Chapter 12 Binary Search and QuickSort Fundamentals of Java

2 Vocabulary Binary search algorithm QuickSort algorithm

Fundamentals of Java 3 Binary Search Figure 12-9: List for the binary search algorithm with all numbers visible Figure 12-8: Binary search algorithm (searching for 320)

Fundamentals of Java 4 Binary Search (cont.) Table 12-4: Maximum number of steps needed to binary search lists of various sizes

Fundamentals of Java 5 Binary Search (cont.) binary searches are O(log n).

Fundamentals of Java 6 Binary Search (cont.) Figure 12-10: Steps in an iterative binary search for the number 320

Fundamentals of Java 7 Binary Search (cont.)

Fundamentals of Java 8 Quicksort Sorting algorithms, such as insertion sort and bubble sort, are O(n 2 ). Quick Sort is O(n log n). – Break array into two parts and then move larger values to one end and smaller values to other end. – Recursively repeat procedure on each array half.

Fundamentals of Java 9 Quicksort (cont.) Figure 12-11: An unsorted array Phase 1:

Fundamentals of Java 10 Quicksort (cont.) Phase 1 (cont.):

Fundamentals of Java 11 Quicksort (cont.) Phase 1 (cont.):

Fundamentals of Java 12 Quicksort (cont.) Phase 1 (cont.):

Fundamentals of Java 13 Quicksort (cont.) Phase 1 (cont.):

Fundamentals of Java 14 Quicksort (cont.) Phase 1 (cont.): Phase 2 and beyond: Recursively perform phase 1 on each half of the array.

Fundamentals of Java 15 Quicksort (cont.) Complexity analysis: – Amount of work in phase 1 is O(n). – Amount of work in phase 2 and beyond is O(n). – In the typical case, there will be log 2 n phases. – Overall complexity will be O(n log 2 n).

Fundamentals of Java 16 Quicksort (cont.) Implementation: