Sorting and searching arrays binary search algorithm

Sorting And Searching
Arrays
The Binary Search Algorithm

Binary Search Algorithm-Advantages of
Binary Search
 Binary search s more efficient with large arrays
 Binary search’s only requirement is – must be
sorted in ascending order.
 Starts in the middle instead of at the beginning
 The search is over if the desired value is in
that element. Otherwise,

Binary Search Algorithm
 Instead of testing the first element in the array, the binary
search starts with the element in the middle and if that
element has the desired value, then the search is over
 If the value in the middle is not the desired element, then it is
either greater than or less than the value being searched.
 If it is greater, then the desired value(if it is in the list) will be
found somewhere in the first half of the array.
 If it is less, then the desired value will be found somewhere in
the last half of the array(if it is in the list)

 If the desired value isn't found in the middle element, the
procedure is repeated for half the array. Example: if the last
half of the array is to be searched, the algorithm tests its
middle element.
 If the value still isn't found in the middle element, the search
is narrowed to the quarter of the array before or after that
element.
 The search continues until a value is either found or there is
no more elements to test.

 The Binary Search Algorithm uses three variables to mark
positions within the array: first, last, and middle.
 The first and last variables mark the boundaries of the portion of
array currently being searched and are initialized with the
subscripts of the arrays first and last elements.
 The subscript halfway between the first and last element is
calculated and stored in the middle variable.
 If the middle element of the array does not contain the search
value, then first or last variables are adjusted so that only the
top or bottom half of the array is searched during the next
iteration. This cuts the portion of the array being searched in half
each time the loop fails to locate the search value.

Binary Search Algorithm-Efficiency
of a binary search.
 Each time a binary search fails to find the desired item, it e
eliminates half of the remaining portion of the array that must be
searched.
 Example: if a binary search fails to find an item on the first
attempt in an array with 1000 elements, the number of elements
that remains to be searched is 500. if the value is not found on
the second attempt, the number of elements that remains to be
searched is 250, and so on.
 The process continues until the binary search has either located
the desired item or determined that it is not in the array.
 With 1000 elements, the binary search takes no more than 10
comparisons. A sequential search would take an average of 500
comparisons, so the binary search his much more efficient.

1 Module main()
2 // Constant for array sizes
3 Constant Integer SIZE = 6
4
5 // Array of instructor names, already sorted in
6 // ascending order.
7 Declare String names[SIZE] = "Hall", "Harrison",
8 "Hoyle", "Kimura",
9 "Lopez", "Pike"
10
11 // Parallel array of instructor phone numbers.
12 Declare String phones[SIZE] = "555-6783", "555-0199",
13 "555-9974", "555-2377",
14 "555-7772", "555-1716"
15
16 // Variable to hold the last name to search for.
17 Declare String searchName
18
19 // Variable to hold the subscript of the name.
20 Declare Integer index
21

22 // Variable to control the loop.
23 Declare String again = "Y"
24
25 While (again == "Y" OR again == "y")
26 // Get the name to search for.
27 Display "Enter a last name to search for."
28 Input searchName
29
30 // Search for the last name.
31 index = binarySearch(names, searchName, SIZE)
32
33 If index ! = -1 Then
34 // Display the phone number.
35 Display "The phone number is ", phones[index]
36 Else
37 // The name was not found in the array.
38 Display searchName, " was not found."
39 End If
40
41 // Search again?
42 Display "Do you want to search again? (Y=Yes, N=No)"
43 Input again
44 End While
45
46 End Module

47
48 // The binarySearch function accepts as arguments a String
49 // array, a value to search the array for, and the size
50 // of the array. If the value is found in the array, its
51 // subscript is returned. Otherwise, -1 is returned,
52 // indicating that the value was not found in the array.
53 Function Integer binarySearch(String array[], String value,
54 Integer arraySize)
55 // Variable to hold the subscript of the first element.
56 Declare Integer first = 0
57
58 // Variable to hold the subscript of the last element.
59 Declare Integer last = arraySize - 1
60
61 // Position of the search value
62 Declare Integer position = -1
63
64 // Flag
65 Declare Boolean found = False
66
67 // Variable to hold the subscript of the midpoint.
68 Declare Integer middle

69
70 While (NOT found) AND (first <= last)
71 // Calculate the midpoint.
72 Set middle = (first + last) / 2
73
74 // See if the value is found at the midpoint...
75 If array[middle] == value Then
76 Set found = True
77 Set position = middle
78
79 // Else, if the value is in the lower half...
80 Else If array[middle] > value Then
81 Set last = middle - 1
82
83 // Else, if the value is in the upper half...
84 Else
85 Set first = middle + 1
86 End If
87 End While
88
89 // Return the position of the item, or -1
90 // if the item was not found.
91 Return position
92 End Function

88
89 // Return the position of the item, or -1
90 // if the item was not found.
91 Return position
92 End Function
Program Output (with Input Shown in Bold)
Enter a last name to search for.
Lopez [Enter]
The phone number is 555-7772
Do you want to search again? (Y=Yes, N=No)
Y [Enter]
Harrison [Enter]
The phone number is 555-0199
Y [Enter]
Lee [Enter]
Lee was not found.
N [Enter]

Sorting and searching arrays binary search algorithm

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