mirror of
https://github.com/mfocko/blog.git
synced 2024-11-22 21:13:47 +01:00
116 lines
3 KiB
Markdown
116 lines
3 KiB
Markdown
---
|
|
id: pyramid-slide-down
|
|
slug: /recursion/pyramid-slide-down
|
|
title: Introduction to dynamic programming
|
|
description: |
|
|
Solving a problem in different ways.
|
|
tags:
|
|
- java
|
|
- recursion
|
|
- exponential
|
|
- greedy
|
|
- dynamic-programming
|
|
- top-down-dp
|
|
- bottom-up-dp
|
|
last_update:
|
|
date: 2023-08-17
|
|
---
|
|
|
|
In this series we will try to solve one problem in different ways.
|
|
|
|
## Problem
|
|
|
|
The problem we are going to solve is one of _CodeWars_ katas and is called
|
|
[Pyramid Slide Down](https://www.codewars.com/kata/551f23362ff852e2ab000037).
|
|
|
|
We are given a 2D array of integers and we are to find the _slide down_.
|
|
_Slide down_ is a maximum sum of consecutive numbers from the top to the bottom.
|
|
|
|
Let's have a look at few examples. Consider the following pyramid:
|
|
|
|
```
|
|
3
|
|
7 4
|
|
2 4 6
|
|
8 5 9 3
|
|
```
|
|
|
|
This pyramid has following slide down:
|
|
|
|
```
|
|
*3
|
|
*7 4
|
|
2 *4 6
|
|
8 5 *9 3
|
|
```
|
|
|
|
And its value is `23`.
|
|
|
|
We can also have a look at a _bigger_ example:
|
|
|
|
```
|
|
75
|
|
95 64
|
|
17 47 82
|
|
18 35 87 10
|
|
20 4 82 47 65
|
|
19 1 23 3 34
|
|
88 2 77 73 7 63 67
|
|
99 65 4 28 6 16 70 92
|
|
41 41 26 56 83 40 80 70 33
|
|
41 48 72 33 47 32 37 16 94 29
|
|
53 71 44 65 25 43 91 52 97 51 14
|
|
70 11 33 28 77 73 17 78 39 68 17 57
|
|
91 71 52 38 17 14 91 43 58 50 27 29 48
|
|
63 66 4 68 89 53 67 30 73 16 69 87 40 31
|
|
4 62 98 27 23 9 70 98 73 93 38 53 60 4 23
|
|
```
|
|
|
|
Slide down in this case is equal to `1074`.
|
|
|
|
## Solving the problem
|
|
|
|
:::caution
|
|
|
|
I will describe the following ways you can approach this problem and implement
|
|
them in _Java_[^1].
|
|
|
|
:::
|
|
|
|
For all of the following solutions I will be using basic `main` function that
|
|
will output `true`/`false` based on the expected output of our algorithm. Any
|
|
other differences will lie only in the solutions of the problem. You can see the
|
|
`main` here:
|
|
|
|
```java
|
|
public static void main(String[] args) {
|
|
System.out.print("Test #1: ");
|
|
System.out.println(longestSlideDown(new int[][] {
|
|
{ 3 },
|
|
{ 7, 4 },
|
|
{ 2, 4, 6 },
|
|
{ 8, 5, 9, 3 }
|
|
}) == 23 ? "passed" : "failed");
|
|
|
|
System.out.print("Test #2: ");
|
|
System.out.println(longestSlideDown(new int[][] {
|
|
{ 75 },
|
|
{ 95, 64 },
|
|
{ 17, 47, 82 },
|
|
{ 18, 35, 87, 10 },
|
|
{ 20, 4, 82, 47, 65 },
|
|
{ 19, 1, 23, 75, 3, 34 },
|
|
{ 88, 2, 77, 73, 7, 63, 67 },
|
|
{ 99, 65, 4, 28, 6, 16, 70, 92 },
|
|
{ 41, 41, 26, 56, 83, 40, 80, 70, 33 },
|
|
{ 41, 48, 72, 33, 47, 32, 37, 16, 94, 29 },
|
|
{ 53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14 },
|
|
{ 70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57 },
|
|
{ 91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48 },
|
|
{ 63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31 },
|
|
{ 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23 },
|
|
}) == 1074 ? "passed" : "failed");
|
|
}
|
|
```
|
|
|
|
[^1]: cause why not, right!?
|