Dymanic programming

Local vs Global consideration

We are able to make local observations and choices, but it is hard to see the global consequences.

Sometimes a local initial sacrifice can globally lead to a better overall solution.

recursive backtracking always has the basic structure as 8-queen problem

Optimal substructure

optimal substructure means :

every optimal solution to a problem contains optimal solutions to subproblems

same as brute force algorithm, but there may be an exponential numbers of paths.

how would you iterate through all paths?

sometimes we can exploit the structure to speed up the algorithm.

a greedy algorithm prunes off all branches except the one that looks best.

memoization

remember the solutions for the sub-instances so that if ever it needs to be solved again, the answer can be used.

exponential redoing work...waste time

The dynamic programming reverses the recursive backtracking algorithm, one is up-down, and one is down-up.