][box_z-1] + box_y)
+ if box_y <= x and box_z <= y:
+ max_tmp = max(
+ max_tmp, max_height[i-1][box_y-1][box_z-1] + box_x)
+ max_height[i][x][y] = max_tmp
+ return max_height[n-1][max_dimension][max_dimension]
+