c language session 4

7/31/2019 C Language Session 4

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M.S. Ramaiah School of Advanced Studies, Bengaluru

Data Structures

Session delivered by:Session delivered by:

Deepak VaradamDeepak Varadam

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Session Objectives To understand the basic sorting and searching methods

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Topics Sorting algorithms Searching algorithms

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Sorting Sorting is the process ofarranging a set of similar information into

an increasing or decreasing order. Sorting algorithms have also been extensively analyzed and are well

understood.

Sorting is typically undertaken for one of two reasons:

1. Searching will be a key operation on the data searching sorteddata is more efficient than searching unsorted data.

2. Sorted data can be presented in a meaningfulmanner.

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Sorting contd

There are three general methods for sorting arrays Exchange -Eg. Bubble sort

Selection -Eg. Selection sort

Insertion -Eg. Insertion sort

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Bubble sort It is the most well known sorting technique

It is an exchange sort

It involves repeated comparison and if necessary, the exchange of

adjacent elements

The elements are like bubbles in a tank of water-each seeks its

own level It is driven by two loops

Given that there are count elements in the array.

The outer loop causes the array to be scanned count-1 times and ensures

that in the worst case, every element is in its proper position when the

function terminates. The inner lop actually performs the comparisons and exchanges

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Bubble Sort contd To see how the bubble sort works, assume that the array to be sorted is

dcab. Each pass is shown here.Initial d c a b

pass1 a d c b

pass2 a b d c

pass3 a b c d

With the bubble sort, the number of comparisons is always the same

because the two for loops repeat the specified number of times

whether the list is initially ordered or not.

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Bubble Sort contd

The bubble sort always performs (n2

-n) . It is derived from the factthat the outer loop executes n-1 times and the inner loop executes an

average of n/2 times.

An n-squared algorithm is ineffective when applied to large no of

elements because the execution time grows exponentially relative to

the no of elements(for the average and worst case) The no of exchanges is zero for the best case.

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Selection sort A selection sort selects the element with the lowest value and

exchange it with the first element From the remaining n-1 elements ,the element with the smallest

key is found and exchanged with the second element and so forth

The exchanges continue to the last two elements

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Selection Sort Contd As with the bubble sort the outer loop executes n-1 times and the

inner loop averages n/2 times As a result it requires1/2(n2-n) comparisons

This is an n squared algorithm, which makes it too slow for

sorting a large number of items

Although the number of comparisons for both bubble sort andselection sort is the same, the number of exchanges in the average

case is far less for the selection sort.

Initial d c a b

pass1 a c d bpass2 a b d c

pass3 a b c d

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Insertion Sort

Insertion sort initially sorts the first two members of the array.

Next it inserts the third member into its sorted position in relationto the first two members. Then it inserts the fourth element and so

on

The process continues until all elements have been sorted.

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Insertion Sort contd

Unlike the bubble and selection sorts, the number of

comparisons that occur during an insertion sort depends uponhow the list is initially ordered.

If the list is in order, the number of comparisons is n-1;ow.its

performance is on the order ofn-squared.

Insertion sort has two advantages It behaves naturally. ie. It works the least when the array is

already sorted and the hardest when the array is sorted in

reverse order.

It leaves the order of the equal keys the same. This means that

if a list is sorted by two keys, it remain sorted for both keys

after an insertion sort.

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Searching

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Searching

Searching is theprocess of traversing through a set of recordslooking for

a specific key value. Generally, the purpose of the search is to reportwhether or not the target key is present. Often, the search will also return

one (or more) of the following:

the location of the target key value within the data set;

the rest of the record associated with that key;

apointerto the rest of the record associated with that key.

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Searching Searching can be conducted on unordered data. This is usually

the least efficient searching method. Searching can be conducted on ordered (sorted) data.

Searching sorted data is generally far more efficient than

searching unordered data.

If it is known that searching is a major and frequently invokedtask, then it is worth the overhead to sort data first.

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Searching Techniques The sequential search is basically a loop starting at the

beginning of the set, step through each item one at a time,stopping if the target is found.

The Binary Search is a highly efficient searching algorithm.However, it has two preconditions:

The data must be stored in a directly indexable structure (i.e.,

an array) The data must be ordered.

