## Data Structure and Algorithms

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Data Structure and Algorithms

It is important to learn all concept of Data structure if any programmer want to build a scalable application. Its doesn’t matter which program you used for developed.

What is an Algorithm?

Algorithm is set of well-structured instruction which is used to solve the problem. It is created independents of underlying language. Algorithm is used to manipulate data in different ways such as sorting data items, searching and inserting data items.

#### Characteristics of an Algorithm

There are five important characteristics of an algorithms which is used while designing program are as follows:
1. Finiteness: An Algorithm must be terminate after infinite number of steps with finite amount of time.
2. Unambiguous: Each steps of Algorithm are clear, unambiguous and precisely define.
3. Input: An algorithm must have finite number of input or must have zero input.
4. Output: Algorithms must have at least one desired output or may be more defined output.
5. Effectiveness: The algorithms must be effective. Each step must be executed at finite time.

#### Example of Algorithm Programming

Write an algorithm to add two numbers and number entered by user.

Step 1 : Start

Step 2 : Declare variable as number1, number2 and sum

Step 3 : Read value number1 and number2

Step 4 : Add number1 and number2 and assign value to sum number1+number2 sum

Step 5 : Display sum

Step 6 : Stop

#### Algorithm Analysis

The Algorithm are analyzed in two ways. The first way is before implementation and second is after implementation:
1. Priori Analysis: Priori analysis is theoretical analysis whose efficiency is counted by various method.
2. Posterior Analysis: This type of analysis totally depends on system. SO can only implementation this analysis after running in the system.
Categories of Algorithm
1. Search: This Algorithm is used to search items in the Data table.
2. Delete: It is used to Delete items from Data structure.
3. Update: It is used to update items in Data structure.
4. Sort: It is used to Sort items in order.
5. Insert: It is used insert item in Data structure.
Time Complexity:

The amount of time taken by algorithms to execute the complex is known as Time Complexity. The time complexity is defined by Numeral function T(n). Where T(n) is number of steps for constant time interval.

Space complexity:

Space complexity of Algorithm defined for memory space in its life cycle. The space complexity of any algorithm P is S(P) = C + SP(I). Where as S(I) is variable part and C is the fixed parts of Algorithm.

##### Searching in Algorithm
Searching Algorithm is used to check the elements from any data structure where data is stored. The Searching algorithm is divided into two parts:
1. Sequential search: The best example of the Sequential search is Linear search. The array is traversed sequentially and each element is checked
2. Interval Search: This type of searching algorithms is applied only for sorted data. Interval search is more efficient searching algorithm than Linear search. Every time it targets the middle of search structure and divide the search space in half. Example of interval search is Binary search.
1. Liner search: Linear search is type of sequential search. This is very simple search algorithm. In this type of search, data is search on all items one by one. If the match is found it return the particular item otherwise search will in progress till end of the Data collection.
Pseudo Code:
```LinearSearch(a,n,key)
Begin
for j = 0 to n-1 by 1 do
if a[j] == key then
return J;
endif
endfor
return -1;
End

```
2. Binary Search: Binary Search algorithm is one of the popular search algorithms with execution complexity is O (log n). This search only works for sorted set of elements. Starting with the interval cover all array or list. If the value of the search key is small than items in half of interval, lower half narrow interval is applied. This algorithm work on the principle Divide and conquer approach in which the list is divided into two equal half and then item is compared with the middle elements of the list. After applying this if the match is found then location of the middle items can throw back, otherwise we search on half depending on the output came by the match in first step.
Pseudo Code:
```begin compStr(String1 , String2)
i = 0;
While (String1 [j] == String2 [i] && String1 [j] != '\0')
j++;
end While
If (String1 [j] > String2[j])
return -1;
end If

return (String1 [j] < String2[j]);

end compStr

begin Binary_Search (listOfProduct, toSearch, start , end)
If start > end
retunn -1
end If

middle = start + end / 2
if listOfProduct[mid] is Empty
left = mid - 1;
right = mid + 1;

while (true):
If left < start && right > end
return -1;
End If
If right<=end && !listOfProduct[right] isEmpty
mid = right;
break;
End If
if  left>=start  && !listOfProduct[left].isEmpty
mid = left;
break;
End If
right++;
left--;
End While

end If

if   compStr (str, listOfProduct [mid]) == 0
return mid;
end If

if  (compStr (str, listOfProduct [mid]) < 0)
return Binary_Search (arr, str, mid+1, end);
end If
//search is small than mid
return Binary_Search (listOfProduct, start, str, mid-1);

end Binary Search

```
Complexity of Binary search are following:
1. Worst case → O(log n)
2. Average case → O(log n)
3. Best case → O(1)

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