Problem of the Day

Problem of the Day • Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another?

Problem of the Day • Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another? • Take the 2nd glass & pour it into the 5th glass!

CSC 212 – Data Structures Lecture 35:Tree Traversals

Trees • Represent hierarchical relationships • Parent-child basis of this abstract data type • Real-world example: organization chart

Traversing Linear Collections • Trees are another Collection of data • Nodes usually used to hold elements in BinaryTree • ADT uses generic type to specify type of element • Want to iterate through tree’s elements • Not required, but order obvious for linear structures • Follow ArrayList’s indices from lowest to highest • Iterator for LinkedList follows nodes

Traversing Linear Collections • Trees are another Collection of data • Nodes usually used to hold elements in BinaryTree • ADT uses generic type to specify type of element • Want to iterate through tree’s elements • Not required, but order obvious for linear structures • Follow ArrayList’s indices from lowest to highest • Iterator for LinkedList follows nodes But how do we do this for Trees?

Tree Traversals • Several different, predictable orderings • Preorder honors thy elders and treats them well

Tree Traversals • Several different, predictable orderings • Preorder honors thy elders and treats them well • This traversal will start with parent THEN do kids

Preorder Traversal AlgorithmpreOrder(tree, v) /* Process v*/ foreach(w: v.children()) preOrder(tree, w); Table of Contents Chapter 1 Appendix A Chapter 2 Section 1.1 Section 1.2 Section 2.1 Section 2.2 Section 1.2.1 Section 1.2.2 Section 1.2.3

Preorder Traversal • Visit node first, then visit its children • Normal ordering found in every chapter book • Start each section before going into contents: Table of Contents §1, §1.1,§1.2, §1.2.1, §1.2.2, §1.2.3§2, §2.1,§2.2Appendix A

Tree Traversals • Several different, predictable orderings • Postorder places children first: morals also important

Postorder Traversal • Several different, predictable orderings • Postorder places children first: morals also important • For postorder traversal do children THEN do parent

Postorder Traversal • Several different, predictable orderings • Postorder places children first:morals also important • For postorder traversal do children THEN do parent

Postorder Traversal AlgorithmpostOrder(tree, v) foreach(w : v.children()) postOrder(tree, w); /* Process v*/ Csc212/ Activities/ Midterm1.tex Projects/ Activity01.tex Activity02/ Project01.tex Project02.tex Problems.tex Solution.tex Solution02.png

Postorder Traversal • Node visits children before it is processed • Needed to compute directory’s disk space • First look at size of contentsthen the main directory • Important whenever leaves contain actual data • Visits external nodes, then works way up the tree • In this traversal, after its descendants node processed

Binary Trees • Pre- & post-order identical for binary trees • Also offer additional type of traversal • Traversals used again, so do not let this slip • Equation trees are canonical examples • Using them, the different approaches can be seen • Lets (old) Professors reminisceover HP calculators • Kind of stupid, but is actually used in programs

Inorder Traversal - • AlgorithminOrder(tree,v)if(tree.hasLeft(v))inOrder(tree,tree.left(v)) • /* Process v*/ • if (tree.hasRight(v))inOrder(tree,tree.right(v)); + / 1 * 4 2 6 3

Inorder Traversal - • Traversal visits equation in proper order: (1 + (6 * 3)) - (4 / 2) • Binary search trees use this again & again • AlgorithminOrder(tree,v)if(tree.hasLeft(v))inOrder(tree,tree.left(v)) • /* Process v*/ • if (tree.hasRight(v))inOrder(tree,tree.right(v)); + / 1 * 4 2 6 3

Problem of the Day