Graphs & Trees.

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Presentation transcript:

Graphs & Trees

Graphs Nodes connected by Edges

Directed Graphs Directed Graph : Edges are one way

Trees Trees: A trunk from the roots Divides into branches Ends in leaves

Tree Strucures Directed graph with: Single root node with no parent Edge Node

Tree Strucures Directed graph with: Single root node (no parent) Parent nodes point to 1+ child nodes

Trees… Categorizations

Trees… Brackets

Trees… HTML documents

Trees… Image recognition

Expression Tree Represents mathematical expression (15 – 1) / 7

Expression Tree

Expression Tree

Traversal Most operations involve complete traversal

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handleing may involve recursion Handle left child Handle self Handle right child Handleing may involve recursion

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString: Handle left child Handle self Handle right child

Traversal BinaryOp toString code Puts ( ) around node’s output

Traversal Most operations involve complete traversal Relative order of Left Self Right depends on job

Traversal Evaluate: Evaluate left Evaluate right Do math using left & right

Traversal Evaluate: Evaluate left Evaluate right Do math using left & right

Traversal Evaluate code