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108 lines
3.3 KiB
Markdown
108 lines
3.3 KiB
Markdown
---
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title: Flood Fill Algorithm
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---
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## Flood Fill Algorithm
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Flood fill is an algorithm mainly used to determine a bounded area connected to a given node in a multi-dimensional array. It is
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a close resemblance to the bucket tool in paint programs.
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The most approached implementation of the algorithm is a stack-based recursive function, and that's what we're gonna talk about
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next.
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### How does it work?
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The problem is pretty simple and usually follows these steps:
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1. Take the position of the starting point.
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2. Decide whether you want to go in 4 directions (**N, S, W, E**) or 8 directions (**N, S, W, E, NW, NE, SW, SE**).
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3. Choose a replacement color and a target color.
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4. Travel in those directions.
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5. If the tile you land on is a target, replace it with the chosen color.
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6. Repeat 4 and 5 until you've been everywhere within the boundaries.
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Let's take the following array as an example:
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The red square is the starting point and the gray squares are the so called walls.
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For further details, here's a piece of code describing the function:
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```cpp
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int wall = -1;
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void flood_fill(int pos_x, int pos_y, int target_color, int color)
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{
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if(a[pos_x][pos_y] == wall || a[pos_x][pos_y] == color) // if there is no wall or if i haven't been there
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return; // already go back
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if(a[pos_x][pos_y] != target_color) // if it's not color go back
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return;
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a[pos_x][pos_y] = color; // mark the point so that I know if I passed through it.
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flood_fill(pos_x + 1, pos_y, color); // then i can either go south
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flood_fill(pos_x - 1, pos_y, color); // or north
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flood_fill(pos_x, pos_y + 1, color); // or east
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flood_fill(pos_x, pos_y - 1, color); // or west
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return;
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}
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```
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As seen above, my starting point is (4,4). After calling the function for the start coordinates **x = 4** and **y = 4**,
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I can start checking if there is no wall or color on the spot. If that is valid i mark the spot with one **"color"**
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and start checking the other adjacent squares.
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Going south we will get to point (5,4) and the function runs again.
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### Exercise problem
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I always considered that solving a (or more) problem/s using a newly learned algorithm is the best way to fully understand
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the concept.
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So here's one:
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**Statement:**
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In a bidimensional array you are given n number of **"islands"**. Try to find the largest area of an island and
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the corresponding island number. 0 marks water and any other x between 1 and n marks one square from the surface corresponding
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to island x.
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**Input**
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* **n** - the number of islands.
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* **l,c** - the dimensions of the matrix.
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* the next **l** lines, **c** numbers giving the **l**th row of the matrix.
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**Output**
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* **i** - the number of the island with the largest area.
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* **A** - the area of the **i**'th island.
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**Ex:**
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You have the following input:
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```cpp
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2 4 4
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0 0 0 1
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0 0 1 1
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0 0 0 2
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2 2 2 2
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```
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For which you will get island no. 2 as the biggest island with the area of 5 squares.
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### Hints
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The problem is quite easy, but here are some hints:
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1. Use the flood-fill algorithm whenever you encounter a new island.
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2. As opposed to the sample code, you should go through the area of the island and not on the ocean (0 tiles).
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