Binary TreesBinary Trees36
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Flood Fill Graph-Based Approach

Problem Statement

The Flood Fill problem is a classic image processing task. Given a 2D array image where each element represents the color of a pixel, a starting pixel coordinate (sr, sc), and a newColor, your task is to 'flood fill' the area connected to the starting pixel.

A pixel is considered 'connected' if it has the same color as the starting pixel and is connected 4-directionally (up, down, left, or right).

Replace all such connected pixels with newColor.

Examples

Image Start (sr, sc) newColor Output
[[1,1,1],[1,1,0],[1,0,1]]
[1, 1] 2 [[2,2,2],[2,2,0],[2,0,1]]
[[0,0,0],[0,1,1]]
[1, 1] 1 [[0,0,0],[0,1,1]]
[[1]]
[0, 0] 1 [[1]]
[[0,0],[0,0]]
[0, 0] 3 [[3,3],[3,3]]
[]
[0, 0] 1 []
[[1,1,2,2],[1,2,2,0],[1,1,0,0],[0,0,0,0]]
[0, 0] 9 [[9,9,2,2],[9,2,2,0],[9,9,0,0],[0,0,0,0]]
[[1,1,1,1],[1,0,0,1],[1,0,1,1],[1,1,1,1],[0,0,0,0]]
[1, 1] 5 [[1,1,1,1],[1,5,5,1],[1,5,1,1],[1,1,1,1],[0,0,0,0]]

Visualization Player

Solution

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.

Algorithm Steps

  1. Store the original color of the pixel at (sr, sc).
  2. If original color is same as newColor, return the image.
  3. Use BFS or DFS to explore from (sr, sc):
    1. Push starting pixel to the stack or queue.
    2. While the stack/queue is not empty:
      1. Pop a pixel and change its color to newColor.
      2. Push its 4-directional neighbors if they have the original color.
  4. Return the modified image.

Code

JavaScript
function floodFill(image, sr, sc, newColor) {
  const originalColor = image[sr][sc];
  if (originalColor === newColor) return image;

  const rows = image.length;
  const cols = image[0].length;
  const queue = [[sr, sc]];

  const directions = [[0, 1], [1, 0], [0, -1], [-1, 0]];
  image[sr][sc] = newColor;

  while (queue.length > 0) {
    const [r, c] = queue.shift();
    for (const [dr, dc] of directions) {
      const nr = r + dr, nc = c + dc;
      if (nr >= 0 && nr < rows && nc >= 0 && nc < cols && image[nr][nc] === originalColor) {
        image[nr][nc] = newColor;
        queue.push([nr, nc]);
      }
    }
  }
  return image;
}

console.log(floodFill([[1,1,1],[1,1,0],[1,0,1]], 1, 1, 2));

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)If the starting pixel's color is already the new color, the algorithm returns immediately without modifying the image.
Average CaseO(m × n)In most practical scenarios, a portion of the image is filled, and the algorithm visits those connected pixels once.
Worst CaseO(m × n)If the entire image consists of the same color, the algorithm may visit every pixel, making it linear in the size of the image.

Space Complexity

O(m × n)

Explanation: In the worst case, the stack or queue can hold all pixels of the image if they are all connected and need to be processed.


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