Package g2801_2900.s2812_find_the_safest_path_in_a_grid

Class Solution

java.lang.Object
g2801_2900.s2812_find_the_safest_path_in_a_grid.Solution
public class Solution extends java.lang.Object
2812 - Find the Safest Path in a Grid.

Medium

You are given a 0-indexed 2D matrix grid of size n x n, where (r, c) represents:

  • A cell containing a thief if grid[r][c] = 1
  • An empty cell if grid[r][c] = 0

You are initially positioned at cell (0, 0). In one move, you can move to any adjacent cell in the grid, including cells containing thieves.

The safeness factor of a path on the grid is defined as the minimum manhattan distance from any cell in the path to any thief in the grid.

Return the maximum safeness factor of all paths leading to cell (n - 1, n - 1).

An adjacent cell of cell (r, c), is one of the cells (r, c + 1), (r, c - 1), (r + 1, c) and (r - 1, c) if it exists.

The Manhattan distance between two cells (a, b) and (x, y) is equal to |a - x| + |b - y|, where |val| denotes the absolute value of val.

Example 1:

Input: grid = [[1,0,0],[0,0,0],[0,0,1]]

Output: 0

Explanation: All paths from (0, 0) to (n - 1, n - 1) go through the thieves in cells (0, 0) and (n - 1, n - 1).

Example 2:

Input: grid = [[0,0,1],[0,0,0],[0,0,0]]

Output: 2

Explanation:

The path depicted in the picture above has a safeness factor of 2 since:

  • The closest cell of the path to the thief at cell (0, 2) is cell (0, 0).

The distance between them is | 0 - 0 | + | 0 - 2 | = 2.

It can be shown that there are no other paths with a higher safeness factor.

Example 3:

Input: grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]]

Output: 2

Explanation:

The path depicted in the picture above has a safeness factor of 2 since:

  • The closest cell of the path to the thief at cell (0, 3) is cell (1, 2).

The distance between them is | 0 - 1 | + | 3 - 2 | = 2.

  • The closest cell of the path to the thief at cell (3, 0) is cell (3, 2).

The distance between them is | 3 - 3 | + | 0 - 2 | = 2.

It can be shown that there are no other paths with a higher safeness factor.

Constraints:

  • 1 <= grid.length == n <= 400
  • grid[i].length == n
  • grid[i][j] is either 0 or 1.
  • There is at least one thief in the grid.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maximumSafenessFactor(java.util.List<java.util.List<java.lang.Integer>> grid)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maximumSafenessFactor

      public int maximumSafenessFactor(java.util.List<java.util.List<java.lang.Integer>> grid)