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Sliding Puzzle

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

You are given a 2x3 board with tiles numbered from 1 to 5 and one empty space represented by 0. The goal is to transform the board into [[1,2,3],[4,5,0]] by sliding tiles into the empty space. The board is represented as a 2D array where board[i][j] is the tile at position (i, j). Return the minimum number of moves required to solve the puzzle, or -1 if it's not solvable.

Example 1
    
  
  • Input: board = [[1,2,3],[4,0,5]]
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  • Output: 1
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  • Explanation:
    
    Step 1: The initial state is [[1,2,3],[4,0,5]].
    
    Step 2: We can slide the 5 tile into the empty space: [[1,2,3],[4,5,0]].
    
    Step 3: We have reached the target state with 1 move.
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Example 2
    
  
  • Input: board = [[4,1,2],[5,0,3]]
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  • Output: 5
    • 
  
  • Explanation:
    
    Step 1: The initial state is [[4,1,2],[5,0,3]].
    
    Step 2: Through a series of optimal moves sliding tiles into the empty space
    
    Step 3: We can reach the target state [[1,2,3],[4,5,0]] with a total of 5 moves.
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Constraints
    
  
  • board.length == 2
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  • board[i].length == 3
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  • 0 ≤ board[i][j] ≤ 5
    • 
  
  • Each value board[i][j] is unique
    • 
  
  • Time Complexity: O(6!)
    • 
  
  • Space Complexity: O(6!)
    •
ArraysAlgorithmsTech MahindraWalmart
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Hint
Solution

Solution Hints

    
  
  • Use breadth-first search (BFS) to find the shortest path from the start state to the goal state.
    • 
  
  • Represent each board state as a string for easy comparison and storing in visited set.
    • 
  
  • For each state, generate all possible next states by moving the empty space in valid directions.
    • 
  
  • Keep track of the number of moves made to reach each state.
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  • Use a visited set to avoid revisiting board configurations.
    •

Steps to solve by this approach:

 Step 1: Convert the 2D board into a 1D string representation for easier manipulation and state comparison.

 Step 2: Define the target state "123450" that represents the solved puzzle.

 Step 3: Create a mapping of all possible moves for each position where the empty space (0) can be.

 Step 4: Use BFS to explore all possible board states, starting from the initial state.

 Step 5: For each state, check if it matches the target state. If yes, return the current number of moves.

 Step 6: Generate all next possible states by swapping the empty space with adjacent positions.

 Step 7: Keep track of visited states to avoid cycles and optimize search.

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