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Problem solution · Java

The Maze III

The Maze III: a Java solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
41 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For The Maze III, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 41 lines of Java from the credited upstream file 499.java.
  • The implementation visibly relies on sequence storage.
  • 1 loop block detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeThe Maze III · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public String findShortestWay(int[][] maze, int[] ball, int[] hole) {    dfs(maze, ball[0], ball[1], hole, 0, 0, 0, "");    return ans;  }   private String ans = "impossible";  private int minSteps = Integer.MAX_VALUE;   private void dfs(int[][] maze, int i, int j, int[] hole, int dx, int dy, int steps,                   final String path) {    if (steps >= minSteps)      return;     if (dx != 0 || dy != 0) { // Both are zeros for the initial ball position.      while (i + dx >= 0 && i + dx < maze.length && j + dy >= 0 && j + dy < maze[0].length &&             maze[i + dx][j + dy] != 1) {        i += dx;        j += dy;        ++steps;        if (i == hole[0] && j == hole[1] && steps < minSteps) {          minSteps = steps;          ans = path;        }      }    }     if (maze[i][j] == 0 || steps + 2 < maze[i][j]) {      maze[i][j] = steps + 2; // +2 because maze[i][j] == 0 || 1.      if (dx == 0)        dfs(maze, i, j, hole, 1, 0, steps, path + "d");      if (dy == 0)        dfs(maze, i, j, hole, 0, -1, steps, path + "l");      if (dy == 0)        dfs(maze, i, j, hole, 0, 1, steps, path + "r");      if (dx == 0)        dfs(maze, i, j, hole, -1, 0, steps, path + "u");    }  }}

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