Question 2 is the algorithm in the 2nd picture cickson] denotes the book by Jeff Erickson (available for free online at http://jeffellinois.edu/teaching/algorithms/).OPV] denotes the book by Dasgupta, Papadimitriou, and Vazirani (the required text-k).(1) Question 1: Let G be a directed graph (not necessarily acyclic) in which everyvertex v has a distinct integer weight W v]. Describe an algorithm to find thelength of the longest directed path in G whose vertex weights define a strictlyincreasing sequence. Hint: Use DFS and dynamic programming. Let T[v] bethe length of the longest directed path ending at v whose vertex weights define anincreasing sequence.(2) Question 2: 4.3 of [DPV]. Your algorithm should run in O(|V|³) time. Hint: usethe matrix representation of the graph.吕口F3000F4F5F6F7F8F9F10#$&45678ERYUDFGHJKCVNMa >B Figure 4.3 Breadth-first search.procedure bfs (G, s)Input:Graph G = (V, E), directed or undirected; vertex sE VFor all vertices u reachable from s, dist(u) is setOutput:to the distance from s to u.for all u E V:dist(u) = ∞dist(s) = 0Q = [s] (queue containing just s)while Q is not empty:u = eject(Q)for all edges (u,v) E E:if dist(v) = ∞:inject(Q,v)dist(v) = dist(u)+129吕0F3F5F6F7F8F9F10@$%&*一24679.WEYUSDGHKCVM.* COBw #

Hey there, I am writing the required solution of the above stated question.Please do find the…

Answered: S.edu/teaching/algorithms/). enotes the…

S.edu/teaching/algorithms/). enotes the book by Dasgupta, Papadimitriou, and Vazirani uestion 1: Let G be a directed graph (not necessarily acycl

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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Question

Question 2 is the algorithm in the 2nd picture

cickson] denotes the book by Jeff Erickson (available for free online at http://jeffe
llinois.edu/teaching/algorithms/).
OPV] denotes the book by Dasgupta, Papadimitriou, and Vazirani (the required text-
k).
(1) Question 1: Let G be a directed graph (not necessarily acyclic) in which every
vertex v has a distinct integer weight W v]. Describe an algorithm to find the
length of the longest directed path in G whose vertex weights define a strictly
increasing sequence. Hint: Use DFS and dynamic programming. Let T[v] be
the length of the longest directed path ending at v whose vertex weights define an
increasing sequence.
(2) Question 2: 4.3 of [DPV]. Your algorithm should run in O(|V|³) time. Hint: use
the matrix representation of the graph.
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B

Figure 4.3 Breadth-first search.
procedure bfs (G, s)
Input:
Graph G = (V, E), directed or undirected; vertex sE V
For all vertices u reachable from s, dist(u) is set
Output:
to the distance from s to u.
for all u E V:
dist(u) = ∞
dist(s) = 0
Q = [s] (queue containing just s)
while Q is not empty:
u = eject(Q)
for all edges (u,v) E E:
if dist(v) = ∞:
inject(Q,v)
dist(v) = dist(u)+1
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Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.

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