## Path Lengths of Binary Search Trees |

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### Contents

Definitions | 8 |

Section U Huffmans Algorithm and TC Algorithm | 23 |

Section 5 Problems in Which the Optimum Tree is Almost | 29 |

4 other sections not shown

### Common terms and phrases

_ 2q algorithm 5-2 alphabetical order Binary Search Trees binary tree canonical minimum cost circular node combine completely extended tree construct a binary construct an optimum construction sequence denoted entry external path length Given n terminal Hence Huffman's algorithm internal circular internal nodes interval of internal interval of nodes interval of terminal Knapsack problems left to right lemma is clearly level q maximum path length minimum cost tree minimum external path minimum weighted path nal nodes nodes with weights number appearing number of internal number of nodes number of terminal obtained OO OO OO optimum tree optimum value order from left problem 8.3 Proof Q.E.D. Lemma right subtree root satisfies second table shown in Figure Step sum of weights T-C algorithm Theorem tree is equal tree that solves tree to problem tree with minimum uniform tree University of Wisconsin weighted path length weights of terminal whole tree zeroth level