Download - Algorithm Efficiency and Sorting · Data Abstraction and Problem Solving with JAVA Walls and Mirrors Frank M. Carrano and Janet J. Prichard ... An insertion sort partitions the array

Data Abstraction and Problem Solving with JAVA Walls and MirrorsFrank M. Carrano and Janet J. Prichard © 2001 Addison Wesley

Data Abstraction and Problem Solving with JAVA:Data Abstraction and Problem Solving with JAVA:Walls and MirrorsWalls and Mirrors

CarranoCarrano / / PrichardPrichard

Algorithm Efficiency and SortingAlgorithm Efficiency and Sorting

Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley

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


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


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


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


Figure 9.4Figure 9.4A selection sort of an array of five integers


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


Figure 9.6Figure 9.6An insertion sort partitions the array into two regions


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


Figure 9.8Figure 9.8A mergesort with an auxiliary temporary array


Figure 9.9Figure 9.9A mergesort of an array of six integers


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


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


Figure 9.12Figure 9.12A partition about a pivot


Figure 9.13Figure 9.13kSmall versus quicksort


Figure 9.14Figure 9.14Invariant for the partition algorithm


Figure 9.15Figure 9.15Initial state of the array


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


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


Figure 9.18aFigure 9.18aDeveloping the first partition of an array when the pivot is the first item


Figure 9.18bFigure 9.18bDeveloping the first partition of an array when the pivot is the first item


Figure 9.19Figure 9.19A worst-case partitioning with quicksort


Figure 9.20Figure 9.20A average-case partitioning with quicksort


Figure 9.21Figure 9.21A radix sort of eight integers


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