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**Unformatted text preview: **tree with the root r . Each T i is called a subtree of T , and each r i is a child of r , and r is a parent of r i . A binary tree is a rooted tree of which each vertex has no more than 2 children. A full binary tree is a binary tree of which each vertex has either 0 or 2 children. The height h ( T ) of a rooted tree T is 1. 0 if T consists of a single vertex; February 15 Recursive structures, Page 4 13.3 Rooted trees 2. max { h ( T i ) : i = 1 ...n } + 1 if T 1 ...T n are subtrees of v . Fact. If T is a binary tree with n vertices, then n ≤ 2 h ( T )+1-1. February 15 Recursive structures, Page 5 13.4 Lower bound for sorting Theorem. Any sorting algorithm based on pair-wise comparisons must compare ≥ n log 2 n-cn times, for some constant c > 0 to sort n numbers. February 15 Recursive structures, Page 6...

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- Winter '07
- YaoyunShi
- Graph Theory, Recursion, Golden ratio