2257. Count Unguarded Cells in the Grid

Description

You are given two integers m and n representing a 0-indexed m x n grid. You are also given two 2D integer arrays guards and walls where guards[i] = [rowi, coli] and walls[j] = [rowj, colj] represent the positions of the ith guard and jth wall respectively.

A guard can see every cell in the four cardinal directions (north, east, south, or west) starting from their position unless obstructed by a wall or another guard. A cell is guarded if there is at least one guard that can see it.

Return the number of unoccupied cells that are not guarded.

 

Example 1:

Input: m = 4, n = 6, guards = [[0,0],[1,1],[2,3]], walls = [[0,1],[2,2],[1,4]]
Output: 7
Explanation: The guarded and unguarded cells are shown in red and green respectively in the above diagram.
There are a total of 7 unguarded cells, so we return 7.

Example 2:

Input: m = 3, n = 3, guards = [[1,1]], walls = [[0,1],[1,0],[2,1],[1,2]]
Output: 4
Explanation: The unguarded cells are shown in green in the above diagram.
There are a total of 4 unguarded cells, so we return 4.

 

Constraints:

• 1 <= m, n <= 105
• 2 <= m * n <= 105
• 1 <= guards.length, walls.length <= 5 * 104
• 2 <= guards.length + walls.length <= m * n
• guards[i].length == walls[j].length == 2
• 0 <= rowi, rowj < m
• 0 <= coli, colj < n
• All the positions in guards and walls are unique.

 

Solutions

Solution: Simulation

• Time complexity: O(mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {number} m
 * @param {number} n
 * @param {number[][]} guards
 * @param {number[][]} walls
 * @return {number}
 */
const countUnguarded = function (m, n, guards, walls) {
  const cells = Array.from({ length: m }, () => Array.from({ length: n }, () => false));
  let result = m * n - guards.length - walls.length;

  for (const [row, col] of guards) {
    cells[row][col] = 'G';
  }

  for (const [row, col] of walls) {
    cells[row][col] = 'W';
  }

  const checkGuarded = (row, col, isGuarded) => {
    const cell = cells[row][col];

    if (cell === 'G' || cell === 'W') {
      return cell === 'G';
    }
    if (isGuarded && !cell) {
      cells[row][col] = true;
      result -= 1;
    }
    return isGuarded;
  };

  for (let row = 0; row < m; row++) {
    let isGuarded = false;

    for (let col = 0; col < n; col++) {
      isGuarded = checkGuarded(row, col, isGuarded);
    }
    isGuarded = false;

    for (let col = n - 1; col >= 0; col--) {
      isGuarded = checkGuarded(row, col, isGuarded);
    }
  }

  for (let col = 0; col < n; col++) {
    let isGuarded = false;

    for (let row = 0; row < m; row++) {
      isGuarded = checkGuarded(row, col, isGuarded);
    }
    isGuarded = false;

    for (let row = m - 1; row >= 0; row--) {
      isGuarded = checkGuarded(row, col, isGuarded);
    }
  }
  return result;
};