Dining Table Seating Arrangement | Codevita | Python Solution

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)

Sample Input 1:
1
2 5

Sample Output 1:

10

Explanation:

R = 2, N = 5

(1,2,3) & (4,5)

(1,2,4) & (3,5)

(1,2,5) & (3,4)

(1,3,4) & (2,5)

(1,3,5) & (2,4)

(1,4,5) & (2,3)

(2,3,4) & (1,5)

(2,3,5) & (1,4)

(2,4,5) & (1,3)

(3,4,5) & (1,2)

Arrangements like

(1,2,3) & (4,5)

(2,1,3) & (4,5)

(2,3,1) & (4,5) etc.

But as it is a round table,all the above arrangements are same.

Psuedocode:

•     Input No.of.Testcases
•     Input Table and people in space delimiters.
•     if table>=people print(1)
•     else:
•         find no.of.people in type A table and no.of.people in type B table.
•         Find no.of Type A and Type B table.
•         Establish factorial Array.
•         Divide people in groups using formula derived
•         After dividing them arrange them in tables and find the possible arrangements using formula.
•         Print the arrangements.

Program:

	for i in range(int(input())):
	table,people=map(int,input().split())
	if table>=people:
	print(1)
	else:
	PA=people//table
	PB=PA+1
	TB=people%table
	TA=table-TB
	fact=[1,1]
	for i in range(2,people+2):
	x=i*fact[i-1]
	fact.append(x)
	#To find no.of.possible ways to divide people among groups
	divide=fact[people]//((fact[PA]**TA)*(fact[PB]**TB)*fact[TA]*fact[TB])
	#To find no.of.arrangements in a circular table
	if PB>=4:
	arrange=int(divide*(fact[PA-1]/2)**TA*(fact[PB-1]/2)**TB)
	else:
	arrange=divide
	print(arrange)

view raw DiningTableSeatingArr.py hosted with ❤ by GitHub