Graphs

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Graphs
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Types of Records

• One link For stack and queue.
• Two links For double ended queue.
• Many links

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Order is important
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Searching in a Graph

• A Generic algorithm
• Let G(V,E) be the graph.
• Let D be a data structure (well later see which
  one).

For unmarked vertex v VISIT(v) end
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VISIT(v)

• D INSERT(v)
• While D?Ø do
• x REMOVE(D)
• visit and mark x
• for all unmarked w adjacent to x do
• D INSERT(w)
• end
• end

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Depth-First Search

• D is LIFO
• D PUSH(v)
• While D?Ø do
• x POP(D)
• visit and mark x
• for all unmarked w adjacent to x do
• D PUSH(w)
• end
• end

A
B
C
E
F
D
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Breadth-First Search

• D is FIFO
• D ENQUEUE(v)
• While D?Ø do
• x DEQUEUE(D)
• visit and mark x
• for all unmarked w adjacent to x do
• D ENQUEUE(w)
• end
• end

A
B
C
E
F
D
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???? ????????

• ????? ?? ??????????? ??? ???? ?????? ???
• ???? ???? ??????? ???? ???? ??? ??????
• ?? ???????? ????? ???? ???? ???? ????? ?????.

????? 1
??????? 1
????? 2
??????? 2
???? ??????
???? ??????
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Algorithm
Topological-Sort() Call DFS to
compute finish time for each vertex Insert vertex
finished into the beginning of linked list Return
the linked list of vertices ???? ???
?????? ????? ???? O(VE).
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Example
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Example