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:
- Finiteness: An Algorithm must be terminate after infinite number of steps with finite amount of time.
- Unambiguous: Each steps of Algorithm are clear, unambiguous and precisely define.
- Input: An algorithm must have finite number of input or must have zero input.
- Output: Algorithms must have at least one desired output or may be more defined output.
- 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
Step 5 : Display sum
Step 6 : Stop
The Algorithm are analyzed in two ways. The first way is before implementation and second is after implementation:
Categories of Algorithm
- Priori Analysis: Priori analysis is theoretical analysis whose efficiency is counted by various method.
- Posterior Analysis: This type of analysis totally depends on system. SO can only implementation this analysis after running in the system.
- Search: This Algorithm is used to search items in the Data table.
- Delete: It is used to Delete items from Data structure.
- Update: It is used to update items in Data structure.
- Sort: It is used to Sort items in order.
- Insert: It is used insert item in Data structure.
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 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:
- Sequential search: The best example of the Sequential search is Linear search. The array is traversed sequentially and each element is checked
- 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.
Complexity of Binary search are following:
- 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.
for j = 0 to n-1 by 1 do
if a[j] == key then
- 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.
begin compStr(String1 , String2)
i = 0;
While (String1 [j] == String2 [i] && String1 [j] != '\0')
If (String1 [j] > String2[j])
return (String1 [j] < String2[j]);
begin Binary_Search (listOfProduct, toSearch, start , end)
If start > end
middle = start + end / 2
if listOfProduct[mid] is Empty
left = mid - 1;
right = mid + 1;
If left < start && right > end
If right<=end && !listOfProduct[right] isEmpty
mid = right;
if left>=start && !listOfProduct[left].isEmpty
mid = left;
if compStr (str, listOfProduct [mid]) == 0
if (compStr (str, listOfProduct [mid]) < 0)
return Binary_Search (arr, str, mid+1, end);
//search is small than mid
return Binary_Search (listOfProduct, start, str, mid-1);
end Binary Search
- Worst case → O(log n)
- Average case → O(log n)
- Best case → O(1)