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] = [row_i, col_i] and walls[j] = [row_j, col_j] represent the positions of the i^th guard and j^th 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 <= row_i, row_j < m
0 <= col_i, col_j < n
All the positions in guards and walls are unique.

Solution

count-unguarded-cells-in-the-grid.py

class Solution:
    def countUnguarded(self, rows: int, cols: int, guards: List[List[int]], walls: List[List[int]]) -> int:
        grid = [[1] * cols for _ in range(rows)]

        for x, y in walls:
            grid[x][y] = -1

        def goLeft(x, y):
            dy = y - 1
            while dy >= 0 and grid[x][dy] != 2 and grid[x][dy] != -1:
                grid[x][dy] = 2
                dy -= 1

        def goRight(x, y):
            dy = y + 1
            while dy < cols and grid[x][dy] != 3 and grid[x][dy] != -1:
                grid[x][dy] = 3
                dy += 1

        def goTop(x, y):
            dx = x - 1
            while dx >= 0 and grid[dx][y] != 4 and grid[dx][y] != -1:
                grid[dx][y] = 4
                dx -= 1

        def goBottom(x, y):
            dx = x + 1
            while dx < rows and grid[dx][y] != 5 and grid[dx][y] != -1:
                grid[dx][y] = 5
                dx += 1

        guards.sort(key = lambda x : (-x[1], x[0]))

        for x, y in guards:
            goLeft(x, y)

        guards.sort(key = lambda x : (x[1], x[0]))

        for x, y in guards:
            goRight(x, y)

        guards.sort(key = lambda x : (-x[0], x[1]))
        for x, y in guards:
            goTop(x, y)

        guards.sort(key = lambda x : (x[0], x[1]))
        for x, y in guards:
            goBottom(x, y)

        for x, y in guards:
            grid[x][y] = -1

        res = 0

        for x in range(rows):
            for y in range(cols):
                if grid[x][y] == 1:
                    res += 1

        return res