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Sliding Puzzle Problem

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 15

You are given an n x n board containing n² - 1 tiles and one empty space. The tiles are numbered from 1 to n² - 1. A move consists of sliding a tile horizontally or vertically into the empty space.

Example 1
    

  • Input: board = [[1,2,3],[4,0,5],[7,8,6]]
    • 

  • Output: 4
    • 

  • Explanation: 
      

    • Step 1: The initial state is:
1 2 3
4 0 5
7 8 6
      • 

    • Step 2: The goal state is:
1 2 3
4 5 6
7 8 0
      • 

    • Step 3: We can solve this in 4 moves:
  - Move 5 down to get [[1,2,3],[4,8,0],[7,5,6]]
  - Move 8 right to get [[1,2,3],[4,0,8],[7,5,6]]
  - Move 4 down to get [[1,2,3],[0,4,8],[7,5,6]]
  - Move 1 right to get [[0,1,3],[2,4,8],[7,5,6]]
      • 

    • Step 4: Therefore, the minimum number of moves required is 4.
      • 

    

    •
Example 2
    

  • Input: board = [[1,2,3],[4,5,0]]
    • 

  • Output: 1
    • 

  • Explanation: 
      

    • Step 1: The initial state is:
1 2 3
4 5 0
      • 

    • Step 2: The goal state is:
1 2 3
4 5 0
      • 

    • Step 3: Since the initial state is already the goal state, the answer is 0.
      • 

    

    •
Constraints
    

  • 2 ≤ n ≤ 4
    • 

  • board.length == n
    • 

  • board[i].length == n
    • 

  • 0 ≤ board[i][j] ≤ n² - 1
    • 

  • Each number in board appears exactly once.
    • 

  • Time Complexity: O(n! * n²), where n is the board size.
    • 

  • Space Complexity: O(n! * n²), where n is the board size.
    •
Hash MapAlgorithmsDeloitteGoldman Sachs
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Hint
Solution

Solution Hints

    
    
  • Use breadth-first search (BFS) to find the shortest path to the solution.
    • 
    
  • Represent the board state as a string for easy comparison and hashing.
    • 
    
  • Generate all possible next states by moving the empty space in the four directions.
    • 
    
  • Keep track of visited states to avoid cycles.
    • 
    
  • Check if the puzzle is solvable before attempting to solve it.
    •

Steps to solve by this approach:

 Step 1: Convert the 2D board to a string representation for easier handling and hashing

 Step 2: Define the goal state based on the board dimensions

 Step 3: Use breadth-first search (BFS) to explore all possible moves from the initial state

 Step 4: For each state, find the position of the empty space (0) and try moving it in four directions

 Step 5: Track visited states to avoid cycles and return the minimum number of moves when the goal is reached

Submitted Code :