I knew the problem but froze a bit on the 'print all solutions' part because I'd only ever coded the 'count solutions' version before.
Use backtracking to place queens row by row, ensuring no two queens attack each other by checking columns and diagonals. At each row, try all columns, and if safe, place a queen and recurse; when a solution is found, record it. Prune invalid placements early to reduce search space.
Pro tip: Mention that you can optimize safety checks using sets or boolean arrays for columns and diagonals, reducing time complexity from O(N!) to O(N!) with lower constant factors. Also, note that for N=1 there is one solution, and for N=2,3 there are none, showing awareness of edge cases.
Confirm the problem: place N queens on an N×N board so that no two attack each other. Clarify output format (e.g., list of board configurations) and constraints (e.g., N ≤ 9 for typical interviews).
Explain that backtracking is ideal because it incrementally builds candidates and abandons a candidate as soon as it determines it cannot lead to a valid solution.
Represent the board with a 1D array where index is row and value is column. Use sets or boolean arrays to track occupied columns, diagonals (row+col), and anti-diagonals (row-col) for O(1) safety checks.
Write a recursive function that places a queen in the current row, iterating over all columns. If safe, mark the column and diagonals, recurse to the next row, then unmark (backtrack). When row equals N, record the solution.
Discuss time complexity O(N!) and space O(N). Mention edge cases: N=1 (one solution), N=2,3 (no solutions), and that the number of solutions grows rapidly.
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