Traversals

1
Traversals

• A systematic method to visit all nodes in a tree
• Binary tree traversals
• Pre-order root, left, right
• In-order left, root, right
• Post-order left, right, root
• General graph traversals (searches)
• Depth-first search
• Breadth-first search

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Inorder(tree t)

• if t nil
• return
• inorder(t.left)
• visit(t) // e.g., print it
• inorder(t.right)

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Inorder (Infix)

• 1 2 3 5 6 7 8 9 10
• (a BST will always work well with in-order
  traversal)

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Pre-order (Prefix)

• 5 2 1 3 8 6 7 10 9

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Post-order (Postfix)

• 1 3 2 7 6 9 10 8 5

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Post-order

• 1 3 6 10 -

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Depth-first search (DFS)????? ?????))

• DFS Search one subtree completely before other
• Pre-order traversal is an example of a DFS
• Visit root, left subtree (all the way), visit
  right subtree
• We can do it in other order
• Visit root, right subtree, left subtree

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Depth-first search (DFS)

• DFS visit all descendents before siblings

5 2 1 3 8 6 7 10 9
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DFS(tree t)

• q ? new stack
• push(q, t)
• while (not empty(q))
• curr ? pop(q)
• visit curr // e.g., print curr.datum
• push(q, curr.left)
• push(q, curr.right)
• This version for binary trees only!

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Breadth-first search (BFS)(????? ?????)

• BFS visit all siblings before their descendents

5 2 8 1 3 6 10 7 9
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BFS(tree t)

• q ? new queue
• enqueue(q, t)
• while (not empty(q))
• curr ? dequeue(q)
• visit curr // e.g., print curr.datum
• enqueue(q, curr.left)
• enqueue(q, curr.right)
• This version for binary trees only!

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DFS(tree t)

• q ? new stack
• push(q, t)
• while (not empty(q))
• curr ? pop(q)
• visit curr // e.g., print curr.datum
• push(q, curr.left)
• push(q, curr.right)
• This version for binary trees only!

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DFS(tree t)

• Void Graphdfs (Vertex v)
• v.visted true
• for each w adjacent to v
• if (!w.visited)
• dfs(w)
• This version for any type of trees (graph)

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Graphs vs. Trees

• Graphs dont have any root
• Graphs can be directed or undirected
• Trees only grow down (upside-down)
• (Why do trees grow upside down for Computer
  scientists???)
• Graphs can have cycles, trees cant (why?)

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DFS Example on Graph
sourcevertex
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AVL (Adelson, Velskii, Landis)

• Balance the tree (not our targil)
• The left and right branches of the tree can only
• differ by one level
• Ensures log N depth (much better for searching)
• Takes log N to add or delete

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5
Not AVL Tree
3
4
1
AVL Tree
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AVL Trees

• Trees often need to be rotated when deleting or
  inserting to keep AVL balance
• Nice link on this process
• Sample AVL code