![Linear Search Algorithm
• Linear Search( Array A, Values X)
• Step 1: set i to 1
• Step 2: if i > n then go to step 7
• Step 3: if A[i] = X then go to step 6
• Step 4: set i to i+1
• Step 5: go to step 2
• Step 6: print element x found at index i and go to step 8
• Step 7: print element not found
• Step 8: exit
25/4/2020
4](https://image.slidesharecdn.com/datastructureandalgorithms-210429030858/85/Data-structure-and-algorithms-4-320.jpg)
![Selection Sort
What is selection sort?
• Selection sort is a simple sorting algorithm.
• In this technique, the smallest element is
interchanged with the first element of the array.
• Then the next smallest element is interchanged with
the second element of the array.
• This process of searching the next smallest element
and placing it in its proper position continues until
all records have been sorted in ascending order.
Algorithm
For i<-1 to n-1 do
min<-i
for j<-i+1 to n do
if A[j]<A[i] then
min<-j
if min!=i then
temp<-A[i]
A[i]<-A[min]
A[min]<-temp
25/4/2020
17](https://image.slidesharecdn.com/datastructureandalgorithms-210429030858/85/Data-structure-and-algorithms-17-320.jpg)
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Data structure and algorithms
- 1. Data Structure And Algorithms UNIT-5 Searching, hashing and sorting 25/4/2020 1 Submitted by Bhanupratap Singh Hirwani
- 2. Searching • The process of locating target data is known as searching. • Searching is the process of finding the location of the target among a list of object. • The two basic search techniques are the followings: -sequential search -binary search 25/4/2020 2
- 3. Linear Search • The linear search is a sequential search which uses a loop to step through an array, starting with the first element. • It compares each element with the value being searched for, and stops when either the value is found or the end of the array is encountered. • A search will be unsuccessful if all the elements are read and desired element is not found 25/4/2020 3
- 4. Linear Search Algorithm • Linear Search( Array A, Values X) • Step 1: set i to 1 • Step 2: if i > n then go to step 7 • Step 3: if A[i] = X then go to step 6 • Step 4: set i to i+1 • Step 5: go to step 2 • Step 6: print element x found at index i and go to step 8 • Step 7: print element not found • Step 8: exit 25/4/2020 4
- 5. Advantages and Disadvantages • The linear search is a simple- it is very easy to understand and implement • It does not require the data in the array to be stored in any particular order • DISADVANTAGES • It has very poor efficiency because it takes lots of comparisons to find a particular record in big files • Linear search is slower than other searching algorithms 25/4/2020 5
- 6. Binary Search What is Binary Search? • Binary search is an extremely efficient algorithm when it is compared to linear search. • It searches data in minimum possible comparisons. • Binary search use sorted array by repeatedly dividing the search interval in half. Algorithm • Step 1: compare x with the middle element. • Step 2:If x matches with middle element, we return the mid index. • Step 3: Else if x is greater than the mid element, search on right half. • Step 4: Else if x is smaller than the mid element, search on left half 25/4/2020 6
- 7. Example • Assume the following array • Search for 40 • Compare X=40 25/4/2020 7
- 8. Hashing • Hashing is a technique where we can compute the location of the desired record in order to retrieve it in a single access (or comparison) . • Hashing involves less key comparison and searching can performed in constant time. • The goal of hashed search is to find the target data in only one test i.e. O(1)(best complexity). • Hashing is an efficient method to store and retrieve elements. • In hashing function the keys are stored in array which is called hash table. 25/4/2020 8
- 9. Hashing function • The basic idea of hash function Is the transformation of the key into the corresponding location in the hash table. • A Hash function H can be defined as a function as a function that takes key as input and transforms it into a hash table index. • The values returned by hash function are called hash values , hash codes, hash sums, or simply hashes. • Hash function are two types: 1) distribution –independent function ,2) distribution-dependent function. • The distribution independent hash functions are : a) division method, b) mid square method, c) digit folding method. 25/4/2020 9
- 10. Hash Collision • When an element is inserted, if it hashes to the same value as an already inserted element, then we have a collision. • A situation in which the hash function returns the same hash key for more then one record , it is called as collision. 25/4/2020 10
