How to interpret code for counting ways to reach the n’th stair?

Question

I am trying to interpret this code from geeksforgeeks:

def fib(n): 
    if n <= 1: 
        return n 
    return fib(n-1) + fib(n-2) 

def countWays(s): 
    return fib(s + 1) 

s = 4
print "Number of ways = ", 
print countWays(s)

I can't seem to get the correct answer when I substitute the numbers into the function. Here's my thought process:

def countWays(s): 
    return fib(4 + 1) #5

#this goes into fib(n). 5 is not less than or equal to n so I skip to the else statement:

fib(5-1) + fib(5-2) 

#fib(4) + fib(3) since these are still not less than or equal to n I input 
#them into the function again.

 fib(4-1) + fib(3-2) 

#fib(3) + fib(1) now that one of the n is less than or equal to n, 
#I return n and get 4 (3+1). The answer is supposed to be 5.

Your logic should branch down like a tree. Notice when you send 1 number into fib you get a return of two fib functions. So those going in return 4 fib functions, etc. Add some print statements to track the function progress as it going through and it will probably make more sense. — MyNameIsCaleb, Sep 28 '19 at 16:52

score 0 · Accepted Answer · answered Sep 28 '19 at 17:11

Check it out like this:

# Python 3
def fib(n): 
    print(f'Fib: {n}')
    if n <= 1:
        print('End')
        return n
    else:
        print(f'Send: {n-1} and {n-2}')
    return fib(n-1) + fib(n-2) 

def countWays(s): 
    return fib(s + 1) 

s = 4
print("Number of ways = ")
print(countWays(s))

Results

Fib: 5           # A
Send: 4 and 3    # A.B and A.C
Fib: 4           # A.B
Send: 3 and 2    # A.B.1 and A.B.2
Fib: 3           # A.B.1
Send: 2 and 1    # A.B.1.1 and A.B.1.2
Fib: 2           # A.B.1.1
Send: 1 and 0    # A.B.1.1.1 and A.B.1.1.2
Fib: 1           # A.B.1.1.1
End              # (END) A.B.1.1.1       -> 1
Fib: 0           # A.B.1.1.2
End              # (END) A.B.1.1.2       -> 0
Fib: 1           # A.B.1.2
End              # (END) A.B.1.2         -> 1
Fib: 2           # A.B.2
Send: 1 and 0    # A.B.2.1 and A.B.2.2
Fib: 1           # A.B.2.1
End              # (END) A.B.2.1         -> 1
Fib: 0           # A.B.2.2
End              # (END) A.B.2.2         -> 0
Fib: 3           # A.C
Send: 2 and 1    # A.C.1 and A.C.2
Fib: 2           # A.C.1
Send: 1 and 0    # A.C.1.1 and A.C.1.2
Fib: 1           # A.C.1.1
End              # (END) A.C.1.1         -> 1
Fib: 0           # A.C.1.2
End              # (END) A.C.1.2         -> 0
Fib: 1           # A.C.2
End              # (END) A.C.2           -> 1
5                                     # 1 + 0 + 1 + 1 + 0 + 1 + 0 + 1

And now substitute

>>> print(fib(5))
Fib: 5
Send: 4 and 3
Fib: 4
...
Fib: 1
End
5

Same result.

How to interpret code for counting ways to reach the n’th stair?

1 Answers1