Flood Fill
Author: Darren Yao
Contributors: Kevin Sheng, George Pong
Finding connected components in a graph represented by a grid.
Prerequisites
Resources
Resources | ||||
---|---|---|---|---|
IUSACO | module is based off this | |||
CP2 | code + example |
Introduction
Flood fill is an algorithm that identifies and labels the connected component that a particular cell belongs to in a multidimensional array.
For example, suppose that we want to split the following grid into components of connected cells with the same number.
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
Let's start the flood fill from the top-left cell. The color scheme will be red for the node currently being processed, blue for nodes already visited, and uncolored for nodes not yet visited.
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
2 | 2 | 1 |
2 | 1 | 2 |
2 | 2 | 1 |
As opposed to an explicit graph where the edges are given, a grid is an implicit graph. This means that the neighbors are just the nodes directly adjacent in the four cardinal directions.
Usually, grids given in problems will be by , so the first line of the input contains the numbers and . In this example, we will use a two-dimensional integer array to store the grid, but depending on the problem, a two-dimensional character array or a two-dimensional boolean array may be more appropriate. Then, there are rows, each with numbers containing the contents of each square in the grid. Example input might look like the following (varies between problems):
3 4 1 1 2 1 2 3 2 1 1 3 3 3
And we’ll want to input the grid as follows:
#include <iostream>using namespace std;const int MAX_N = 1000;int grid[MAX_N][MAX_N];int row_num;int col_num;
Implementation
When doing flood fill, we will maintain an array of booleans to keep track of which squares have been visited, and a global variable to maintain the size of the current component we are visiting. Make sure to store the grid, the visited array, dimensions, and the current size variable globally.
This means that we want to recursively call the search function for the squares above, below, and to the left and right of our current square. Due to its recursive nature, floodfill can be thought of as a modified version of DFS. The algorithm to find the size of a connected component in a grid using flood fill is as follows (we’ll also maintain a 2D visited array).
The code below shows the global/static variables we need to maintain while doing flood fill and the flood fill algorithm itself:
const int MAX_N = 1000;int grid[MAX_N][MAX_N]; // the grid itselfint row_num;int col_num;bool visited[MAX_N][MAX_N]; // keeps track of which nodes have been visitedint curr_size = 0; // reset to 0 each time we start a new componentvoid floodfill(int r, int c, int color) {if ((r < 0 || r >= row_num || c < 0 || c >= col_num) // if out of bounds
Example - Counting Rooms
Focus Problem – try your best to solve this problem before continuing!
Implementation
Warning!
Recursive implementations of flood fill sometimes lead to
- Stack overflow if you didn't include the appropriate compiler options for adjusting the stack size
- Memory limit exceeded if you run the recursive implementation on a really big grid (i.e., running the above code on a grid may exceed 256 MB)
- Non-recursive implementations generally use less memory than recursive ones.
A non-recursive implementation of flood fill adds adjacent nodes to a stack or queue, similar to BFS, and is usually implemented as follows:
#include <iostream>#include <stack>#include <string>using namespace std;const int MAX_N = 2500;const int R_CHANGE[]{0, 1, 0, -1};const int C_CHANGE[]{1, 0, -1, 0};
Problems
Status | Source | Problem Name | Difficulty | Tags | |
---|---|---|---|---|---|
Silver | Easy | Show TagsFlood Fill | |||
CF | Easy | Show TagsFlood Fill | |||
Old Silver | Easy | Show TagsBinary Search, Flood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Normal | Show TagsFlood Fill | |||
Silver | Hard | Show TagsFlood Fill | |||
Silver | Hard | Show TagsFlood Fill | |||
Silver | Hard | Show TagsFlood Fill |
Module Progress:
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