Minimum Cost to Make a Valid Path in a Grid — Algorithm Visualization & Coding Challenge
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Understanding Minimum Cost to Make a Valid Path in a Grid
Detailed explanation and reference materialsProblem Overview
Problem Summary: Minimum Cost to Make a Valid Path in a Grid
You are given a grid with m x n dimensions, where each cell contains an arrow pointing to one of four directions:
- Right (1): Move to the cell on the right.
- Left (2): Move to the cell on the left.
- Down (3): Move to the cell below.
- Up (4): Move to the cell above.
- You start at the top-left corner
(0, 0)and aim to reach the bottom-right corner(m-1, n-1)by following the arrows. - If necessary, you can modify the arrow in a cell at a cost of
1. - The goal is to calculate the minimum cost required to create at least one valid path from the start to the end of the grid.
Examples:
-
Input:
[[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]
Output:
3Explanation: Modify arrows in 3 cells to create a valid path from
(0, 0)to(3, 3). -
Input:
[[1,1,3],[3,2,2],[1,1,4]]Output:
0
Explanation: A valid path already exists without any modifications. -
Input:
[[1,2],[4,3]]
Output:1
Explanation: Modify one cell's arrow to create a valid path.
Constraints:
1 <= m, n <= 100- Each cell contains a value from
1to4.
Starter Code
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