tree traversal Oct. 25/26, 2017 1 2 Tree Traversal How to visit - PowerPoint PPT Presentation

COMP 250 Lecture 20 tree traversal Oct. 25/26, 2017 1

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Tree Traversal How to visit (enumerate, iterate through, traverse… ) all the nodes of a tree ? 3

depthfirst (root){ // “ preorder ” if (root is not empty){ visit root for each child of root depthfirst( child ) 1 } } 4

depthfirst (root){ // “ preorder ” if (root is not empty){ visit root for each child of root depthfirst( child ) } 1 } 2 3 5

depthfirst (root){ // “ preorder ” if (root is not empty){ visit root for each child of root depthfirst( child ) } 1 } 2 3 4 5 6

depthfirst (root){ // “ preorder ” if (root is not empty){ visit root for each child of root depthfirst( child ) } 1 } 8 2 7 9 3 4 10 11 5 6 7

Preorder Traversal e.g. Printing a directory (visit = print) My Documents Documents (directory) Music (directory) Eminem (directory) Lose Yourself (file) Work Research Music Videos Raffi (directory) Shake My Sillies Out (file) Baby Beluga (file) Videos (directory) COMP Eminem Raffi : (file) 250 Work (directory) COMP250 (directory) : Research (directory) Shake my Baby Lose sillies out Beluga Yourself : 8

“Visit” implies that you do something at that node. Analogy: you aren’t visiting London UK if you just fly through Heathrow. 9

depthfirst (root){ // “ postorder ” if (root is not empty){ for each child of root depthfirst( child ) visit root } } Q: Which node is visited first? 10

depthfirst (root){ // “ postorder ” if (root is not empty){ for each child of root depthfirst( child ) visit root } } 1 11

depthfirst (root){ // “ postorder ” if (root is not empty){ for each child of root depthfirst( child ) visit root } } 1 2 12

depthfirst (root){ // “ postorder ” if (root is not empty){ for each child of root depthfirst( child ) visit root } } 5 1 4 2 3 13

depthfirst (root){ // “ postorder ” if (root is not empty){ for each child of root depthfirst( child ) visit root 11 } } 10 5 6 7 1 4 8 9 2 3 14

Example 1 postorder: recall last lecture height(v) { 4 if (v is a leaf) 3 2 1 return 0 else{ h = 0 1 0 0 2 1 for each child w of v h = max(h, height(w)) 0 1 0 0 0 return 1 + h } 0 0 } visit = return value of height 15

Example 2 Postorder: What is the total number of bytes in all files in a directory? 16

numBytes(root){ if root is a leaf return number of bytes at root else { sum = 0 for each child of root{ sum += numBytes(child) } return sum } } B y ‘visit’ here, we mean determining the number of bytes for a node, e.g. If we were to store ‘sum’ at the node. 17

NOTE: Same call sequence occurs for preorder vs postorder. Letter order corresponds to depthfirst() call order a h b g i c d j k e f 18

Call stack for depthfirst() a h b g i c d j k e f e f c d d d d d i j k b b b b b b b b b g h h h h h h h a a a a a a a a a a a a a a a a a a a a a 19

Call stack for depthfirst() a h b g i c d j k e f e f c d d d d d i j k b b b b b b b b b g h h h h h h h a a a a a a a a a a a a a a a a a a a a a 20

Call stack for depthfirst() a h b g i c d j k e f e f c d d d d d i j k b b b b b b b b b g h h h h h h h a a a a a a a a a a a a a a a a a a a a a 21

Call stack for depthfirst() a h b g i c d j k e f e f c d d d d d i j k b b b b b b b b b g h h h h h h h a a a a a a a a a a a a a a a a a a a a a 22

Tree traversal Recursive • depth first (pre- versus post-order) Non-Recursive • using a stack • using a queue 23

treeTraversalUsingStack(root){ initialize empty stack s s.push(root) while s is not empty { cur = s.pop() visit cur // moving ‘visit cur’ to be for each child of cur // after for loop s.push(child) // changes nothing } } 24

treeTraversalUsingStack(root){ initialize empty stack s s.push(root) while s is not empty { cur = s.pop() visit cur } } 25

treeTraversalUsingStack(root){ initialize empty stack s s.push(root) while s is not empty { cur = s.pop() visit cur for each child of cur s.push(child) } } 26

What is the order of nodes visited ? 27

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 28

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 29

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 30

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 31

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 32

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 33

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 34

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 35

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 36

treeTraversalUsingStack(root){ a initialize empty stack s s.push(root) while s is not empty { h b g cur = s.pop () visit cur i c d j k for each child of cur s.push(child) } e f } k j j j h i i i i i f g g g g g g g g g d e e e a _ b b b b b b b b b b b _ c c c c c c c _ 37

Stack based method is depth first, but visits children from right to left a h b g i c d j k e f recursive abcdefghijk non-recursive (stack) ahkjigbdfec 38

Pre- or post order? treeTraversalUsingStack(root){ initialize empty stack s s.push(root) while s is not empty { cur = s.pop () Moving the visit does visit cur not make it post order. for each child of cur Why not? s.push(child) visit cur } } 39

What if we use a queue instead? treeTraversal UsingStack (root){ treeTraversal UsingQueue (root){ initialize empty stack s initialize empty queue q s.push(root) q.enqueue(root) while s is not empty { while q is not empty { cur = s.pop() cur = q.dequeue() visit cur visit cur for each child of cur for each child of cur s.push(child) q.enqueue(child) } } } } 40

treeTraversalUsingQueue(root){ Queue state initialize empty queue q at start of the q.enqueue(root) while loop while q is not empty { cur = q.dequeue() a visit cur for each child of cur q.enqueue(child) } } a d b c e f g h i j k 41