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