[SOLVED] how can i generate this series of sequence using recursion?

how can i generate this series of sequence using recursion?

the question goes like this We define sequences Sn as follows.

S1 is a sequence of length 1 containing a single 1. Sn(n is an integer greater than or equal to 2) is a sequence obtained by concatenating Sn−1 ,n,Sn−1 in this order.

For example, S 2 and S 3 is defined as follows.

S 2 is a concatenation of S1 , 2, and S1 , in this order, so it is 1,2,1. S3 is a concatenation of S2 , 3, and S2 , in this order, so it is 1,2,1,3,1,2,1. Given N, print the entire sequence S N .

i want to create a string function and decrease it value using functions like stoi and genrate the sequence recursively and print the output

Solution

The problem description you got already provided the recurrence relation and the base case:

Base case: 𝑆₁ = 1
Recurrence: 𝑆_𝑛 = 𝑆_𝑛−1, 𝑛, 𝑆_𝑛−1

And this is really it. You can formulate this in pseudo code like this, but it really is just a different syntax to express the same thing:

function S(n):
    if n == 1 then:  ' Base case
        output(1)
    else:            ' Recursion
        S(n-1)
        output(n)
        S(n-1)
    end if

I would actually shift the base case to 𝑆₀ and define it as "nothing". Then the pseudo code becomes:

function S(n):
    if n > 0 then:
        S(n-1)
        output(n)
        S(n-1)
    end if

In an actual implementation in a programming language, you would replace output with whichever construct is appropriate. Like in Python you could go for a generator:

def generate_S(n):
    if n > 0:
        yield from generate_S(n-1)
        yield n
        yield from generate_S(n-1)

print(*generate_S(3))

This outputs:

1 2 1 3 1 2 1