- 11. Collision resolution technique • If there is a problem of collision occurs then it can be handled by apply some technique.these techniques are called as collision resolution techniques. • If the element to be inserted is mapped to the same location, where an element is already inserted then we have a collision and it must be resolved. • There are several strategies for collision resolution. The most commonly used are: 1) separate chaining- it used with open hashing. 2) open addressing- it used with closed hashing. 25/4/2020 11
- 12. Separate Chaining(open hashing) • Separate chaining based on collision avoidance. • The idea is to keep a list of all elements that hash to the same value. -the array elements are pointers to the first nodes of the lists. -A new item is inserted to the front of the list. • Advantages: - batter space utilization for large items. -simple collision handling : searching link list. -deletion is quick and easy : deletion from the linked list. 25/4/2020 12
- 14. Sorting • Sorting is the operation of arranging the records of a table according to the key value of each record, or it can be defined as the process of converting an unordered set of elements to an ordered set of elements. • Sorting is a process of organizing data in a certain order to help retrieve it more efficiently. • Sorting techniques can be divided into two categories. These are: 1) Internal sorting , 2) external sorting. • Any sort algorithm that uses main memory exclusively during the sorting is called as internal sort algorithm • Any sort algorithm that uses external memory, such as tape or disk, during the sorting is called as external sorting. • Internal sorting is faster then external sorting. 25/4/2020 14
- 15. Internal Sorting |External Sorting • The various internal sorting techniques are the following: 1. Bubble sort 2. Selection sort 3. Insertion sort 4. Quick sort 5. Shell sort 6. Heap sort 7. Radix sort 8. Bucket sort • Merge sort is used in external sorting 25/4/2020 15
- 16. Bubble Sort What is bubble sort? • Bubble sort is simple algorithm which is used to sort a given set of n elements provided in form of an array with n number of elements. • Bubble sort compares all the element one by one and sort them based on their values. • The bubble sort derives its name from the fact that the smallest data item bubbles up to the top of the sorted array. Algorithm for bubble sort 1. Starting with the first element(index=0), compare the current element with the next element of the array. 2. If the current element is greater than the next element of the array, swap them. 3. If the current element is less than the next element, move to the next element. Repeat step 1 25/4/2020 16
- 17. Selection Sort What is selection sort? • Selection sort is a simple sorting algorithm. • In this technique, the smallest element is interchanged with the first element of the array. • Then the next smallest element is interchanged with the second element of the array. • This process of searching the next smallest element and placing it in its proper position continues until all records have been sorted in ascending order. Algorithm For i<-1 to n-1 do min<-i for j<-i+1 to n do if A[j]<A[i] then min<-j if min!=i then temp<-A[i] A[i]<-A[min] A[min]<-temp 25/4/2020 17
- 18. Radix sort • Radix sort algorithm different than other sorting algorithms . • It does not use key comparisons to sort an array. • The radix sort treats each data items as a character string. • First it groups data items according to their rightmost character and put these groups into order with respect to this right most character. • Then combine these groups. • We repeat these groupings and combining operation for all other character positions in the data items from the right most to the left most character position. • At the end, the sort operation will be completed 25/4/2020 18
- 19. Heap Sort • Heap is a special tree based data structure, that satisfies the following special heap properties: 1)shape property , 2)heap property • Heap sort is the one of the fastest sorting algorithm, which achieves the speed as that of quick sort and merge sort. • The advantages of heap sort are as follows: • It dose not use recursion, and it is efficient for any data order. • It achieves the worst-case bounds better than those of quick sort. • And for the list, it is better than merge sort since it needs only a small and constant of space apart from the list being sorted 25/4/2020 19
- 20. Merge Sort(external sort) • The most common algorithm used in external sorting is the merge sort. • Merging is the process of combining two or more sorted files into the third sorted file. • The merge sort algorithm is base on the classical divide-and-conquer paradigm. • Divide-and-conquer algorithm works in three steps: 1. Divide the problem into multiple small problems. 2. Conquer the subproblems by solving them. The idea is to break down the problem into atomic subproblems, where they are actually solved. 3. Combine the solutions of the subproblems to find the solution of the actual problem. 25/4/2020 20