Binary search tree: Each node has one key and at mosttwo children

Trinary search tree: Each node has one or two keys and at

most three children n-ary search tree: Each node has up to (n-1) keys and atmost n children

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The Sequential Search

The sequential search is simple to code.

The following function searches a integer array of known lengthuntil a match of the specified key is found.

int sequential_search(int items[], int count, int key)

{int t;

for(t=0; t


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The Binary Search

The Binary Search has two preconditions:

The data must be stored in a directly indexable structure (i.e., anarray)

The data must be ordered.

The Binary Search works:

Compute the middle point of the array Compare the value at the midpoint against the target

If the midpoint value is greater than the target, repeat the search inthe top half of the array (i.e., the lower index positions)

If the midpoint value is smaller than the target, repeat the search inthe bottom half of the array (i.e., the higher index positions)

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The Binary SearchConsider an array with 13 entries, in index positions 0 through 12, and a

search target of59.

Initialization:

low = 0, high = (n-1);

Step One:

Compute the midpoint: mid = (low + high) / 2 = 6 Check the midpoint value against the target: a[mid] is 42, so not found;

If not found, decide where to repeat: a[mid] (42) is less than the target(59), so the search is repeated in the upper end of the array by settinglow = mid+1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 126

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The Binary Search

Step Two:

Compute the midpoint: mid = (low + high) / 2 = (7 + 12)/2 = 9 Check the midpoint value against the target: a[mid] is 63, so not found;

If not found, decide where to repeat: a[mid] (63) is greater than the target

(59), so the search is repeated in the lower end of the array by setting high

= mid-1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 126 97

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The Binary Search

Step Three:

Compute the midpoint: mid = (low + high) / 2 = (7 + 8)/2 = 7

Check the midpoint value against the target: a[mid] is 47, so not found;

If not found, decide where to repeat: a[mid] (47) is less than the target

(59), so the search is repeated in the upper end of the array by settinglow = mid+1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 126 97 8

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The Binary Search

Step Four:


Check the midpoint value against the target: a[mid] is 59, so target

found;

low

high

mid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 126 97 8

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The Binary Search

Consider the same array, but this time search for a target that is notpresent, say 28

Initialization:

low = 0, high = (n-1);

Step One:

Compute the midpoint: mid = (low + high) / 2 = 6

Check the midpoint value against the target: a[mid] is 42, so notfound;

If not found, decide where to repeat: a[mid] (42) is greater than thetarget (28), so the search is repeated in the lower end of the array by

setting high = mid-1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 126

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The Binary Search

Step Two:


Check the midpoint value against the target: a[mid] is 21, so not

found;

If not found, decide where to repeat: a[mid] (21) is less than the

target (28), so the search is repeated in the upper end of the arrayby setting low = mid+1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 12652

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The Binary Search

Step Three:


Check the midpoint value against the target: a[mid] is 30, so notfound

If not found, decide where to repeat: a[mid] (30) is greater than thetarget (28), so the search is repeated in the lower end of the array bysetting high = mid-1

low highmid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 1262 53 4

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The Binary Search

Step Four:


Check the midpoint value against the target: a[mid] is 26, so not

found

If not found, decide where to repeat: a[mid] (26) is less than the

target (28), so repeat the search in the upper end of the array by

setting low = mid+1

low

high

mid

10 17 21 26 30 35 42 47 59 63 68 73 84

0 12642 3 5

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The Binary Search

Step Five: The value of the low index has exceeded the value of thehigh index, which tells us that the target is not present in the array, so

the search ends with a failure

lowhigh

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0 12642 3 5

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SummarySorting is typically undertaken for one of two reasons:

Searching will be a key operation on the data (searching sorted

data is more efficient than searching unsorted data;

Sorted data can be presented in a meaningful manner

There are three general methods for sorting arrays: Bubble Sort,

Selection Sort and Insertion Sort

Searching is the process of traversing through a set of records

looking for a specific key value

The Binary Search has two preconditions:The data must be stored in a directly indexable structure (i.e.,

an array)

The data must be ordered.

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Thank You

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c language session 4

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