Available Captures for Rook - Solution & Explanation

Problem Overview: You’re given an 8x8 chessboard represented as a matrix. A white rook 'R' can move horizontally or vertically until it hits another piece. Pawns 'p' can be captured, while bishops 'B' block the rook’s path. The task is to count how many pawns the rook can capture in the four cardinal directions.

Approach 1: Direction-Based Iteration (O(n) time, O(1) space)

First locate the rook’s position by scanning the board. Once found, simulate the rook’s movement in the four directions: up, down, left, and right. For each direction, iterate step-by-step through the board. If you encounter a bishop 'B', the path is blocked and you stop exploring that direction. If you encounter a pawn 'p', increment the capture count and stop because the rook captures only the first piece in that direction.

This approach relies on simple iteration over a matrix and direct simulation of chess movement rules. The key insight is that the rook only cares about the first non-empty square in each direction. Because there are only four directions and at most 8 cells per direction, the traversal is extremely efficient. Time complexity is O(n) where n represents the board dimension, and space complexity remains O(1) since no extra structures are needed.

Approach 2: Multi-Directional Traversal with Early Exit (O(n) time, O(1) space)

This variation treats each direction as an independent traversal starting from the rook. Instead of scanning the board multiple times, you locate the rook once and then expand outward in four directions using directional vectors like (-1,0), (1,0), (0,-1), and (0,1). Each step checks the current square and exits immediately when a blocking bishop or capturable pawn appears.

The early-exit behavior reduces unnecessary checks and keeps the logic clean. The implementation closely resembles typical array or simulation patterns used in grid problems. Every direction stops as soon as a decision is made, ensuring no redundant traversal. The complexity remains O(n) time and O(1) space, but the structure is easier to generalize to larger boards or similar movement problems.

Recommended for interviews: Direction-based iteration is what interviewers expect. It directly models rook movement and shows you understand grid traversal and early stopping conditions. A brute-force board scan shows basic understanding, but directional traversal demonstrates stronger control over matrix simulation patterns.