# CSC301 Data Structures and Algorithm Discussion.

**CSC301 Data Structures and Algorithm Discussion.**

1. An array A contains n integers taken from the interval [0,4n], with repetitions allowed. Describe an efficient algorithm for determining an integer value k that occurs the most often in A. What is the running time of your algorithm?

2. An array A contains n−1 unique integers in the range [0,n−1], that is, there is one number from this range that is not in A. Design an O(n)-time algorithm for finding that number. CSC301 Data Structures and Algorithm Discussion.You are allowed to use additional space besides the array A itself

3. In steps, find the computational complexity of the following loops:

(i) for ( c = 1, i = 1 ; i <= n ; i *= 2)

for (j =1 ; j <= n ; j++)

c++;

(ii) for (cc = 1, i = 1 ; i <= n ; i *= 2) for (j = 1; j <= i ; j++) cc++;

Data Structures are the programmatic way of storing data so that data can be used efficiently. Almost every enterprise application uses various types of data structures in one or the other way. This tutorial will give you a great understanding on Data Structures needed to understand the complexity of enterprise level applications and need of algorithms, and data structures.

## Why to Learn Data Structure and Algorithms?

As applications are getting complex and data rich, there are three common problems that applications face now-a-days.

**Data Search**− Consider an inventory of 1 million(10^{6}) items of a store. If the application is to search an item, it has to search an item in 1 million(10^{6}) items every time slowing down the search. As data grows, search will become slower.CSC301 Data Structures and Algorithm Discussion.

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**Processor speed**− Processor speed although being very high, falls limited if the data grows to billion records.**Multiple requests**− As thousands of users can search data simultaneously on a web server, even the fast server fails while searching the data.

To solve the above-mentioned problems, data structures come to rescue. Data can be organized in a data structure in such a way that all items may not be required to be searched, and the required data can be searched almost instantly.

## Applications of Data Structure and Algorithms

Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output. Algorithms are generally created independent of underlying languages, i.e. an algorithm can be implemented in more than one programming language.

From the data structure point of view, following are some important categories of algorithms −

**Search**− Algorithm to search an item in a data structure.**Sort**− Algorithm to sort items in a certain order.**Insert**− Algorithm to insert item in a data structure.**Update**− Algorithm to update an existing item in a data structure.**Delete**− Algorithm to delete an existing item from a data structure.

The following computer problems can be solved using Data Structures −

- Fibonacci number series
- Knapsack problem
- Tower of Hanoi
- All pair shortest path by Floyd-Warshall
- Shortest path by Dijkstra
- Project scheduling

CSC301 Data Structures and Algorithm Discussion.

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