In this article, we’ll look at The Friends-Travel Problem, which is highly interesting.

** Friends-Travel Problem:**

Assume n friends want to go to a party; they can travel alone or with another friend as a couple. We presume that n motorbikes are offered for n buddies.

We need to figure out how many different ways the n friends can get to the party, either individually or in pairs of two as a couple.

**Answer:**

One can either manually implement the naive technique using loops and if-else statements or use the quicker Recursion approach.

Before going into the problem just have a glance over the recursion.

To solve a larger problem, it is necessary to divide it into smaller difficulties.

Let us consider the lower values of n like ( 1, 2, and 3).

There are only one and two viable options for n = 1 and n = 2, respectively. And for n = 3, there are four alternative outcomes. How?

For each value of n, a friend has two options: either travel alone or search for n-1 friends.

Alternatively, the friend might choose a friend from the n-1 friends to travel with, and we will then look for n-2 friends.

**Examples:**

**Example1:**

**Input:**

Given number of friends = 3

**Output:**

Different ways the 3 friends can get to the party = 4

**Example2:**

**Input:**

Given number of friends = 5

**Output:**

Different ways the 5 friends can get to the party = 26

## Program for Friends-Travel Problem in Python

### Method #1: Using Recursion (Static Input)

**Approach:**

- Give the number(no of friends) as static input and store it in a variable.
- Create a recursive function say numberof_ways() which accepts the given number as an argument and returns the total number of ways friends can get to the party.
- Inside the function, check if the given number is less than 3 using the if conditional statement.
- If it is true, then return the given number.
- Return the value of {numberof_ways(no_frnds-1)) + ((no_frnds-1) * numberof_ways(no_frnds-2)} (Recursive Logic).
- Pass the given number as an argument to the numberof_ways() function and store it in a variable.
- Print the above result.
- The Exit of the Program.

**Below is the implementation:**

# Create a recursive function say numberof_ways() which accepts the given number # as an argument and returns the total number of ways friends can get to the party. def numberof_ways(no_frnds): # Inside the function, check if the given number is less than 3 using the if # conditional statement. if(no_frnds < 3): # If it is true, then return the given number. return no_frnds # Return the value of count_no_ways(no_frnds-1)) + ((no_frnds-1) * # count_no_ways(no_frnds-2) (Recursive Logic). return (numberof_ways(no_frnds-1)) + ((no_frnds-1) * numberof_ways(no_frnds-2)) # Give the number(no of friends) as static input and store it in a variable. no_frnds = 3 # Pass the given number as an argument to the numberof_ways() function and # store it in a variable. rslt = numberof_ways(no_frnds) # Print the above result. print("Different ways the", no_frnds, "friends can get to the party = ", rslt)

**Output:**

Different ways the 3 friends can get to the party = 4

### Method #2: Using Recursion (User Input)

**Approach:**

- Give the number(no of friends) as user input using the int(input()) function and store it in a variable.
- Create a recursive function say numberof_ways() which accepts the given number as an argument and returns the total number of ways friends can get to the party.
- Inside the function, check if the given number is less than 3 using the if conditional statement.
- If it is true, then return the given number.
- Return the value of {numberof_ways(no_frnds-1)) + ((no_frnds-1) * numberof_ways(no_frnds-2)} (Recursive Logic).
- Pass the given number as an argument to the numberof_ways() function and store it in a variable.
- Print the above result.
- The Exit of the Program.

**Below is the implementation:**

# Create a recursive function say numberof_ways() which accepts the given number # as an argument and returns the total number of ways friends can get to the party. def numberof_ways(no_frnds): # Inside the function, check if the given number is less than 3 using the if # conditional statement. if(no_frnds < 3): # If it is true, then return the given number. return no_frnds # Return the value of count_no_ways(no_frnds-1)) + ((no_frnds-1) * # count_no_ways(no_frnds-2) (Recursive Logic). return (numberof_ways(no_frnds-1)) + ((no_frnds-1) * numberof_ways(no_frnds-2)) # Give the number(no of friends) as user input using the int(input()) function and store it in a variable. no_frnds = int(input("Enter some random number = ")) # Pass the given number as an argument to the numberof_ways() function and # store it in a variable. rslt = numberof_ways(no_frnds) # Print the above result. print("Different ways the", no_frnds, "friends can get to the party = ", rslt)

**Output:**

Enter some random number = 5 Different ways the 5 friends can get to the party = 26