Robot Straight-Line Reachable Cells on a 2D Grid with Blockers (8 Directions)

Problem You are given a 2D grid (like a chessboard) with dimensions width × height, using coordinates: 0 ≤ x < width 0 ≤ y < height A robot starts at (x, y). The robot may move in any of 8 directions (N, S, E, W, NE, NW, SE, SW), but once it chooses a direction it must move in a straight line without turning. Some cells are blocked by obstacles given as a list blockers of coordinates. When moving in a direction, the robot: must stay within the grid; cannot pass through a blocker; if it encounters a blocker in that direction, all cells beyond it in that direction are unreachable; can reach every cell from the start up to the boundary or the cell right before the first blocker. Return a list of all reachable coordinates (x', y') across all 8 directions (order does not matter). Input width: integer height: integer x, y: integers, start coordinate blockers: list of (bx, by) coordinates Output list (or set) of all reachable coordinates Constraints 1 ≤ width, height ≤ 1e5 0 ≤ x < width, 0 ≤ y < height 0 ≤ |blockers| ≤ 2e5 blocker coordinates are within the grid and do not include (x, y) Example Input: width = 7, height = 4 start (x, y) = (3, 2) blockers = [(2, 1)] Output: all cells reachable from (3,2) along the 8 straight-line directions until the boundary or the first blocker (exclusive). Example Input 7 4 3 2 1 2 1 Output (order may vary) (4,2) (5,2) (6,2) (2,2) (1,2) (0,2) (3,3) (3,1) (3,0) (4,3) (4,1) (5,0) (2,3) (2,1 is blocked so not included) (1,0)