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Searching
Ref.: D.S. Malik, Data Structures
Using C++
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Searching
n size of the list
f(n) the number of comparisons done by the
search algorithm
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Array-Based Lists
search for 27
compare 27 with list[0] X
compare 27 with list[1] X
compare 27 with list[2]
35
[0] [1] [2] [3] [4] [5] [6] [7]
12 27 18 45 16 38 list
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Array-Based Lists
search for 10
compare 10 with list[0] X
keep going until there is no more data
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Program fragment to find where item
is in the listint loc;
bool found = false;
for (loc = 0; loc < length; loc++)
if (list[loc] == item)
{ found = true;
break;
}
if found
answer = loc;else
answer = -1;
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Unordered Linked Lists Program
fragment to see if item is in the list
nodeType *current;
bool found = false;
current = first;
while (current != NULL && !found)
if (current->info == item)
found = true;
else
current = current->link;
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Ordered Linked Lists Program
fragment to see if item is in the list
nodeType *current;
bool found = false;
current = first;
while (current != NULL && !found)
if (current->info >= item)
found = true;
else
current = current->link;if (found)
found = (current->info == item);
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Doubly Linked Lists
e.g.
first
last
struct nodeType
{
Type info;
nodeType *next;
nodeType *back;
};
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Program fragment to see if item is in
an ordered list
nodeType *current;
bool found = false;
current = first;
while (current != NULL && !found)
if (current->info >= item)
found = true;
else
current = current->next;if (found)
found = (current->info == item);
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Binary Search
Here is a sorted list of 12 numbers:
4
[0] [1] [2] [3] [4] [5] [6] [7]
8 19 25 34 39 45 48list
[8] [9] [10] [11]
66 75 89 95
We want to find whether 75 is in the list.
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Binary Search
First, a number in the middle of the whole list:
4
[0] [1] [2] [3] [4] [5] [6] [7]
8 19 25 34 39 45 48list
[8] [9] [10] [11]
66 75 89 95
list[5] 75
list[5] < 75, therefore, restrict the search tolist[6]
list[11]
Continue in this way until we find 75.
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int first = 0;
int last = length -1;
int mid;
bool found = false;
while (first item)
last = mid -1
else
first = mid + 1;
}if (found)
answer = mid;
else
answer = -1;
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Binary Search
Searching for 89:
4
[0] [1] [2] [3] [4] [5] [6] [7]
8 19 25 34 39 45 48list
[8] [9] [10] [11]
66 75 89 95
Iteration first last mid list[mid]
1 0 11 5 39
Student exercise: Complete the table until 89
is found.
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Binary Search
Student exercises:
1. Create a new table, and search for 34.
2. Create a new table, and search for 22.
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Binary Search
In the following slide is the definition ofclass
orderedArrayListType that implements the
search algorithms for array-based lists.
Important student exercise: Try to understand
every part of this code.
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Binary Search
template
class orderedArrayListType: publicarrayListType
{
public:
int binarySearch(const elemType& item);
orderedArrayListType(int n = 100);
};
