中国数学建模-编程交流-动态规划算法_3(Chinese mathematical modeling programming exchange dynamic programming algorithm _3).doc
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中国数学建模-编程交流-动态规划算法_3(Chinese mathematical modeling programming exchange dynamic programming algorithm _3)
Chinese mathematical modeling programming exchange dynamic programming algorithm
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* topic: dynamic programming algorithms
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Dynamic programming and network flow -- dynamic programming is easy to design and easy to implement
Since the relation between graphs is complex and disorder, it is difficult to present phase features (except for special graphs, such as multi segment Graphs - see example 1), so dynamic programming is not used in graph theory. But there is a class diagram, and its point is ordered, that is, acyclic directed graphs.
In directed acyclic graphs, we can sort the points by topological ordering so that they exhibit ordered features, thus dividing the phases. The algorithm for finding the shortest path in directed acyclic graphs has shown a simple idea of dynamic programming. See the examples below.
[case 16] single source shortest path problem
Known routes and costs from A to J, as shown above, seek minimum cost routes from A to J.
Problem analysis and solution:
This problem is not obvious stages, no specific order between the points (please note with a different example), at least not in accordance with the steps needed to determine the sequence from A to D, such as a shortcut for 4, but only 3 in A-C-D, the better. It seems that the loop can not be implemented in the graph. Not really. Consider the optimal policy from A to J, and each part is also optimal (which can b
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