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2343. Count Unguarded Cells In The Grid

Array Matrix Simulation

Problem - Count Unguarded Cells In The Grid

Medium

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

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class Solution:
    def countUnguarded(self, m: int, n: int, guards: List[List[int]], walls: List[List[int]]) -> int:
        directions = (-1, 0, 1, 0, -1)
        dp = [[0] * n for _ in range(m)]
        for i, j in guards:
            dp[i][j] = 2
        for i, j in walls:
            dp[i][j] = 2
        for i, j in guards:
            for val1, val2 in pairwise(directions):
                x, y = i, j
                while 0 <= x + val1 < m and 0 <= y + val2 < n and dp[x + val1][y + val2] < 2:
                    x, y = x + val1, y + val2
                    dp[x][y] = 1
        return sum(val == 0 for row in dp for val in row)

Submission Stats:

  • Runtime: 363 ms (62.25%)
  • Memory: 39.1 MB (79.08%)