1. Problem Statement As part of dissertation, the University professor has decided to ask the students about their preferences of topic before assigning the problem statements to each one of them. The topics available are: 1. Data mining 2. NLP 3. AI 4. Spatial Data Analysis 5. Image processing 6. Big-Data 7. Graph Mining 8. Machine Learning 9. E-commerce 10.Wireless Mobile communication 11.Cloud computing There are 11 students working with the Professor. Each student can have more than 1 topic which he/she prefers. Your job is to help the professor calculate the number of unique allocation of topics to the students such that everybody gets exactly one topic of their liking and no two students get the same subject allocated. Requirements: 1. Formulate an efficient algorithm using dynamic programming to perform the above task.

2. Analyse the time complexity of your algorithm.

3. Implement the above problem statement using Python 3.7

Input: Input should be taken in through a file called inputPS4.txt which has the fixed format mentioned below using the / as a field separator: Student / < topic 1> / / . Ex: S1 / DM / SDA / WMC / CC S2 / DM / NLP / AI / SDA / IP / GM / EC S3 / DM / SDA / GM / ML / WMC S4 / DM / AI / SDA / IP / GM / ML / WMC / CC S5 / NLP / AI / SDA / BD / EC / WMC / CC S6 / DM / NLP / AI / BD S7 / IP / GM / CC S8 / DM / AI / SDA / CC S9 / AI / IP / BD / WMC / CC S10 / DM / NLP / AI / GM / EC / CC S11 / DM / IP / BD / GM / ML Note that the input data shown here is only for understanding and testing, the actual file used for evaluation will be different. Output: Syntax of the output should be: The total number of allocations possible is: Ex: The total number of allocations possible is: 7588. Display the output in outputPS4.txt.