1. Dynamic Programming 2 Neil Tang 4/22/2010
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Course Survey
Please complete the course survey at:
CS223 Advanced Data Structures and Algorithms

3. CS223 Advanced Data Structures and Algorithms
Class Overview
Basic idea
Matrix multiplication
Ordering matrix multiplication
CS223 Advanced Data Structures and Algorithms

4. 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

5. Matrix Multiplication
C=AB.
If the size of A is wy, then the size of B must be yz, i.e., the number of columns of A must be equal to the number of rows of B.
The size of C is wz and
CS223 Advanced Data Structures and Algorithms

6. CS223 Advanced Data Structures and Algorithms
An Example
Compute ABCD with |A|=5010, |B| = 1040, |C|=4030 and |D|=305.
(((AB)C)D) involves 20,000+60,000+7,500 =87,500 multiplications.
(A((BC)D)) involves 12,000+1,500+2,500 =16,000 multiplications.
(A(B(CD))) involves 6,000+2,000+2,500 =10,500 multiplications.
CS223 Advanced Data Structures and Algorithms

7. Ordering Matrix Multiplications
Consider AleftAleft+1…Ai…Aright
mleft,right =
min leftiright {mleft,i + mi+1,right+cleft-1cicright}
CS223 Advanced Data Structures and Algorithms

8. CS223 Advanced Data Structures and Algorithms
Another Example
right
left
right
left
CS223 Advanced Data Structures and Algorithms

9. Ordering Matrix Multiplications
The time complexity is O(n3)
CS223 Advanced Data Structures and Algorithms