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COMP 250
Lecture 20
tree traversal
- Oct. 25/26, 2017
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tree traversal Oct. 25/26, 2017 1 2 Tree Traversal How to visit - - PowerPoint PPT Presentation
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 2 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
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Tree Traversal
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How to visit (enumerate, iterate through, traverse… ) all the nodes
- f a tree ?
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depthfirst (root){ // “preorder” if (root is not empty){ visit root for each child of root depthfirst( child ) } }
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depthfirst (root){ // “preorder” if (root is not empty){ visit root for each child of root depthfirst( child ) } }
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depthfirst (root){ // “preorder” if (root is not empty){ visit root for each child of root depthfirst( child ) } }
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depthfirst (root){ // “preorder” if (root is not empty){ visit root for each child of root depthfirst( child ) } }
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Preorder Traversal
e.g. Printing a directory (visit = print)
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Documents (directory) Music (directory) Eminem (directory) Lose Yourself (file) Raffi (directory) Shake My Sillies Out (file) Baby Beluga (file) Videos (directory) : (file) Work (directory) COMP250 (directory) : Research (directory) :
My Documents
Music Videos Work Raffi Eminem
COMP 250 Lose Yourself Baby Beluga Shake my sillies out
Research
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“Visit” implies that you do something at that node. Analogy: you aren’t visiting London UK if you just fly through Heathrow.
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depthfirst (root){ // “postorder” if (root is not empty){ for each child of root depthfirst( child ) visit root } }
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Q: Which node is visited first?
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depthfirst (root){ // “postorder” if (root is not empty){ for each child of root depthfirst( child ) visit root } }
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depthfirst (root){ // “postorder” if (root is not empty){ for each child of root depthfirst( child ) visit root } }
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depthfirst (root){ // “postorder” if (root is not empty){ for each child of root depthfirst( child ) visit root } }
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depthfirst (root){ // “postorder” if (root is not empty){ for each child of root depthfirst( child ) visit root } }
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height(v){
if (v is a leaf) return 0 else{ h = 0 for each child w of v h = max(h, height(w)) return 1 + h } }
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Example 1 postorder: recall last lecture
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visit = return value of height
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Example 2 Postorder: What is the total number of bytes in all files in a directory?
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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 } }
By ‘visit’ here, we mean determining the number of bytes for a node, e.g. If we were to store ‘sum’ at the node.
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a
b g h k c d j i e f NOTE: Same call sequence occurs for preorder vs postorder. Letter order corresponds to depthfirst() call order
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b g h k c d j i e f
Call stack for depthfirst()
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
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a
b g h k c d j i e f
Call stack for depthfirst()
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
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a
b g h k c d j i e f
Call stack for depthfirst()
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
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b g h k c d j i e f
Call stack for depthfirst()
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
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Tree traversal
Recursive
- depth first (pre- versus post-order)
Non-Recursive
- using a stack
- using a queue
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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 } }
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treeTraversalUsingStack(root){ initialize empty stack s s.push(root) while s is not empty { cur = s.pop() visit cur } }
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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) } }
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What is the order of nodes visited ?
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i 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 _ 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) } }
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a
b g h k c d j i e f
recursive abcdefghijk non-recursive (stack) ahkjigbdfec
Stack based method is depth first, but visits children from right to left
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Pre- or post order?
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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) visit cur } } Moving the visit does not make it post order. Why not?
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treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } } 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) } }
What if we use a queue instead?
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a
b c d i e f h g j k
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Queue state at start of the while loop
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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a
b c d i e f h g j k
a b c d
Queue state at start of the while loop
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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a
b c d i e f h g j k
a b c d c d e f
Queue state at start of the while loop
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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a
b c d i e f h g j k
a b c d c d e f d e f
Queue state at start of the while loop
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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a
b c d i e f h g j k
a b c d c d e f d e f e f g h i
Queue state at start of the while loop
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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b c d i e f h g j k
a b c d c d e f d e f e f g h i f g h i g h i j k h i j k i j k j k k
treeTraversalUsingQueue(root){ initialize empty queue q q.enqueue(root) while q is not empty { cur = q.dequeue() visit cur for each child of cur q.enqueue(child) } }
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breadth first traversal
a
b c d i e f h g j k
for each level i visit all nodes at level i
- rder visited: abcdefghijk
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Implementation Details Recall: ‘first child, next sibling’
class TreeNode<T>{ T element; TreeNode<T> firstChild; TreeNode<T> nextSibling; : : } class Tree<T>{ TreeNode<T> root; : : }
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