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Lecture 11

# MATH 26507 Lecture 11: Discrete Mat1 Premium

3 Pages
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Winter 2016

Department
Faculty of Applied Science & Technology
Course Code
MATH 26507
Professor
Graves
Lecture
11

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Discrete Math-In Class Exercise
Find the path of min length from X to Y using the breadth first-search algorithm. Show
all steps required to determine shortest path.
Initial set of visited vertices: L = nullset, or 0(strikethrough), u=X(initial vertex),
length(u)=0
vertices adjacent to X are A, B so L={A,B}, each with length 1
remove A from set L, so u=A
vertices adjacent to A that are not in L are B,C
L={B,C} so u=B
vertices adjacent to B that are not in L are C,D
L={C,D} so u=C
vertices adjacent to C that are not in L are D,E
L={D,E} so u=D
vertices adjacent to D that are not in L are E,F
L={E,F} so u=E
vertices adjacent to E that are not in L are F,Y
L={F,Y} and Y is the element of L
The shortest path from X to Y is X->B->D->E->Y
Each time we cross a vertex then we add 1, so 1, 2, 3, 4
The length of the shortest path is 4.
in dykstra's algorithm, "parent" means how we got there
cost to get to a is 0 because we are starting there
set u to vertex with lowest cost
remove u from the set, which becomes {b,c,d,e,z}-refer to example 1.1 from textbook
Exercise:
Find the shortest path from Seattle to Miami using Dijkstraâ€™s
algorithm.
Set of vertices, S={Se,LA,De,Ch,Da,NY,Mi}
vtx Se LA De Ch Da NY Mi
parent Nil Nil Nil Nil Nil Nil Nil
cost 0 Inf Inf Inf Inf Inf inf
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Description
Discrete Math-In Class Exercise Find the path of min length from X to Y using the breadth first-search algorithm. Show all steps required to determine shortest path. Initial set of visited vertices: L = nullset, or 0(strikethrough), u=X(initial vertex), length(u)=0 vertices adjacent to X are A, B so L={A,B}, each with length 1 remove A from set L, so u=A vertices adjacent to A that are not in L are B,C L={B,C} so u=B vertices adjacent to B that are not in L are C,D L={C,D} so u=C vertices adjacent to C that are not in L are D,E L={D,E} so u=D vertices adjacent to D that are not in L are E,F L={E,F} so u=E vertices adjacent to E that are not in L are F,Y L={F,Y} and Y is the element of L The shortest path from X to Y is X->B->D->E->Y Each time we cross a vertex then we add 1, so 1, 2, 3, 4 The length of the shortest path is 4. in dykstra's algorithm, "parent" means how we got there cost to get to a is 0 because we are starting there set u to vertex with lowest cost remove u from the set, which becomes {b,c,d,e,z}-refer to example 1.1 from textbook Exercise: Find the shortest path from Seattle to Miami using Dijkstraâ€™s algorithm. Set of vertices, S={Se,LA,De,Ch,Da,NY,Mi} vtx Se LA De Ch Da NY Mi parent Nil Nil Nil Nil Nil Nil Nil cost 0 Inf Inf Inf Inf Inf inf First step: remove the first vtx, Se, and update table with edges adjacent to Se S={LA,De,Ch,Da,NY,Mi} vtx Se LA De Ch Da NY Mi parent Nil Se
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