blog/algorithms/04-recursion/2023-08-17-pyramid-slide-down/index.md

id	slug	title	description	tags	last_updated
pyramid-slide-down	/recursion/pyramid-slide-down	Introduction to dynamic programming	Solving a problem in different ways.	java recursion exponential greedy dynamic-programming top-down-dp bottom-up-dp	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.

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 Java¹.

:::

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:

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");
}

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1. cause why not, right!? ↩︎