A Practical Introduction to Data Structures and Algorithm Analysis

242 Chap. 7 Internal Sorting4220171328142315i=0 1 2 3 4 5 61320174228142315131417422820231513141542282023171314151728202342131415172028234213141517202328421314151720232842Figure 7.3 An example of Selection Sort. Each column shows the array after theiteration with the indicated value of i in the outer for loop. Numbers above theline in each column have been sorted and are in their final positions.Key = 42Key = 5Key = 23Key = 10(a)Key = 42Key = 5Key = 23Key = 10(b)Figure 7.4 An example of swapping pointers to records. (a) A series of fourrecords. The record with key value 42 comes before the record with key value 5.(b) The four records after the top two pointers have been swapped. Now the recordwith key value 5 comes before the record with key value 42.remember the position of the element to be selected and do one swap at the end.Thus, the number of comparisons is still Θ(n 2 ), but the number of swaps is muchless than that required by bubble sort. Selection Sort is particularly advantageouswhen the cost to do a swap is high, for example, when the elements are long stringsor other large records. Selection Sort is more efficient than Bubble Sort (by aconstant factor) in most other situations as well.There is another approach to keeping the cost of swapping records low thatcan be used by any sorting algorithm even when the records are large. This isto have each element of the array store a pointer to a record rather than store therecord itself. In this implementation, a swap operation need only exchange thepointer values; the records themselves do not move. This technique is illustratedby Figure 7.4. Additional space is needed to store the pointers, but the return is afaster swap operation.