2022-02-27 03:30:01 +00:00
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= Dynamic Programming =
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Dynamic Programming is a paradigm where we systematically and efficeiently
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explore all possible solutions to a problem. Generally, problems suited to DP
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have the following properties
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1) Problem can be broken down into overlaping subproblems
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2) An optimal solution can be formed from optimal solutions to the overlapping
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subproblems derrived from the original problem.
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2022-02-27 03:45:01 +00:00
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Generally, problems requiring a DP algo ask for the optimum value (min/max), or
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the number of ways to do something *AND* future/larger descisions depend on
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earlier descisions. If they do not depend on earlier descisions, then consider
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a [[greedy_algorithm]].
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There are two ways to implement a DP algo:
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== Implimentation ==
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=== Bottom up (Tabulation) ===
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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
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algo, as there is no overhead of recursion.
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Usually implemented as iteration of the problem space
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=== Top down (Memoization) ===
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For memoization we start at the problem we would like to solve then descend
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into the lower and lower subproblems, using a system to store the results of
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our compuations as we descend. This is to ensure we do not do any unnecassy
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computations. T
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Usually implemented as recurssion
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