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Notes for DP
http://www.algorithmist.com/index.php/Dynamic_Programming
To avoid calculate the same thing again and again, we save the results and return them later. This is commonly known as memorization (记忆）.
There are two types of solution: Bottom Up & Up Bottom.
In general, DP generates all enumerations（枚举）, or rather, the smaller breakdown problems, leading towards the larger cases, they eventually lead towards the final enumeration of size n.
Usage:
S1. check if DP is applicable to the problem
S2. recognize the recursive relationshop, whether it is straightforward or hidden, have a pretty good idea of the relationship
Hallmarks:
#1 Optimal substructure:
an optimal solution to a problem(instance) contains optimal solution to subproblems.
#2 Overlapping subproblem:
a recursive solution contains a small number of distinct subproblems repeated many times
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