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Find minimum cost path in a matrix using dp?
By acash, history, 5 years ago, In English

we have to find min cost path in a mtrix from top left to bottom right.

Move allowed -> Right,left,Bottom,Up.

I know suitable approach will be using Dijkstra But can we do this using Dp because here we can move in all 4 direction ,If yes then How?

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5 years ago, # |
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is cost value always non negative?

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5 years ago, # |
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If you can move in all four directions, you have a graph with cycles and then you can't use dp.

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    5 years ago, # ^ |
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    If the cost values are non negative is it still true that we can't use dp.

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      5 years ago, # ^ |
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      Yes. Because what would dp transitions look like? There can be no cycles among them.

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    5 years ago, # ^ |
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    That's how I implemented it can it be more efficient. https://ideone.com/tvKC9r

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      5 years ago, # ^ |
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      Can anyone tell me what will be the time complexity of my solution ? I am using dijkstra on a matrix (in above soln) ?

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        5 years ago, # ^ |
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        Ffs, make a loop over adjacent cells. Don't repeat the same piece of code 4 times.

        What is the number of states (vertices of a graph)? What is the number of transitions (edges)? And finally, what is the complexity of Dijkstra?

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