CS350 CH06 Non Binary Trees
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Transcript of CS350 CH06 Non Binary Trees
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Chapter 06 Non-Binary Trees
Chaminade University of Honolulu
Department of Computer Science
Text by Clifford ShafferModified by Dr. Martins
CS350-Data Structures
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General Trees
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General Tree Node
// General tree node ADTtemplate class GTNode {public:GTNode(const Elem&); // Constructor
~GTNode(); // DestructorElem value(); // Return valuebool isLeaf(); // TRUE if is a leafGTNode* parent(); // Return parentGTNode* leftmost_child(); // First childGTNode* right_sibling(); // Right siblingvoid setValue(Elem&); // Set valuevoid insert_first(GTNode* n);void insert_next(GTNode* n);void remove_first(); // Remove first childvoid remove_next(); // Remove sibling
};
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General Tree Traversal
template void GenTree::printhelp(GTNode* subroot) {
if (subroot->isLeaf()) cout
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Equivalence Class Problem
The parent pointer representation is good foranswering:
Are two elements in the same tree?
// Return TRUE if nodes in different treesbool Gentree::differ(int a, int b) {int root1 = FIND(a); // Find root for aint root2 = FIND(b); // Find root for breturn root1 != root2; // Compare roots
}
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Union/Find
void Gentree::UNION(int a, int b) {int root1 = FIND(a); // Find root for aint root2 = FIND(b); // Find root for bif (root1 != root2) array[root2] = root1;
}int Gentree::FIND(int curr) const {while (array[curr]!=ROOT) curr = array[curr];return curr; // At root
}
Want to keep the depth small.Weighted union rule: Join the tree with fewer nodes
to the tree with more nodes.
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Equiv Class Processing (1)
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Equiv Class Processing (2)
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Path Compression
int Gentree::FIND(int curr) const {if (array[curr] == ROOT) return curr;return array[curr] = FIND(array[curr]);
}
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Lists of Children
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Leftmost Child/Right Sibling (1)
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Leftmost Child/Right Sibling (2)
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Linked Implementations (1)
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Linked Implementations (2)
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Sequential Implementations (1)
List node values in the order they would be visitedby a preorder traversal.
Saves space, but allows only sequential access.
Need to retain tree structure for reconstruction.
Example: For binary trees, us a symbol to marknull links.
AB/D//CEG///FH//I//
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Sequential Implementations (2)
Example: For full binary trees, mark nodesas leaf or internal.
AB/DCEG/FHI
Example: For general trees, mark the end ofeach subtree.
RAC)D)E))BF)))
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Converting to a Binary Tree
Left child/right sibling representationessentially stores a binary tree.
Use this process to convert any general treeto a binary tree.
A forest is a collection of one or more
general trees.
