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Deciding on Sub-Problems for Dynamic Programming

up vote 14 down vote favorite

I have used the technique of dynamic programming multiple times however today a friend asked me how I go about defining my sub-problems, I realized I had no way of providing an objective formal answer. How do you formally define a sub-problem for a problem that you would solve using dynamic programming?

2 Answers

up vote 4 down vote accept

The principle of dynamic programming is to think top-down (i.e recursively) but solve bottom up. So a good strategy for designing a DP is to formulate the problem recursively and generate sub-problems that way.

up vote 3 down vote

My experience is finding out a way to "cut down redundant enumerating with help of storing useful value already enumerated". By the way, Dynamic Programming is really popular in ICPC(International Collegiate Programming Contest. Anyone can have his own feeling about DP after practice several ICPC problems.


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Deciding on Sub-Problems for Dynamic Programming

up vote 14 down vote

I have used the technique of dynamic programming multiple times however today a friend asked me how I go about defining my sub-problems, I realized I had no way of providing an objective formal answer. How do you formally define a sub-problem for a problem that you would solve using dynamic programming?


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up vote 9 down vote

The principle of dynamic programming is to think top-down (i.e recursively) but solve bottom up. So a good strategy for designing a DP is to formulate the problem recursively and generate sub-problems that way.

edit

I claim that's the only strategy. - JeffE Mar 22 '12 at 9:35

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