Compare to Greedy and Divide_and_conquer
Greedy.
Build up a solution incrementally, myopically optimizing some local criterion.
Divide-and-conquer.
Break up a problem into sub-problem into sub-problems, solve each sub-problem independently, and combine solutions to sub-problems to form solution to original problem.
Dynamic programming.
Break up a problem into a series of overlapping sub-problems, and build up solutions to larger and larger sub-problem.
Dynamic programming hallmark
Optimal substructure
An optimal solution to a problem(instance) contains optimal solutions to subproblems.
Overlapping subproblems
A recursive solution contains a “small” number of distinct subproblems repeated many times.
Example:Weighted Interval Scheduling
Memoization是常常和动态规划搭配使用的解决重复计算问题的放法，其原理是自底向上计算值，并储存起来，需要用到的时候直接取存储的值，而不是像递归那样重新计算。
下面就是我说的自底向上的例子：
