## College Rank III TCS CodeVita 2022 Solution

**- Problem Description**

College Admissions are done by allocating a seat to a student based on his/her preference and percentage scored. Students are asked to provide three colleges of their choice. Each college will have a quota of S seats (S can vary per college). Admissions will be processed based on 'percentage scored' and availability of seats as per 'choice of preference'.

Admissions will first be granted based on percentage scored. If there is a tie, on percentage scored, then admission will be granted based on student Id i.e. student with a lower Id will be given preference over student with higher Id.

In Round 1 all admissions will be processed based on students' choice i.e. if a student is eligible to get admitted in any of the 3 colleges, s/he will have to be admitted. Similarly, it will be binding on the student to get admitted. Obviously, first choice will get first preference, second choice will get second preference and so on.

Round 2 will process all the remaining students (those who didn't get admitted in Round 1) according to their percentages and in order of maximum availability of seats in colleges.

For E.g.

<college, vacant seats>

C-1, 15

C-22, 14

C-32, 13

C-43, 12

<student-id, percentage>

Student-88, 64.0

Student-103, 63.7

Student-128, 58.28

Here, now Student-88 will get admitted to C-1.

Now, Student-103 could potentially get admitted to C-1 or C-22. Suppose we mandate that ties should be broken in favour of college with least ID, then again Student-103 will get admitted to C-1. Now C-1 has 13 vacant seats whereas C-22 has 14 vacant seats.

Next, Student-128 will get admitted to C-22. Now again C-1, C-22 and C-32 have 13 vacant seats. So, the next three students (hypothetically) will get admitted to C-1, C-22 and C-32 respectively.

**Help MLA 2 TCS CodeVita 2022 Solution**

**- Constraints**

3<=C<=25

1<=N<=10000

1<=S<=120

### - Input

First line contains two integers viz. C and N where,

C is number of colleges and

N is number of students

Second line contains C spaced integers denoting S1,S2 and so on till SC - where S1 is number of seats in college 1, S2 in college 2 etc.

Next, N lines comprise of 5 data items, viz <student-id, percentage, Choice 1, Choice 2, Choice 3>

**- Output **

Display the cut-off percentages of all the colleges in sorted order (descending order). Display the college with no students in last line as 'n/a.

If there are more than one colleges with 'n/a', then display the colleges along with 'n/a' in ascending order of College Id (C-1 n/a, C-2 n/a, C-10 n/a)

The output format is <college cut-off_percentage>

For better understanding go through the *Examples* given below.

**- Time Limit (secs)**

### - Examples

Input

3 5

3 1 2

Student-1,97.05,C-1,C-3,C-2

Student-2,48.03,C-1,C-2,C-3

Student-3,85.69,C-1,C-3,C-2

Student-4,80.83,C-1,C-3,C-2

Student-5,41.23,C-1,C-2,C-3

Output

C-1 80.83

C-2 48.03

C-3 41.23

Explanation

Here student-1 with highest percentage gets his first preferred college, then the next top scorer, Student-3 gets his first preferred college and so on.

However, we can see that there are only three seats in college 1 so only students with good percentage get admitted (i.e., student-1, student-3, student-4).

Now college 1 allocation quota is complete. Hence no new student can be admitted to college 1. college 2 and college 3 still have one and two seats respectively. Now, Student-2 and Student-5 are yet to be admitted.

Both student's priority is college 2 as second choice, but Student-2 is admitted to college 2 due to higher percentage (i.e., Student-2 Percentage> Student-5 Percentage).

Now there are only 0, 0, 2 seats left in college 1, college 2 and college 3 respectively. So, Student-3 is admitted to college 3 based on his preference. Here there is no need of round 2 as all students are admitted to colleges and none of them are awaiting admissions.

Now, C-1 = [Student-1, Student-3, Student-4], C-2=[Student-2], C-3=[Student-5]. For C-1, Cut-off is 80.83 because Student with least percentage in C-1 is Student-4. Similarly for C-3, it is 41.23 Display these Cut-off in sorted order.

Example 2

Input

5 5

2 1 1 1 2

Student-1,97.05,C-1,C-3,C-2

Student-2,48.03,C-1,C-2,C-3

Student-3,85.69,C-1,C-3,C-2

Student-4,80.83,C-1,C-3,C-2

Student-5,41.20,C-1,C-2,C-3

Output

C-1 85.69

C-3 80.83

C-2 48.03

C-5 41.2

C-4 n/a

Explanation

Here allocation is done based on percentage and preference, that is student with high percentage is admitted based on his choice of preference. So, Student-1, Student-2, Student-3, Student-4 are admitted based on their score and choice.

However, Student-5 is not admitted because all the choice of his/her colleges is full. So, now round 2 starts for student-5. Student-5 is admitted based on his/her percentage and maximum number of seats available in a college.

Student-5 can be admitted to C-5 since it has highest number of vacant seats viz 2.

Now, C-1= [Student-1, Student-3], C-2=[Student-2], C-3=[Student-4], C-4= [ ], C-5=[Student-5].

So, Cut-off for C-4 is 'n/a', because no student is admitted to it and Cut-off for C-5 is 41.23(student with least percentage i.e., 41.23).

Display the cut-offs of colleges in descending order. Since no student got admitted to college 4 display it in last line as C-4 n/a.

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