1. MSIS 655 Advanced Business Applications Programming
Week 12
Searching and Sorting (Ch. 16)
In this chapter you will learn:
To search for a given value in an array using linear search and binary search.
To sort arrays using the iterative selection and insertion sort algorithms.
To sort arrays using the recursive merge sort algorithm.
To determine the efficiency of searching and sorting algorithms.
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12.1

2. Introduction Searching Sorting
Determining whether a search key is present in data
Sorting
Places data in order based on one or more sort keys
In chapter 17 (Data Structure), the linked Lists (nodes) class and linear search function on the list are explained. Also, class Collections (chapter 19) has a method, binarySearch( list ). Those are class specific functions. What I am trying here is more on the logics to figure out the functions.
Examples of searching
Looking up a phone number
Accessing a Web site
Checking a word in the dictionary
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3. Searching Algorithms Linear search Searches each element sequentially
If search key is not present
Tests each element
When algorithm reaches end of array, informs user search key is not present
If search key is present
Test each element until it finds a match
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4. LinearArray.java
(Fig p. 788)
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5. Efficiency of Linear Search
Big O Notation
Indicates the worst-case run time for an algorithm
O(1): Constant
O(n): Linear
O(n2): Quadratic
Sometimes the simplest algorithms perform poorly. Their virtue is that they are easy to program, test and debug. Sometimes more complex algorithms are required to realize maximum performance.
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6. Binary Search More efficient than linear search
Requires elements to be sorted
Tests the middle element in an array
If it is the search key, algorithm returns
Otherwise, if the search key is smaller, eliminates larger half of array
If the search key is larger, eliminates smaller half of array
Each iteration eliminates half of the remaining elements
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7. BinaryArray.java
(pp )
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8. Efficiency of Binary Search
Each comparison halves the size of the remaining array
Results in O(log n)
Called logarithmic run time
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9. Sorting Algorithms Sorting data
Placing data into some particular order
A bank sorts checks by account number
Telephone companies sort accounts by name
End result is always the same – a sorted array
Choice of algorithm affects how you achieve the result and, most importantly, how fast you achieve the result
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10. Selection Sort Simple, but inefficient sorting algorithm
First iteration selects smallest element in array and swaps it with the first element
Each iteration selects the smallest remaining unsorted element and swaps it with the next element at the front of the array
After i iterations, the smallest i elements will be sorted in the first i elements of the array
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11. (pp. 798-799) SelectionSort.java 12/7/2018
For each of the i’s in the first for loop, rest of the array is looked through using the second for loop, and the index of the smallest value is chosen as “smallest” (including ith element and forward).
Swap (int i, int smallest) will swap the value of the Array elements data[ i ] and data[ smallest ]. – data[ i ] becomes the smallest of the array (I’th and forward).
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12. Efficiency of Selection Sort
Outer for loop iterates over n – 1 elements
Inner for loop iterates over remaining elements in the array
Results in O(n2)
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13. Insertion Sort Another simple, but inefficient sorting algorithm
First pass takes the second element and inserts it into the correct order with the first element
Each iteration takes the next element in the array and inserts it into the sorted elements at the beginning of the array
After i iterations, the first i elements of the array are in sorted order
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14. 12/7/2018

15. Merge Sort Combination of Sort algorithm and recursion
To be continued…
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16. Lab activities (Week 12) Exercises (pp. 814-815) 16.5, 16.6
Advanced: 16.7
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