lect notes-DynamicProgramming

# lect notes-DynamicProgramming - Outline Chapter 1 1.1 1.2...

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Outline • Chapter 1: – 1.1, 1.2, 1.3, 1.4, 1.7, 1.8 • Chapter 3: Dynamic Programming • Chapter 5: Binary Tree • Chapter 6: Selected sections • Chapter 2

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Interval Scheduling Problem • Given n intervals of v i and lengths w i . Find the subset of compatible intervals of maximum total value.
Interval Scheduling Problem: Example 0 1 2 3 4 5 6 7 8 3 •(s 1 , f 1 ) = (0, 2) •(s 2 , f 2 ) = (1, 3) •(s 3 , f 3 ) = (0, 4) •(s 4 , f 4 ) = (4, 7) •(s 5 , f 5 ) = (6, 7) Interval 1 Interval 2 Interval 3 Interval 4 Interval 5 Starting and finishing points of the interval 2 2 5 4

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Interval Scheduling Problem: Ideas • Sort intervals by f i • Define F(n) to be the maximum return • F(n) either – Includes (s n , f n ) or – Does not include (s n , f n ) • p(n) subset ~ F(n) – p(1) = 0 – p(2) = 0 – p(5) = 3

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Multiterminal Shortest Paths d ik min(d ik , d ij + d jk ) for j = 1, 2, …, n; forall i,k j p ik = p ij if d ik > d ij + d jk same if d ik d ij + d jk 1 2 3 4 7 12 3 4
Multiterminal Shortest Paths 1 2 3 4 7 12 3 4 1 2 3 7 3 4 4 j=1 5 1 234 1 1 1 1 2 3 4 1 2 3 4 1 234 1134 1 2 3

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## This note was uploaded on 02/19/2008 for the course CSE 202 taught by Professor Hu during the Fall '06 term at UCSD.

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lect notes-DynamicProgramming - Outline Chapter 1 1.1 1.2...

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