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

Number of Distinct Islands Using DFS Shape Encoding

Problem Statement

Given a 2D grid of size N x M consisting of '1's (land) and '0's (water), your task is to find the number of distinct islands. An island is a group of connected '1's (land) in 4 directions (horizontal and vertical). Two islands are considered distinct if and only if their shape (relative position of land cells) is different.

Examples

Grid Distinct Islands Description
[[1,1,0,0],[1,0,0,0],[0,0,1,1],[0,0,0,1]]
2
Two unique island shapes
[[1,1,0],[1,1,0],[0,0,0]]
1
Only one island shape
[[0,0],[0,0]]
0 No land present
[[1]]
1
Single land cell
[[1,0,1],[0,0,0],[1,0,1]]
1
Even though there are four islands, all the four islands have same shape. Therefore, number of uniquely shaped islands is 1.
[[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,0,0]]
3
Three distinct island shapes: L-shape, vertical, and single
[[1,1,0,0],[1,0,0,1],[0,0,0,1],[1,1,1,0],[1,0,0,0]]
3
Three island shapes: top-left block, vertical line, and bottom L-shape

Visualization Player

Solution

Understanding the Problem

We are given a 2D grid consisting of 0s and 1s. Here, '1' represents land, and '0' represents water. An island is a group of connected 1s in the grid, where connections are allowed only in four directions—up, down, left, and right.

Our goal is to count how many distinct island shapes exist. Two islands are considered the same if they have the same shape when shifted to the same origin. That means rotation and flipping do not count; only translation (shifting) is allowed when comparing shapes.

Step-by-Step Solution with Example

step 1: Traverse the grid to find unvisited land cells

We start scanning the grid from the top-left corner. When we encounter a cell with value 1 that hasn't been visited yet, it means we've found the start of a new island.

step 2: Perform DFS to explore the full island

From the current cell, we perform a Depth-First Search (DFS) in all four directions. For each direction we move, we add a corresponding character to a path string to encode the shape. For example, 'U' for up, 'D' for down, 'L' for left, 'R' for right.

step 3: Add backtracking information to avoid false matches

Every time we finish a recursive DFS call and go back to the previous cell, we add a special symbol, such as 'B' for backtrack. This helps us capture the exact structure of the island. For instance, a line and a zig-zag of the same length would produce different signatures.

step 4: Store the encoded shape in a set

Once the DFS is complete for an island, we add the shape signature to a set. This ensures we only keep unique shapes.

step 5: Count the number of unique shapes

At the end of the traversal, the number of distinct islands is simply the size of the set that stores the shape signatures.

Example


Input:
[
  [1,1,0,0,0],
  [1,0,0,0,0],
  [0,0,0,1,1],
  [0,0,0,1,1]
]

We find two islands:
- The first one on the top-left forms a shape with path: "DRB"
- The second one on the bottom-right has the same shape: "DRB"

Even though they are in different locations, their shapes are the same, so the output is: 1

Edge Cases

  • Empty Grid: If the grid is empty, we return 0 since there are no islands.
  • All Water: If every cell is 0, there’s no land to explore. Output is 0.
  • All Land: If every cell is 1, there’s one big island. So, output is 1.
  • Same Size but Different Shapes: If two islands have the same number of cells but different layouts, they are still considered distinct.
  • Multiple Identical Shapes: If multiple islands have the same shape, they’re only counted once because we use a set to store unique patterns.

Finally

This problem helps build a strong foundation in graph traversal and pattern recognition. The key idea is not just visiting islands, but encoding their traversal paths uniquely to compare their shapes. Using DFS with shape encoding and backtracking gives us a reliable way to distinguish islands by structure.

Always consider boundary conditions and edge cases before finalizing your solution. Sets are a powerful way to track distinct patterns without worrying about duplicates.

Algorithm Steps

  1. Initialize an empty set shapes to store unique island signatures.
  2. Iterate through each cell in the grid.
  3. When a land cell ('1') is found that is not visited:
    1. Start a DFS from that cell, marking visited cells.
    2. Track the shape of the island by recording moves relative to the start cell.
    3. Store the shape string in the shapes set.
  4. Return the number of elements in shapes.

Code

JavaScript
function numDistinctIslands(grid) {
  const rows = grid.length, cols = grid[0].length;
  const visited = Array.from({ length: rows }, () => Array(cols).fill(false));
  const shapes = new Set();

  const directions = [
    [0, 1, 'R'], // right
    [0, -1, 'L'], // left
    [1, 0, 'D'], // down
    [-1, 0, 'U'] // up
  ];

  function dfs(r, c, path, dir) {
    if (r < 0 || c < 0 || r >= rows || c >= cols || visited[r][c] || grid[r][c] === 0) return;
    visited[r][c] = true;
    path.push(dir);
    for (const [dr, dc, d] of directions) {
      dfs(r + dr, c + dc, path, d);
    }
    path.push('B'); // Backtrack
  }

  for (let r = 0; r < rows; r++) {
    for (let c = 0; c < cols; c++) {
      if (grid[r][c] === 1 && !visited[r][c]) {
        const path = [];
        dfs(r, c, path, 'S'); // Start
        shapes.add(path.join(''));
      }
    }
  }

  return shapes.size;
}

// Example Usage
console.log("Distinct Islands:", numDistinctIslands([
  [1,1,0,0],
  [1,0,0,0],
  [0,0,1,1],
  [0,0,0,1]
])); // Output: 2

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(m * n)Even in the best case, we must visit every cell to check if it's land or water and track unique shapes.
Average CaseO(m * n)Each cell is visited once, and DFS explores each connected component, tracking the shape.
Worst CaseO(m * n)In the worst case (e.g., entire grid is land), DFS explores all cells, and all must be encoded and compared.

Space Complexity

O(m * n)

Explanation: In the worst case, all cells are part of different islands, requiring separate shape strings and a visited matrix of the same size.


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