问题
I really have no idea how to do this using dynamic programming: Problem: I need to find the 2 largest non overlapping squares of a table For example:
5 6
R F F R R F
F F F F F F
R R F F F F
F F F F F F
F F F F F F
The numbers 5 and 6 are the number of rows and columns respectively, and “R” means reserved and “F” means free. In this case the largest square is
F F F F
F F F F
F F F F
F F F F
and the second largest (non-overlapping with the previous one) is
F F
F F
So far I have put the values into a 2D array, but do not know what to do after. Tried to reference 0-1 knapsack and LCS, but really I have no clue on what values I should put into my table.
回答1:
Well, your first task when designing a dynamic programming algorithm should be to find a recursive solution to the problem. After that is done, converting it to a dynamic programming algorithm is almost trivial ;).
Some tips that could/could not help:
A possible base case is obvious: any two 1 cell squares are always non-overlapping.
Bear in mind that the largest of the two squares can not cover the entire table (because then you wont have a second largest), so it cannot be of rows:columns size.
You should have an "score" to each solution you evaluate, to see what's the best one.This score is obviously size1 + size2, with the condition that size1 should be the maximum possible.
Good luck!!
回答2:
This is a variation of the Longest Common Substring Problem not LCS (Longest common subsequence). Picture two strings you are comparing as being sides of a rectangle with their characters as the squares. An "F" in a square would mean a match between two characters in the strings, and thus the largest square is the longest common substring.
来源：https://stackoverflow.com/questions/1719414/dynamic-programming-finding-largest-non-overlapping-squares