Python Program for Dining Table Seating Arrangement Problem

Problem Statement

In a Conference ,attendees are invited for a dinner after the conference.The Co-ordinator,Sagar arranged around round tables for dinner and want to have an impactful seating experience for the attendees.Before finalizing the seating arrangement,he wants to analyze all the possible arrangements.These are R round tables and N attendees.In case where N is an exact multiple of R,the number of attendees must be exactly N//R,,If N is not an exact multiple of R, then the distribution of attendees must be as equal as possible.Please refer to the example section before for better understanding.
For example, R = 2 and N = 3
All possible seating arrangements are
(1,2) & (3)
(1,3) & (2)
(2,3) & (1)
Attendees are numbered from 1 to N.

Input Format:

• The first line contains T denoting the number of test cases.
• Each test case contains two space separated integers R and N, Where R denotes the number of round tables and N denotes the number of attendees.

Output Format:

Single Integer S denoting the number of possible unique arrangements.

Constraints:

• 0 <= R <= 10(Integer)
• 0 < N <= 20 (Integer)

testcases = int(input())
for i in range(testcases):
    tables, people = map(int, input().split())

    if tables >= people:
        print(1)
    else:
        PA = people // tables
        PB = PA + 1
        TB = people % tables
        TA = tables - TB
        
        # Using DP to store factorials pre-hand
        fact = [1]
        for j in range(1, people + 2):
            fact.append(j*fact[j-1])

        # Dividing people between tables
        divide = fact[people] / (pow(fact[PA], TA) * pow(fact[PB], TB) * fact[TA] * fact[TB])
        if PB >= 4:
            result = divide * (pow(fact[PA - 1] / 2, TA) * pow((fact[PB - 1] / 2), TB))
        else:
            result = divide

        print(int(result))