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

Shortest Distance in a Binary Maze using BFS

Problem Statement

Given an n × m binary matrix grid where each cell can be either 0 or 1, find the shortest path between a source cell and a destination cell. You can only move to a cell with value 1 and you may move only in four directions: up, down, left, and right.

If the path between the source and destination is not possible, return -1.

Note: The source and destination cells must also be 1 to begin with, or the path is impossible.

Examples

Grid Source Destination Shortest Distance Description
[[1,1,0,1],[0,1,1,1],[1,0,0,1],[1,1,1,1]] [0,0] [3,3] 6 Moves: (0,0) → (0,1) → (1,1) → (1,2) → (1,3) → (2,3) → (3,3)
[[1,0,1],[1,1,0],[0,1,1]] [0,0] [2,2] 4 Valid path exists avoiding 0s
[[1,0,0],[0,0,0],[0,0,1]] [0,0] [2,2] -1 No valid path exists
[[1]] [0,0] [0,0] 0 Start and end are the same
[[0]] [0,0] [0,0] -1 Cell is 0; not walkable

Visualization Player

Solution

Understanding the Problem

We are given a binary maze represented as a 2D grid, where each cell contains either a 1 (walkable) or a 0 (blocked). Our goal is to find the shortest path from a given source cell to a destination cell by moving only in four directions: up, down, left, or right. The movement is allowed only through cells containing 1.

Think of each cell as a node in an unweighted graph, and the valid movements between walkable cells as edges. To find the shortest number of steps (i.e., the smallest number of edges), the most appropriate strategy is Breadth-First Search (BFS).

Step-by-Step Solution with Example

step 1: Initialize the distance grid

Create a 2D array dist of the same size as the maze, initialized with Infinity to represent that no cell has been visited yet. Set dist[source] to 0 because that’s where we start.

step 2: Initialize the BFS queue

Use a queue to keep track of cells to explore. Each item in the queue contains the current cell’s coordinates and the distance taken to reach it. Initially, enqueue the source cell with distance 0.

step 3: Process the queue

While the queue is not empty, do the following:

  • Dequeue the front cell.
  • Explore its four neighbors (up, down, left, right).
  • For each neighbor, check if:
    • It lies within the bounds of the maze.
    • It is a walkable cell (value 1).
    • It has not been visited via a shorter path before.
  • If all checks pass, update the neighbor’s distance and enqueue it.

step 4: Check for destination

If we reach the destination cell, we immediately return the current distance. This is guaranteed to be the shortest path because BFS explores all possible paths in increasing order of length.

step 5: If queue is exhausted

If the queue becomes empty without reaching the destination, return -1 to indicate that the destination is unreachable.

Example


Input:
maze = [
  [1, 0, 1, 1],
  [1, 1, 1, 0],
  [0, 1, 0, 1],
  [1, 1, 1, 1]
]
source = (0, 0)
destination = (3, 3)

Output: 7

Explanation:
The shortest path is:
(0,0) → (1,0) → (1,1) → (1,2) → (2,1) → (3,1) → (3,2) → (3,3)
which takes 7 steps.

Edge Cases

  • Source or destination is blocked: If either the source or destination cell contains 0, return -1 immediately.
  • Source equals destination: If the source and destination are the same, return 0 because we are already there.
  • Maze with all zeros: The function should handle this by returning -1.
  • Disconnected components: Even if the maze is mostly walkable, ensure that there is a valid path from source to destination.

Finally

Breadth-First Search is ideal for this problem as it finds the shortest path in unweighted graphs like our binary maze. By using a queue and a distance array, we can ensure we explore the most efficient paths first. Always remember to check for edge cases to make your solution robust and reliable.

Algorithm Steps

  1. Check if the source or destination cell is 0. If yes, return -1.
  2. Initialize a 2D array dist with Infinity. Set the distance for the source cell to 0.
  3. Create a queue and add the source cell to it.
  4. While the queue is not empty:
    1. Pop the front cell (x, y) and its distance d.
    2. For each of the four directions (up, down, left, right):
      1. Compute new cell coordinates (nx, ny).
      2. If (nx, ny) is within bounds, has value 1, and not yet visited or has a longer distance:
        • Update dist[nx][ny] = d+1.
        • Enqueue (nx, ny, d+1).
  5. If the destination is reached, return dist[destX][destY].
  6. If the queue is empty and destination was never reached, return -1.

Code

JavaScript
function shortestPathBinaryMaze(grid, source, destination) {
  const [n, m] = [grid.length, grid[0].length];
  const [srcX, srcY] = source;
  const [destX, destY] = destination;

  if (grid[srcX][srcY] === 0 || grid[destX][destY] === 0) return -1;

  const directions = [[0,1],[1,0],[0,-1],[-1,0]];
  const dist = Array.from({ length: n }, () => Array(m).fill(Infinity));
  dist[srcX][srcY] = 0;

  const queue = [[srcX, srcY, 0]];

  while (queue.length > 0) {
    const [x, y, d] = queue.shift();

    for (const [dx, dy] of directions) {
      const [nx, ny] = [x + dx, y + dy];

      if (nx >= 0 && ny >= 0 && nx < n && ny < m && grid[nx][ny] === 1 && d + 1 < dist[nx][ny]) {
        dist[nx][ny] = d + 1;
        queue.push([nx, ny, d + 1]);
      }
    }
  }

  return dist[destX][destY] === Infinity ? -1 : dist[destX][destY];
}

const grid = [[1,1,1],[0,1,0],[1,1,1]];
console.log("Shortest Distance:", shortestPathBinaryMaze(grid, [0,0], [2,2])); // Output: 4

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