1. Dynamic Programming 1 Neil Tang 4/15/2008
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Class Overview
Basic Idea
Fibonacci numbers
Recursive equation evaluation
All-pairs shortest paths
CS223 Advanced Data Structures and Algorithms

3. CS223 Advanced Data Structures and Algorithms
Basic Idea
Mathematically express the problem in the recursive form.
Solve it by a non-recursive algorithm that systematically records the answers to the subproblems in a table.
CS223 Advanced Data Structures and Algorithms

4. CS223 Advanced Data Structures and Algorithms
Fibonacci Numbers
fib(N) = fib(N-1) + fib(N-2)
CS223 Advanced Data Structures and Algorithms

5. CS223 Advanced Data Structures and Algorithms
Fibonacci Numbers
CS223 Advanced Data Structures and Algorithms

6. CS223 Advanced Data Structures and Algorithms
Fibonacci Numbers
A dynamic programming based algorithm
CS223 Advanced Data Structures and Algorithms

7. Recursive Equation Evaluation
CS223 Advanced Data Structures and Algorithms

8. Recursive Equation Evaluation
CS223 Advanced Data Structures and Algorithms

9. Recursive Equation Evaluation
A dynamic programming based algorithm
CS223 Advanced Data Structures and Algorithms

10. All-pairs Shortest Path
The all-pairs shortest path problem: Given a weighted graph G, find the shortest (minimum cost) path between every pair of nodes in G.
CS223 Advanced Data Structures and Algorithms

11. All-Pairs Shortest Path
Recursive expression for node pair (i, j)
Dk,i,j = min{Dk-1,i,j, Dk-1,i,k+Dk-1,k,j}
CS223 Advanced Data Structures and Algorithms

12. All-Pairs Shortest Path
Time Complexity: O(|V|3)
CS223 Advanced Data Structures and Algorithms