How to Solve Find the Safest Path in a Grid Leetcode Problem - Interview Coder Guide
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How to Solve Find the Safest Path in a Grid Problem

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Medium#2914
LeetCode Problem

Find the Safest Path in a Grid

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)...

ArrayBinary SearchBreadth-First Search+3 more

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Problem Breakdown

Understanding the Find the Safest Path in a Grid Problem

Let's break down this LeetCode problem and understand what makes it challenging in interview settings.

Problem Statement

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.

MediumProblem #2914
LeetCode

Find the Safest Path in a Grid

Related Topics
ArrayBinary SearchBreadth-First SearchUnion FindHeap (Priority Queue)Matrix
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Examples

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.

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