Sorting

Why Sort? Put matching elements together –Uniqueness testing –Deleting duplicates –Frequency Counting –Set operations Prioritize Elements Reconstruct original order Efficient searching (binary search, pairs)

Sorting Algorithms (pp ) Insertion Sort –Least code, least data movement (inversions) Selection Sort –Conceptually simple, fewest swaps Quick Sort –Fastest –Needs careful implementation –Partition algorithm useful on its own

Comparison Functions Use with generalized sorting algorithms Stable Sort –Sort criteria separately (most important last) Unstable Sort –Previously sorted not necessarily still in order –One comparison function handles all criteria

Sorting in C++ (STL) Library functions sort and stable_sort –Iterator bg (beginning of list) –Iterator end (end of list) –Optional BinaryPredicate (default <=) Function that takes two items and returns true if they are in order

Sorting in Java In java.util.Arrays –Array of Objects (Object[] a) –Optional Comparator (default <=)

Search Sequential Search Binary Search –Tricky to get right under pressure Consider stopping condition –Library functions C++ STL: bsearch Java: binarySearch (see pp )

Generalizing Search Sequential –Foreach element If ( correct(element) ) process and break Binary –While (remaining list not empty) If (too-high (middle-of-list)) –Cut off bottom half Else if (too-low (middle-of-list)) –Cut off top half Else process and break

Notes on Binary Search Generalized functions “too-high” and “too- low” might evaluate criteria other than a value –E.g. outcome of function with a given parameter If you can estimate a location better than the middle, use it! (phone book search)