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Dynamic Programming

Introduction

Assembly line scheduling

Assembly line scheduling

Assembly line scheduling

Optimal Substructure

Recursive solution

Assembly line scheduling

Computing the fastest time

Computing the fastest time

Constructing the fastest way

Motivation

• We often want to compare the DNA of two or

more organisms.

• Expressed as a string over the set {A, C, G, T}

• S1=ACCGGTA………..• S1=ACCGGTA………..

• S2=ACCGCTA…………

• How similar are these two strands?

• How long is the longest-common-

subsequence?

Longest common subsequence

Optimal Substructure

Big Idea: The LCS of two sequences contains within it

an LCS of the prefixes of the two sequences.

Recursive formulation

Example

Compute the length of the Optimal

solution

Tables computed by LCS-Length

Constructing the LCS