Minimum Cost to Make at Least One Valid Path in a Grid

arraybreadth-first searchgraph theory

Problem Statement

Given an m x n grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of grid[i][j] can be:

1 which means go to the cell to the right. (i.e go from grid[i][j] to grid[i][j + 1] )

2 which means go to the cell to the left. (i.e go from grid[i][j] to grid[i][j - 1] )

3 which means go to the lower cell. (i.e go from grid[i][j] to grid[i + 1][j] )

4 which means go to the upper cell. (i.e go from grid[i][j] to grid[i - 1][j] )

Notice that there could be some signs on the cells of the grid that point outside the grid.

You will initially start at the upper left cell (0, 0) . A valid path in the grid is a path that starts from the upper left cell (0, 0) and ends at the bottom-right cell (m - 1, n - 1) following the signs on the grid. The valid path does not have to be the shortest.

You can modify the sign on a cell with cost = 1 . You can modify the sign on a cell one time only .

Return the minimum cost to make the grid have at least one valid path .

Examples

Example 1

Input: grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]
Output: 3
You will start at point (0, 0).
The path to (3, 3) is as follows. (0, 0) --> (0, 1) --> (0, 2) --> (0, 3) change the arrow to down with cost = 1 --> (1, 3) --> (1, 2) --> (1, 1) --> (1, 0) change the arrow to down with cost = 1 --> (2, 0) --> (2, 1) --> (2, 2) --> (2, 3) change the arrow to down with cost = 1 --> (3, 3)
The total cost = 3.

Example 2

Input: grid = [[1,1,3],[3,2,2],[1,1,4]]
Output: 0
You can follow the path from (0, 0) to (2, 2).

Example 3

Input: grid = [[1,2],[4,3]]
Output: 1

Constraints

m == grid.length

n == grid[i].length

1 <= m, n <= 100

1 <= grid[i][j] <= 4

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBreadth-First Search