Provinci summer training 2010June 17: Recursion and recursive decent parser June 24: Greedy algorithms and stable marriage July 1: Holiday July 8: Math and number theory July 15: Coordinate geometry July 22: Black rain?July 29: Graph, MST, bipartite matching Aug 5: Black rain?Aug 12: Individual contest 1Aug 19: Individual contest 2 Aug 26: Dynamic programming Sep 2: RevisionSep 9: Team formation test

Recursion

1. Do something

2. Repeat

Any algorithm that have the above format is using "recursion".

Properties: Easy to design and write Tend to be slow (because trying all possibilities)

Greedy algorithms

1. Make a choice that looks good (greedy choice)

2. Repeat if the problem is not yet solved

Easy to design and write Tend to be fast (because make only 1 greedy

choice) Finding the correct greedy choice and proving

the correctness is usually hard.

Dynamic programming

The optimal solution

easier proble

m

easier proble

m

easier proble

m

easier proble

m

easier proble

m

easier proble

m

easier proble

m

Example 1. Magic bubbles

Given a sequence of n bubbles with colors Red, Green and Blue and a table of possible transformations. Determine whether we can form a bubble with targeted color.

Dynamic programming

Solution for [1,n]

[1,1] [1,2]

[2,3] [2,4]

[1,n]

[3,4]

[2,2]

Example 2. Cutting Sticks (UVA10003)

Dynamic programming

Solution for [1,n]

[1,1]

[2,3][1,2]

[2,2]

[3,4]

[4,4][3,3]

Optimal substructures

[1,3]

Overlapping subproblems

Example 3. Matrix multiplication

Example 4. Longest common subsequence

Example 5. Edit distance

Example 6. Prize collection

Example 7. Longest increasing subsequence

Example 8. Subset sum

Example 9. Optimal binary search tree

Example 10. Knapsack problem