![Linear search algorithm
Linear_search(A[], n, e)
Step 1) Set i = 0 and loc = 0.
Step 2) repeat steps 3, 4 while(loc=0 && i<n)
Step 3) if A[i] = e, then set loc = i;
Step 4) Set i = i+1
Step 5) If loc = 0 , then, element ‘e’ is not in array
Step 6) else return i (location of e).
Here, A= name of array
n= size of array A
i= used for index of array
e= element to be searched
loc= this will store the location of searched element
Complexity = O(n)](https://image.slidesharecdn.com/searching-231129061003-8e9ce0a2/85/Searching-in-Data-Structure-4-320.jpg)
![Binary search
Here, we compare search elements ‘e’ with the middle element of array A,
that is A[mid], where mid = n/2. and n = size of array.
In binary search array elements must be sorted (either in ascending or
descending order)
If e = A[mid] we have found element
If e < A[mid] restrict search to A[0] to A[m-1]
If e > A[mid] restrict search to A[m+1] to A[n-1]](https://image.slidesharecdn.com/searching-231129061003-8e9ce0a2/85/Searching-in-Data-Structure-6-320.jpg)
![Algorithm of binary search
Binary_search(A[], n, e)
Step 1) set low = 0, high = n-1
Step 2) repeat steps 3 and 4 while(low<=high)
Step 3) mid = (low + high)/2
Step 4) if (e == A[mid])
Return mid
Else if (e< A[mid])
High = mid – 1
Else low = mid + 1
Step 5) return -1
Here, low = lower bound of array A of size n
high = upper bound of array A
e= element to be searched
::Complexity = O(log n)](https://image.slidesharecdn.com/searching-231129061003-8e9ce0a2/85/Searching-in-Data-Structure-7-320.jpg)
Searching in Data Structure
- 2. Searching Methods Two popular methods for searching Linear search Binary search
- 3. Linear search In linear search, we compare every elements of the array one by one in a sequential manner until a match is found
- 4. Linear search algorithm Linear_search(A[], n, e) Step 1) Set i = 0 and loc = 0. Step 2) repeat steps 3, 4 while(loc=0 && i<n) Step 3) if A[i] = e, then set loc = i; Step 4) Set i = i+1 Step 5) If loc = 0 , then, element ‘e’ is not in array Step 6) else return i (location of e). Here, A= name of array n= size of array A i= used for index of array e= element to be searched loc= this will store the location of searched element Complexity = O(n)
- 5. Advantages & Disadvantages Advantages: We can apply for both sorted and unsorted data. Best case running time complexity is O(1) Disadvantages: Worst case Running Time complexity is O(n) 5
- 6. Binary search Here, we compare search elements ‘e’ with the middle element of array A, that is A[mid], where mid = n/2. and n = size of array. In binary search array elements must be sorted (either in ascending or descending order) If e = A[mid] we have found element If e < A[mid] restrict search to A[0] to A[m-1] If e > A[mid] restrict search to A[m+1] to A[n-1]
- 7. Algorithm of binary search Binary_search(A[], n, e) Step 1) set low = 0, high = n-1 Step 2) repeat steps 3 and 4 while(low<=high) Step 3) mid = (low + high)/2 Step 4) if (e == A[mid]) Return mid Else if (e< A[mid]) High = mid – 1 Else low = mid + 1 Step 5) return -1 Here, low = lower bound of array A of size n high = upper bound of array A e= element to be searched ::Complexity = O(log n)
- 8. Advantages & Disadvantages Advantages Worst case running time complexity is O(logn). Perform better than linear search Disadvatages We can use only for the sorted data. 8