Maximum Height by Stacking Cuboids

arraydynamic programmingsorting

Problem Statement

Given n cuboids where the dimensions of the i ^th cuboid is cuboids[i] = [width _i , length _i , height _i ] ( 0-indexed ). Choose a subset of cuboids and place them on each other.

You can place cuboid i on cuboid j if width _i <= width _j and length _i <= length _j and height _i <= height _j . You can rearrange any cuboid's dimensions by rotating it to put it on another cuboid.

Return the maximum height of the stacked cuboids .

Examples

Example 1

Input: cuboids = [[50,45,20],[95,37,53],[45,23,12]]
Output: 190
Cuboid 1 is placed on the bottom with the 53x37 side facing down with height 95.
Cuboid 0 is placed next with the 45x20 side facing down with height 50.
Cuboid 2 is placed next with the 23x12 side facing down with height 45.
The total height is 95 + 50 + 45 = 190.

Example 2

Input: cuboids = [[38,25,45],[76,35,3]]
Output: 76
You can't place any of the cuboids on the other.
We choose cuboid 1 and rotate it so that the 35x3 side is facing down and its height is 76.

Example 3

Input: cuboids = [[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]
Output: 102
After rearranging the cuboids, you can see that all cuboids have the same dimension.
You can place the 11x7 side down on all cuboids so their heights are 17.
The maximum height of stacked cuboids is 6 * 17 = 102.

Constraints

n == cuboids.length

1 <= n <= 100

1 <= width _i , length _i , height _i <= 100

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming