The Art of Computer Programming: Sorting and searchingFinally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually. The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e ISBN: 0321751043 |
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Page 199
... [ log2 ( m + " ) ] m ( 2 ) comparisons are required . If we set man and let no , while a is fixed , Stirling's approximation tells us that log2 ( an + n ) = n ( ( 1 + a ) 1082 ( 1 + a ) - = n ( ( 1+ a ) log2 ( 1 + a ) — a log2 a ) — log2 ...
... [ log2 ( m + " ) ] m ( 2 ) comparisons are required . If we set man and let no , while a is fixed , Stirling's approximation tells us that log2 ( an + n ) = n ( ( 1 + a ) 1082 ( 1 + a ) - = n ( ( 1+ a ) log2 ( 1 + a ) — a log2 a ) — log2 ...
Page 629
... [ log2 Σ1≤x≤m { } k ! ] and this is asymptotically n log2 m ( cf. Eq . 1.2.6–49 ) . 12. ( a ) If there are no redundant comparisons , we can arbitrarily assign an order to keys which are actually equal , when they are first compared ...
... [ log2 Σ1≤x≤m { } k ! ] and this is asymptotically n log2 m ( cf. Eq . 1.2.6–49 ) . 12. ( a ) If there are no redundant comparisons , we can arbitrarily assign an order to keys which are actually equal , when they are first compared ...
Page 630
... [ log2 t ( l ( x ) ) ] ≤ [ log2 t ( x ) ] — 1 and [ log2 t ( r ( x ) ) ] ≤ [ log2 t ( x ) ] 1. The first condition is equivalent to 2t ( l ( x ) ) t ( x ) ≤ 2log2t ( x ) t ( x ) , and the second condition is equivalent to t ( x ) — 2t ...
... [ log2 t ( l ( x ) ) ] ≤ [ log2 t ( x ) ] — 1 and [ log2 t ( r ( x ) ) ] ≤ [ log2 t ( x ) ] 1. The first condition is equivalent to 2t ( l ( x ) ) t ( x ) ≤ 2log2t ( x ) t ( x ) , and the second condition is equivalent to t ( x ) — 2t ...
Contents
Tableaux and Involutions | 48 |
Chapter 6Searching | 389 |
Answers to Exercises | 571 |
Copyright | |
2 other sections not shown
Common terms and phrases
a₁ assume asymptotic average number B-tree b₁ balanced trees binary search binary tree bubble sort buffers CACM CMPA Compare consider contains corresponding decreasing defined deletion digit digital search tree distribution elements empty ENT1 equal example exercise external nodes external path length Fibonacci Fibonacci tree formula function hash heapsort hence initial runs input integers internal sorting K₁ keys largest linear probing LINK LLINK log2 memory merge pattern minimum multiset number of comparisons number of inversions number of probes obtained operations optimum output permutation phase position possible priority queue probability problem Program Prove quicksort radix sorting random records replacement selection rewind RLINK search tree Section sequence shows smallest sorting algorithm sorting method sorting network step subfile successful search tableau tape Theorem total number