Efficient Sorting Algorithms for Various Problem Sizes

Figure 9.1 Time requirements as a function of the problem size n

Figure 9.2 When n ≥ 2, 3 * n2 exceeds n2 - 3 * n + 10

Figure 9.3a A comparison of growth-rate functions: a) in tabular form

Figure 9.3b A comparison of growth-rate functions: b) in graphical form

Selection Sort Bubble Sort Insertion Sort Mergesort Quicksort Radix Sort Sorting Algorithms

Figure 9.4 A selection sort of an array of five integers

Figure 9.5 The first two passes of a bubble sort of an array of five integers: a) pass 1; b) pass 2

Figure 9.6 An insertion sort partitions the array into two regions

Figure 9.7 An insertion sort of an array of five integers.

Figure 9.8 A mergesort with an auxiliary temporary array

Figure 9.9 A mergesort of an array of six integers

Figure 9.10 A worst-case instance of the merge step in mergesort

Figure 9.11 Levels of recursive calls to mergesort given an array of eight items

Figure 9.12 A partition about a pivot

Figure 9.13 kSmall versus quicksort

Figure 9.14 Invariant for the partition algorithm

Figure 9.15 Initial state of the array

Figure 9.16 Moving theArray[firstUnknown] into S1 by swapping it with theArray[lastS1+1] and by incrementing both lastS1 and firstUnknown

Figure 9.17 Moving theArray[firstUnknown] into S2 by incrementing firstUnknown

Figure 9.18a Developing the first partition of an array when the pivot is the first item

Figure 9.18b Developing the first partition of an array when the pivot is the first item

Figure 9.19 A worst-case partitioning with quicksort

Figure 9.20 A average-case partitioning with quicksort

Figure 9.21 A radix sort of eight integers

Figure 9.22 Approximate growth rates of time required for eight sorting algorithms