Post on 11-Jan-2016
description
Alyce BradyAlyce Brady
CS 470: Data StructuresCS 470: Data Structures
CS 510: Computer Algorithms CS 510: Computer Algorithms
Post-order Traversal:Post-order Traversal:
Left Child - Right Child - RootLeft Child - Right Child - Root
Depth-First Search
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
HH
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
HH
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
HH
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H IH I
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H IH I
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I DH I D
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I DH I D
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I DH I D
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I DH I D
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D JH I D J
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D JH I D J
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D JH I D J
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J KH I D J K
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J KH I D J K
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K EH I D J K E
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K EH I D J K E
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E BH I D J K E B
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E BH I D J K E B
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E BH I D J K E B
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E BH I D J K E B
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E BH I D J K E B
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B LH I D J K E B L
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B LH I D J K E B L
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B LH I D J K E B L
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L MH I D J K E B L M
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L MH I D J K E B L M
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M FH I D J K E B L M F
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M FH I D J K E B L M F
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M FH I D J K E B L M F
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M FH I D J K E B L M F
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F NH I D J K E B L M F N
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F NH I D J K E B L M F N
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F NH I D J K E B L M F N
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N OH I D J K E B L M F N O
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N OH I D J K E B L M F N O
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N O GH I D J K E B L M F N O G
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N O GH I D J K E B L M F N O G
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N O G CH I D J K E B L M F N O G C
A
B C
D E F G
H I J K L M N O
Post-order Traversal:Left Child - Right Child - Root
H I D J K E B L M F N O G CH I D J K E B L M F N O G C
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
H I D J K E B L M F N O G C AH I D J K E B L M F N O G C A
Post-order Traversal:Left Child - Right Child - Root
A
B C
D E F G
H I J K L M N O
H I D J K E B L M F N O G C AH I D J K E B L M F N O G C A
Pseudo-Code forPost-order Traversal
post-traversepost-traverse
post-traverse left subtreepost-traverse left subtree
post-traverse right subtreepost-traverse right subtree
visit current nodevisit current node e.g., print valuee.g., print value
Time and Space Complexityfor Depth-First Search Algs.
Time ComplexityTime Complexity– Visit each node three timesVisit each node three times O(n)O(n)
first arrivalfirst arrival return from left childreturn from left child return from right childreturn from right child
Space ComplexitySpace Complexity– Stack to handle recursionStack to handle recursion
Stack length = depth of treeStack length = depth of tree best case: lg nbest case: lg n worst case: nworst case: n O(n)O(n)
Time and Space Complexityfor Depth-First Search Algs.