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N-Queens Problem

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

Write a C# program to implement the SolveNQueens(int n) function that returns all distinct solutions to the N-Queens puzzle. Each solution contains a distinct board configuration of placing N queens on an N×N chessboard such that no two queens threaten each other. This means no two queens can share the same row, column, or diagonal.

Example 1
    
  
  • Input: n = 4
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  • Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
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  • Explanation: 
    
      
      
    • There are two distinct solutions to the 4-queens puzzle as shown in the output.
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Example 2
    
  
  • Input: n = 1
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  • Output: [["Q"]]
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  • Explanation: 
    
      
      
    • There is exactly one solution when n = 1.
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Constraints
    
  
  • 1 <= n <= 9
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  • Each solution must be represented as a board configuration where 'Q' indicates a queen and '.' indicates an empty space
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  • Time Complexity: O(n!)
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  • Space Complexity: O(n^2)
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RecursionBacktracking PwCTutorix
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Hint
Solution

Solution Hints

    
  
  • Use backtracking with a recursive approach
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  • Keep track of which columns, diagonals, and anti-diagonals are occupied
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  • A diagonal can be represented by (row - col), and an anti-diagonal by (row + col)
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  • Place queens one row at a time and check for conflicts
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  • Build the board representation once a valid solution is found
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Steps to solve by this approach:

 Step 1: Create a one-dimensional array to represent queen positions where the index represents the row and the value represents the column.
 Step 2: Use a backtracking approach to place queens one row at a time.
 Step 3: For each row, try placing a queen in each column and check if it's valid (doesn't conflict with previously placed queens).
 Step 4: A position is valid if no other queen is in the same column or diagonal.
 Step 5: If a valid position is found, place the queen and recursively try to solve for the next row.
 Step 6: If all queens are placed successfully (reached the nth row), add the current configuration to the result.
 Step 7: If a solution can't be found with the current configuration, backtrack by removing the queen and trying the next column.

Submitted Code :