Preprocess the board to count queens in each row, column, and both diagonal directions, then for each query point sum the counts from the four lines intersecting at that point, subtracting duplicates if the point itself has a queen. Use hash maps or arrays to store counts for O(1) lookup per query.
Pro tip: Clarify upfront whether queens can attack through other queens (they can) and whether a queen on the query point counts as attacking itself (usually no). This shows attention to edge cases and avoids incorrect assumptions.
Confirm the attack rules, whether multiple queens can occupy the same cell, and if a queen on the query point should be counted. Ask about input size constraints to guide complexity choices.
Create data structures to count queens per row, column, and both diagonals. For diagonals, use keys like (row - col) and (row + col) to identify each diagonal uniquely.
Iterate through the list of queens once, incrementing the corresponding row, column, and diagonal counters. This takes O(Q) time where Q is the number of queens.
For each query point (r, c), sum the counts from its row, column, and two diagonals. If a queen is present at (r, c), subtract 1 to avoid counting it as attacking itself (if required).
State that preprocessing is O(Q) and each query is O(1), giving overall O(Q + K) time and O(N) space for the counters, which is optimal.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the board as a grid and for each queen, cast rays in all 8 directions until hitting a rock or the board edge. Use a precomputed structure like a sorted list of rocks per row/column/diagonal to quickly find the first blocker, then mark cells before the blocker as attacked. This yields O(Q * (R + C)) time with O(R + C) space, where Q is number of queens and R, C are board dimensions.
Pro tip: Mention that you can precompute the nearest rock in each direction for every cell using dynamic programming or binary search, turning the per-queen ray casting into O(1) lookups per direction. This shows you think about scalability and trade-offs between preprocessing time and query time.
Confirm the board size, number of queens, number of rocks, and whether multiple queens can attack the same cell. Ask if rocks can be placed on queens or if queens can be placed on rocks.
Decide on a data structure: a 2D grid for the board, plus sets or sorted lists for rock positions per row, column, and diagonal. This allows O(log n) or O(1) lookup of the nearest rock.
For each row, column, and diagonal, store the indices of rocks in sorted order. Optionally, precompute for each cell the nearest rock in each of the 8 directions using DP.
For each queen, iterate in 8 directions. At each step, check if the next cell is a rock; if so, stop. Otherwise, mark the cell as attacked and continue. Use the precomputed structures to jump directly to the first rock.
Discuss time and space complexity. If many queries, consider precomputing attack maps for all possible queen positions or using bitsets for faster marking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.