Google Kickstart| Solution of python Problem of Trains

 Google Kickstart

Train Problem In Python

There are number intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at number  of these intermediate stations so that no two stopping stations are consecutive?

Testcases1:

Input:

Tstation=10

n=5

Output:

6

Testcases2:

Input:

Tstation=15

n=6

Output=210

#In this program there is just to find no of ways i.e we have learnt already in class11  maths permutation and combination chapter  ch-7.

So here just to find the combination i.e in how many ways the train can stop without consecutive station.

"""

Write a program to count the ways to stop the train without consecutive stations

Factorial means 4!=4*3*2*1=24

5=5*4*3*2*1=120

This is docs string 

"""

#Let initialize the program and understand the program by dividing in small parts

#first input total number of intermediate station

#Then take input how many stations train has to stop without consecutive stations ley understand 

# 1 2 3 4 5 6 7 8 9 10 11 12

#here 1 is represent first station similarily numbers represnt name of station

#Tstation is a variable to input totoal number of station

Tstation=int(input("Enter a number of total stations:"))

#n is a number of stations where train will stop

n=int(input("Enter in how many stations have to stop the train without consecutive station: "))

Noofways=0

#here if we have to stop only at 4 stations in between 12 stations,so

#first we will remove four station where train will stop.

#Now remainings are 

 #   #   #   #   #    #    #    #     # 

#And space between these remaing stations are 9 .

#so no of ways of where train will not stop is 9 C4 ways

#because nCr=(n!)/((n-r)!*r!)

#therefore 9C4=9!/(9-4)!*4!

 ! this sign represent factorial of that number

#Here remaining mean if Tstation=12 and n=4 then remaining=12-4+1=9

remaining=Tstation-n+1

#now we will go to math library to get factorial function to get factorial of the numbers

from math import factorial

Noofways=(factorial(remaining))//(factorial(n)*factorial(remaining-n))

#Then use print() function to print number of ways

print(Noofways)

Let us understand by read steps given below:

1.First if you have to  know to make the combinations and to find ways .Then  Take a input of total no. of stations using input() function and type  caste in int() function, Similarily take input of number of stations that at  how many stations train will stop .

2.Then assume number of ways is 0.

3.You know if there is 12 stations and train will stop at 4 stations will consecutive station,So remove 4 stations then remaining station are 8,but in between the stations there 9 places are left where there would must be 4 station in between the place .So we will find the combinations of 9 stations in which for 4 stations where train will stop.

4.Use formula n C r = n!/(n-r)! * r!

5.Then use print function to print number of ways.

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