Data Structures: Sorting and Searching, Summaries of Data Structures and Algorithms

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Data Structures

Chapter# 05

Sorting and Searching

Introduction to Sorting

• (^) The process of arranging data in a specified order according to a given criteria is called sorting.
• (^) The numeric type data may be arranged either in ascending or descending order.
• (^) Similarly character type data may be arranged in alphabetical order.
• (^) Sorting is a fundamental operation performed by the computer.
• (^) It is mostly used to arrange records in databases.

Selection Sort

• (^) Suppose an array ‘ABC’ with ‘n’ elements ABC[0], ABC[1].... ABC[N-1] is in memory.
• (^) The selection sort technique for sorting array ‘ABC’ is as follows:
• (^) Select the first element and compare it with the rest of the elements.
• (^) If the next compared element is less than the selected element then swap the selected element with compared element, otherwise compare the selected element with the next element in the array.
• (^) This mechanism will find the smallest element in the list and put it in the first position in the first phase.
• (^) In the second phase, it will find the second smallest element in the list and put it in the second position and so on.
• (^) Thus array ‘ABC’ is sorted after ‘n-1’ passes

Selection Sort Example: 30 49 26 13 55 36 So 13 is the smallest element and placed it in first position

Pass 1:

Pass 3: Pass 4:

Pass 5:

• (^) In selection sort, select first and compare it with ‘N-1’ elements, if found small value interchange it, otherwise compare it with the next element.
• (^) Thus elements are sorted after ‘N-1’ passes.
• (^) Here is as algorithm which demonstrates the selection sort techniques.

Insertion Sort:

• (^) The insertion sort works by inserting each item

into its proper place in the final list.

• (^) Consider an array ‘A’ with ‘n’ elements A[0], A[1],

A[2]..... A[n-1] is in the memory.

• (^) The insertion sort algorithm scans ‘A’ from A[0] to

A[n-1] inserting each element into its proper

position in the previously sorted sub array i.e.

Pass 1: A[0] by itself sorted. Pass 2: A[1] is inserted before or after A[0], so that A[0], A[1] are to be sorted. Pass 3: A[2] is inserted into its proper place in A[0], and A[1] before A[0], between A[0] and A[1], or after A[1], so that A[0], A[1], A[2] are to be sorted. Pass N: A[n-1] is inserted into its proper place in A[0], A[1], A[2]... A[n-1] so that they are to be sorted.

Pass 4: 25 48 57 37 12 92

Pass 5: 25 37 48 57 12 92

Pass 6: 12 25 37 48 57 92

Pay Attention to the Code Example

For Insertion Sort

Pass 1

Pass 2

Pass 3 Pass 4 (^) 17 15 15 17 15 17 35 37 49

Searching

• (^) Computer systems are often used to store large amounts of data from which individual records are retrieved according to some search criterion.
• (^) The process of finding a specific data item or record from a list is called Searching.
• (^) The efficient storage of data to facilitate fast searching is an important task.
• (^) All other operations like inserting, deletion, etc are dependent on this operation.
• (^) Different techniques are used to carry out search operations. The commonly used search methods are: - (^) Sequential Search (Linear Search) - (^) Binary Search

Sequential Search

• (^) The sequential(Linear) search is a simple and straightforward technique to search a specified item in an unordered list.
• (^) The specified value is searched in the list sequentially, i.e. starting from the first element to the last element in the list in a sequence.
• (^) When the required value is found, search operation stops.
• (^) The sequential search is a slow process.
• (^) It is used for small amounts of data.
• (^) This method is not recommended for large amount of data.