Answered: Algorithm: Weighted Interval Scheduling…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Algorithm: Weighted Interval Scheduling & Dynamic Programming (Knapsack, Edit Distance)

Give an algorithm in pseudocode that will produce the minimal-cost sequence of edit operations for strings u and v from the array C computed by following algorithm (in picture). Give proofs of correctness and running time for your algorithm.

(Given 2 strings u = a1..am and v = b1..bn, find edit distance d(u,v)

1. procedure DISTANCE(u = a1 ·..am, V= b1 · . - bn,d)
2. C[0, 0] +0
3.
for i from 1 to m do
C[i, 0] + d(ai, e) + C[i – 1,0]
for j from 1 to n do
C[0, j] + d(e,b;) + C[0, j – 1]
4.
5.
6.
7.
for i from 1 to m do
for j from 1 to n do
C[i, j] - min{d(a;, b;) + C[i – 1, j – 1], d(a;, e) + C[i – 1,j], d(ɛ, b;) + C[i, j – 1]}
return C[m, n]
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