Understanding the Problem
The Flood Fill algorithm is like using the paint bucket tool in an image editor. Given a 2D image (represented as a matrix), a starting pixel (row, col), and a new color, the goal is to change the color of the starting pixel and all its connected pixels (horizontally and vertically) that have the same original color.
We need to ensure we do not affect diagonally adjacent pixels, and we must avoid visiting out-of-bound positions or repeatedly coloring the same pixel.
Step-by-Step Solution with Example
Step 1: Understand the input and what must change
Suppose the input image is:
[
[1, 1, 1],
[1, 1, 0],
[1, 0, 1]
]
The starting pixel is at position (1, 1), and the new color is 2. The original color at that pixel is 1. So we must flood all connected 1’s from that position and change them to 2.
Step 2: Decide the traversal approach
We can use either DFS (Depth-First Search) or BFS (Breadth-First Search). DFS can be implemented recursively, whereas BFS uses a queue. In either approach, we keep visiting neighbors in four directions: up, down, left, and right.
Step 3: Base condition check
If the color of the starting pixel is already the new color, we return the image as is. This avoids unnecessary work or infinite recursion.
Step 4: Start the traversal and coloring
Using DFS, we visit the starting pixel and recursively move to its neighbors that share the same color. We color each visited pixel with the new color before moving deeper.
Step 5: Watch the bounds and avoid reprocessing
For every neighbor, we ensure it's within image bounds and hasn’t already been colored. This prevents out-of-bounds errors or visiting the same node again and again.
Step 6: Final result after flood fill
After applying flood fill, the image becomes:
[
[2, 2, 2],
[2, 2, 0],
[2, 0, 1]
]
All connected 1’s starting from position (1, 1) have been changed to 2.
Edge Cases
Edge Case 1: Starting pixel already has the new color
If the color at the start is already equal to the new color, no change should be done. This is to avoid infinite recursion or redundant operations.
Edge Case 2: Empty image
If the image is empty or has no pixels, the function should return it as is without error.
Edge Case 3: Boundary and corner starts
Starting from edges or corners should be handled correctly. This means extra care in checking if neighbors go out of bounds.
Edge Case 4: Large connected region
If a large portion of the image is connected and needs coloring, recursion could cause stack overflow. In such cases, BFS is preferred for safety.
Finally
The flood fill algorithm is a classic graph traversal problem. It can be solved using either DFS or BFS. The key to solving it efficiently lies in careful boundary checks, preventing re-coloring, and handling base conditions properly.
This problem builds a strong understanding of how grid-based traversal works, and introduces concepts like visited tracking, direction arrays, and recursion/iteration trade-offs.
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