The Art of Computer Programming, Volume 3: Sorting and Searching, Second Edition by Donald E. Knuth

Author:Donald E. Knuth [Knuth, Donald E.]
Language: eng
Format: epub, pdf
Publisher: Addison-Wesley Professional
Published: 1998-11-05T23:00:00+00:00

Fig. 5. A comparison tree that corresponds to binary search when N = 16.

When N is 16, the first comparison made by the algorithm is K : K8; this is represented by the root node in the figure. Then if K < K8, the algorithm follows the left subtree, comparing K to K4; similarly if K > K8, the right subtree is used. An unsuccessful search will lead to one of the external square nodes numbered through ; for example, we reach node if and only if K6 < K < K7.

The binary tree corresponding to a binary search on N records can be constructed as follows: If N = 0, the tree is simply . Otherwise the root node is

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