Title: | Mathematics at DEC |
Moderator: | RUSURE::EDP |
Created: | Mon Feb 03 1986 |
Last Modified: | Fri Jun 06 1997 |
Last Successful Update: | Fri Jun 06 1997 |
Number of topics: | 2083 |
Total number of notes: | 14613 |
Newsgroups: net.puzzle,net.math Path: decwrl!decvax!genrad!wjh12!talcott!gjk Subject: Questions thrice about binary trees. Posted: Sat Nov 17 13:22:33 1984 Example: There are five binary trees that have three nodes. They are: x - x - x - nil x - x -nil x -nil x -nil x - x - nil | | | | | | | | | nil nil nil nil x -nil x - x -nil x -nil x nil | | | | | \ nil nil nil x -nil nil nil | nil Easy question: How many binary trees are there with four nodes? Harder question: How many binary trees are there with fifty nodes? (You are allowed to use a computer.) Yet harder question: If B(n) is the number of binary trees with n nodes, what is log(B(10,000,000)) to the nearest integer? (Use of a computer is highly recommended.) Note: Consulting a book on combinatorics is considered cheating.
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184.1 | HARE::STAN | Fri Nov 23 1984 14:56 | 21 | ||
Newsgroups: net.puzzle,net.math Path: decwrl!decvax!genrad!mit-eddie!godot!harvard!seismo!brl-tgr!ron Subject: Re: Questions thrice about binary trees. (SPOILER) Posted: Tue Nov 20 12:25:14 1984 > Harder question: How many binary trees are there with fifty nodes? (You are > allowed to use a computer.) > > Yet harder question: If B(n) is the number of binary trees with n nodes, > what is log(B(10,000,000)) to the nearest integer? (Use of a computer is > highly recommended.) > > Note: Consulting a book on combinatorics is considered cheating. B(50) = 1978261657756160653623774456 I cheated, but Macsyma helps. If my hasty calculations are correct. O(log(B(n)) = O(n*log(n)) | |||||
184.2 | old one | HERON::BUCHANAN | The was not found. | Mon Mar 15 1993 14:08 | 31 |