By Mehlhorn K., Sanders P.
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Additional info for Concise algorithmics, the basic toolbox
Although different comparison relations for the same data type may make sense, the most frequent relations are the obvious order for numbers and the lexicographic order (see Appendix A) for tuples, strings, or sequences. ) Ordering strings is not always as obvious as it looks. For example, most European languages augment the Latin alphabet with a number of accented characters. For comparisons, accents are essentially omitted. Only ties are broken so that Mull≤M¨ull etc. 2 b) In German telephone books (but not in Encyclopedias) a second way to sort words is used.
1 Simple Sorters Perhaps the conceptually simplest sorting algorithm is selection sort: Start with an empty output sequence. Select the smallest element from the input sequence, delete it, and add it to the end of the output sequence. Repeat this process until the input sequence is exhausted. Here is an example , 4, 7, 1, 1 ❀ 1 , 4, 7, 1 ❀ 1, 1 , 4, 7 ❀ 1, 1, 4 , 7 ❀ 1, 1, 4, 7 , . e. needs no additional storage beyond the input array and a constant amount =⇒ of space for loop counters etc. [todo] we will learn about a more sophisticated implementation where the input sequence is maintained as a priority queue that supports repeated selection of the minimum element very efficiently.
The reason for this charade is that it allows the hash function to store internal state like random coefficients. LEDA offers several hashing based implementations of dictionaries. The class ha rray Key, Element implements an associative array assuming that a hash function intHash(Key&) is defined by the user and returns an integer value that is then mapped to a table index by LEDA. [check. hashtable implements unbounded hash tables using the function hashCode defined in class Object as a hash function.