Find a Word Along One Fixed Direction in a Grid

Determine whether a word appears in a letter grid along one straight direction. After choosing a starting cell and direction, keep that same direction for every subsequent letter. Do not turn, jump, wrap around, or revisit a prior cell. Implement `word_exists(board: string[], word: string) -> bool`. ### Constraints & Assumptions - The board is rectangular, with 1 through 100 rows and columns. All characters are uppercase ASCII letters. - The word has 1 through 100 uppercase letters. - This practice version permits all eight nonzero adjacent directions: horizontal, vertical, and diagonal, in either orientation. The source explicitly fixes straight-line movement but does not enumerate the permitted directions. - A one-letter word is present if any board cell contains it. - A path must remain inside the board for its entire length. - This is a straight-line word-search game, not a path that may change direction after each letter. ### Examples ```text board = ["ABC","DEF","GHI"] word = "AEI" result = true ``` ```text board = ["ABC","DEF","GHI"] word = "ABE" result = false ``` `ABE` would require turning after the second letter, which is not allowed. ```hint Choose the direction once After selecting `(dr, dc)`, the k-th letter must be at `(start_row + k*dr, start_col + k*dc)`. There is no new direction choice at later letters. ```