Problem · Matrix
Minimum-Weight Top-to-Bottom Grid Path
Problem statement
You are given a rectangular matrix weights. A value of -1 marks a blocked cell. Every other value is a positive traversal cost.
You may start at any unblocked cell in the top row. From an unblocked cell, you may move one cell up, down, left, or right, staying inside the matrix and never entering a blocked cell.
The problem statement continues
ProExamples
Example 1
weights = [[1,50,50,50],[1,1,1,50],[50,50,1,50]]return = 5The cheapest path is (0,0) -> (1,0) -> (1,1) -> (1,2) -> (2,2), with total cost 1 + 1 + 1 + 1 + 1 = 5. It uses more moves than the direct expensive routes.
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