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N-Queens Problem

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

Write a Java program to solve the N-Queens puzzle. The N-Queens puzzle is the problem of placing N chess queens on an N×N chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal.

Return all distinct solutions to the N-Queens puzzle as a list of lists. Each solution contains a distinct board configuration of the N-Queens placement, where 'Q' indicates a queen and '.' indicates an empty space.

Example 1
    
  
  • Input: n = 4
    • 
  
  • Output: [
 [".Q..",
  "...Q",
  "Q...",
  "..Q."],
 
 ["..Q.",
  "Q...",
  "...Q",
  ".Q.."]
]
    • 
  
  • Explanation: 
    
    Step 1: For a 4×4 board, we need to place 4 queens.
    
    Step 2: In the first solution, queens are placed at positions (0,1), (1,3), (2,0), and (3,2).
    
    Step 3: In the second solution, queens are placed at positions (0,2), (1,0), (2,3), and (3,1).
    
    Step 4: Both solutions ensure no two queens threaten each other.
  
    •
Example 2
    
  
  • Input: n = 1
    • 
  
  • Output: [["Q"]]
    • 
  
  • Explanation: 
    
    Step 1: For a 1×1 board, there is only one place to put the queen.
    
    Step 2: The only solution is to place a queen at position (0,0).
  
    •
Constraints
    
  
  • 1 <= n <= 9
    • 
  
  • Each solution must contain n queens on an n×n board
    • 
  
  • Time Complexity: O(N!), where N is the number of queens
    • 
  
  • Space Complexity: O(N^2)
    •
Backtracking PwCZomato
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Hint
Solution

Solution Hints

    
  
  • Use backtracking to explore all possible placements.
    • 
  
  • Start placing queens row by row, trying each column in a row.
    • 
  
  • Before placing a queen, check if the position is under attack by any previously placed queens.
    • 
  
  • To check if a position is safe, verify no queens exist in the same column, diagonal, or anti-diagonal.
    • 
  
  • Use arrays or sets to track occupied columns and diagonals.
    • 
  
  • If you reach the last row successfully, you've found a valid solution. Add it to the result.
    • 
  
  • After exploring all possibilities with a queen at a position, backtrack and try the next position.
    •

Steps to solve by this approach:

 Step 1: Initialize an empty n×n chessboard filled with '.' characters.

 Step 2: Create sets to track occupied columns and diagonals.

 Step 3: Start backtracking from the first row (row 0).

 Step 4: For each column in the current row, check if placing a queen is safe.

 Step 5: If safe, place the queen, mark the column and diagonals as occupied, and move to the next row.

 Step 6: If all queens are placed (reached row n), add the current board configuration to results.

 Step 7: After exploring all possibilities with a queen at the current position, backtrack by removing the queen and its constraints from the tracking sets.

Submitted Code :