vimwiki/tech/dynamic_programming.wiki

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= Dynamic Programming =
Dynamic Programming is a paradigm where we systematically and efficeiently
explore all possible solutions to a problem. Generally, problems suited to DP
have the following properties
1) Problem can be broken down into overlaping subproblems
2) An optimal solution can be formed from optimal solutions to the overlapping
subproblems derrived from the original problem.
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Generally, problems requiring a DP algo ask for the optimum value (min/max), or
the number of ways to do something *AND* future/larger descisions depend on
earlier descisions. If they do not depend on earlier descisions, then consider
a [[greedy_algorithm]].
There are two ways to implement a DP algo:
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== Implimentation ==
=== Bottom up (Tabulation) ===
For tabulation we start at the lowest sub problem and work our way up to the
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desired solution. Generally bottom up is the fastest way to implement a dp
algo, as there is no overhead of recursion.
Usually implemented as iteration of the problem space
=== Top down (Memoization) ===
For memoization we start at the problem we would like to solve then descend
into the lower and lower subproblems, using a system to store the results of
our compuations as we descend. This is to ensure we do not do any unnecassy
computations. T
Usually implemented as recurssion