# Flood Fill Algorithm

May 20, 2023

The **Flood Fill Algorithm** is a recursive strategy used to fill closed areas of an image or a two-dimensional array with a chosen color. The algorithm starts at a given point (seed) and then checks the neighboring pixels to determine whether they should also be filled. It is used in computer graphics, image processing, and many other applications where it is necessary to fill closed areas with a specific color.

## Brief history and development

The flood fill algorithm has been around since the early days of computer graphics. It was first used in the 1960s in computer graphics software to fill polygons with colors. Since then, it has been used in many other applications such as image processing, computer games, and engineering design.

## Purpose and usage of the Algorithm

The purpose of the flood fill algorithm is to fill a closed area with a particular color. This is useful in many applications such as image processing, where it is often necessary to fill certain areas of an image with a specific color. The algorithm is also used in computer games, where it can be used to fill certain areas of a game map with different colors to distinguish different regions.

## Key concepts and principles

The key concept behind the flood fill algorithm is recursion. The algorithm starts at a given point (seed) and then checks the neighboring pixels to determine whether they should also be filled. This process is then repeated for each neighboring pixel until all the pixels that should be filled have been filled.

The algorithm uses a stack to keep track of the pixels that need to be filled. Initially, the seed pixel is pushed onto the stack, and then the algorithm starts to pop pixels off the stack and fill them with the desired color. Each time a pixel is filled, its neighboring pixels are checked to see if they should also be filled. If they should, they are pushed onto the stack, which ensures that they will be filled later.

## Pseudocode and implementation details

The following pseudocode describes the flood fill algorithm:

```
floodFill(x, y, fillColor, targetColor)
if the color of the pixel at (x, y) is not equal to targetColor
return
if the color of the pixel at (x, y) is equal to fillColor
return
set the color of the pixel at (x, y) to fillColor
floodFill(x + 1, y, fillColor, targetColor)
floodFill(x - 1, y, fillColor, targetColor)
floodFill(x, y + 1, fillColor, targetColor)
floodFill(x, y - 1, fillColor, targetColor)
```

This pseudocode assumes that the image is represented as a two-dimensional array. The x and y parameters specify the coordinates of the pixel that is being filled. The `fillColor`

parameter specifies the color that is used to fill the pixel, and the `targetColor`

parameter specifies the color that should be replaced.

The implementation of the flood fill algorithm can vary depending on the programming language and the application. In some cases, it may be necessary to use a queue instead of a stack to ensure that the algorithm fills pixels in a particular order. Additionally, there are many optimization techniques that can be used to improve the performance of the algorithm, such as memoization and multi-threading.

## Examples and use cases

The flood fill algorithm is used in many different applications, including:

- Image processing: The flood fill algorithm is used to fill closed regions of an image with a specific color. This is useful in applications such as photo editing software, where it may be necessary to change the color of certain areas of an image.
- Computer games: The flood fill algorithm is used to fill certain areas of a game map with different colors to distinguish different regions. This is useful in games such as strategy games, where it is important to know which areas are controlled by which players.
- Engineering design: The flood fill algorithm is used in engineering applications to fill closed regions of a design with different colors to indicate different materials or properties. This is useful in applications such as finite element analysis, where it is necessary to know the properties of different regions of a design.

## Advantages and disadvantages

Some advantages of the flood fill algorithm include:

- Simplicity: The algorithm is relatively simple to implement and can be used in many different applications.
- Efficiency: The algorithm has a time complexity of O(n), where n is the number of pixels in the image. This makes it a relatively fast algorithm, even for large images.
- Flexibility: The algorithm can be adapted to work with different data structures and can be optimized for specific applications.

Some disadvantages of the flood fill algorithm include:

- Recursion depth: The algorithm can cause a stack overflow if the recursion depth is too deep. This can be avoided by using an iterative approach or optimizing the algorithm.
- Performance: The performance of the algorithm can be affected by the size and complexity of the image being processed. This can be addressed by using optimization techniques such as memoization and multi-threading.

## Related algorithms or variations

There are many variations of the flood fill algorithm, including:

- Boundary fill: The boundary fill algorithm is a variation of the flood fill algorithm that fills an area between two boundaries. It is commonly used in computer graphics applications.
- Seed fill: The seed fill algorithm is a variation of the flood fill algorithm that fills an area around a given seed point. It is used in computer graphics and image processing applications.
- Scanline fill: The scanline fill algorithm is a variation of the flood fill algorithm that fills an area by scanning the image line by line. It is commonly used in computer graphics applications.