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79. Word Search 🔗

Date: Jun 11, 2024

Tags: backtracking

Description

Given an m x n grid of characters board and a string word, return true if word exists in the grid.

The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.

Example 1:

      Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCCED"
      Output: true
      

Example 2:

      Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "SEE"
      Output: true
      

Example 3:

      Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCB"
      Output: false
      

Constraints:

  • m == board.length
  • n = board[i].length
  • 1 <= m, n <= 6
  • 1 <= word.length <= 15
  • board and word consists of only lowercase and uppercase English letters.

Follow up: Could you use search pruning to make your solution faster with a larger board?

Optimal (Backtracking)

const getValidNeighbours =
  ({ cols, rows }: { rows: number; cols: number }) =>
  ([r, c]: number[]) => {
    return r >= 0 && r < rows && c >= 0 && c < cols;
  };

function exist(board: string[][], word: string): boolean {
  const cols = board[0].length;
  const rows = board.length;

  if (cols === 1 && rows === 1 && board[0][0] === word) return true;

  const visited: boolean[][] = Array.from({ length: rows }, () => Array(cols).fill(false));

  const validNeighbours = getValidNeighbours({ cols, rows });

  function walk(r: number, c: number, subword: string): boolean {
    if (subword.length === word.length) return subword === word;
    if (board[r][c] !== word[subword.length] || visited[r][c]) return false;

    visited[r][c] = true;
    subword += board[r][c];

    const neighbours = [
      [r + 1, c],
      [r - 1, c],
      [r, c + 1],
      [r, c - 1],
    ].filter(validNeighbours);

    for (const [x, y] of neighbours) {
      if (walk(x, y, subword)) return true;
    }

    visited[r][c] = false;
    return false;
  }

  for (let i = 0; i < rows; i++) {
    for (let j = 0; j < cols; j++) {
      if (walk(i, j, '')) return true;
    }
  }

  return false;
}

export { exist };