disk_stacking

README

Disk Stacking

You're given a non-empty array of arrays where each subarray holds three integers and represents a disk. These integers denote each disk's width, depth, and height, respectively. Your goal is to stack up the disks and to maximize the total height of the stack. A disk must have a strictly smaller width, depth, and height than any other disk below it.

Write a function that returns an array of the disks in the final stack, starting with the top disk and ending with the bottom disk. Note that you can't rotate disks; in other words, the integers in each subarray must represent [width, depth, height] at all times.

You can assume that there will only be one stack with the greatest total height.

Sample Input

disks = [[2, 1, 2], [3, 2, 3], [2, 2, 8], [2, 3, 4], [1, 3, 1], [4, 4, 5]]

Sample Output

[[2, 1, 2], [3, 2, 3], [4, 4, 5]]
// 10 (2 + 3 + 5) is the tallest height we can get by
// stacking disks following the rules laid out above.

Hints

Hint 1
Try building an array of the same length as the array of disks. At each index i in this new array, store the height of the tallest tower that can be created with the disk located at index i at the bottom.

Hint 2
Consider sorting the disks by width, depth, or height for a slight optimization.

Hint 3
Can you efficiently keep track of potential towers in another array? Instead of storing entire sequences of disks, try storing the indices of previous disks. For example, at index 3 in this other array, store the index of the before-last disk in the tallest tower whose base is the disk at index 3.

Optimal Space & Time Complexity
O(n^2) time | O(n) space - where n is the number of disks

Documentation

Index

• func DiskStacking(input [][]int) [][]int
• type Disk
• type Disks
  • func (disks Disks) Len() int
  • func (disks Disks) Less(i, j int) bool
  • func (disks Disks) Swap(i, j int)

Functions

func DiskStacking

func DiskStacking(input [][]int) [][]int

Types

type Disk

type Disk []int

type Disks

type Disks []Disk

func (Disks) Len

func (disks Disks) Len() int

func (Disks) Less

func (disks Disks) Less(i, j int) bool

func (Disks) Swap

func (disks Disks) Swap(i, j int)