Lecture "Introduction to Computational Thinking", exercise 2

[essepuntato]

What is the result of applying the latest natural language definition of the Fibonacci function in Section "Natural languages vs. programming languages" using “7” as input?

[MattiaSpadoni]

Input= 7 Output= (?)

n=7 a=1 b=1 c=2; n-- n= 6 a=1 b=2 c=3; n-- n= 5 a=2 b=3 c=5; n-- n= 4 a=3 b=5 c=8; n-- n=3 (now I can return "c") a= 5 b=8 C= 13;

Output= 13

[ilsamoano]

The function for calculating the nt​ h Fibonacci number takes as input an integer “n”. If “n” is less than or equal to 0, then 0 is returned as result. Otherwise, if “n” is equal to 1, then 1 is returned. Otherwise, return the sum of the same function with “n-1” as input and still the same function with “n-2” as input.

def Fibo(n): 
    if n<0: 
        return 0 
    elif n==1: 
        return 1
    else: 
        return Fibo(n-1)+Fibo(n-2) 

print(Fibo(7)) 

output: 13

(for code explanation: https://www.geeksforgeeks.org/program-for-nth-fibonacci-number/)

[simayguzel]

def F(n): if (n == 0) : return 0 if (n == 1 or n== 2) : return 1 else: return F(n-1)+F(n-2)

print (F(7))

Output: 13

[mangiafrangette]

The function for calculating the nt​ h Fibonacci number takes as input an integer “n”. If “n” is less than or equal to 0, then 0 is returned as result. Otherwise, if “n” is equal to 1, then 1 is returned. Otherwise, return the sum of the same function with “n-1” as input and still the same function with “n-2” as input.

def Fibo(n): 
    if n<0: 
        return 0 
    elif n==1: 
        return 1
    else: 
        return Fibo(n-1)+Fibo(n-2) 

print(Fibo(7)) 

output: 13

(for code explanation: https://www.geeksforgeeks.org/program-for-nth-fibonacci-number/)

Add an equal on line 2 ("if n is less than or equal to 0 [...]"). if n <= 0: Also, maybe is not clear to everyone that is written in Python. Good job!

[delfimpandiani]

The function for calculating the n-th Fibonacci number takes as input an integer “n”. If “n” is less than or equal to 0, then 0 is returned as result. Otherwise, if “n” is equal to 1, then 1 is returned. Otherwise, return the sum of the same function with “n-1” as input and still the same function with “n-2” as input.

def F(n): if (n <= 0) : return 0 if (n == 1 or n== 2) : return 1 else: return F(n-1)+F(n-2)

F(7) = 13 The logic behind this result is the following:

F(7) = F(6) + F(5) = 8 + 5 = 13 F(6) = F(5) + F(4) = 5 + 3 = 8 F(5) = F(4) + F(3) = 3 + 2 = 5 F(4) = F(3) + F(2) = 2 + 1 = 3 F(3) = F(2) + F(1) = 1 + 1 = 2 F(2) = F(1) + F(0) = 1 + 0 = 1 F(1) = 1 F(0) = 0

[tceron]

a = 1;
b = 1;
while (1) { c = a + b; }
if (n <= 3) return c;
a = b;
b = c; { c = a + b; }
n--; (which means to subtract 1)

Input = 7

n= 7 a= 1 b= 1 c = 2 n-- (subtract one) n=6 (n <= 3 so return c) n= 6 a= 1 b= 2 c = 3 n-- n= 5 n= 5 a= 2 b= 3 c = 5 n-- n= 4 n= 4 a= 3 b= 5 c = 8 n= 3
n= 3 a= 5 b= 8 c = 13

{ c = a + b; } So the output is 13.

[lisasiurina]

Input= 7

If (n <=0) then return 0 If (n <=2) then return 1 If (n <=3) then return c

а=1 b=1 c=a+b

a=b b=c

If n=7 a=1 b=1 c=2; 
then n-- 
If n n= 6 a=1 b=2 c=3;
 then n-- 
If n= 5 a=2 b=3 c=5; 
then n-- If n= 4 a=3 b=5 c=8; 
then n-- 
If n=3 a= 5 b=8 C= 13; then return 13 Output 13

[friendlynihilist]

The function for calculating the n^th Fibonacci number takes as input an integer “n”. If “n” is less than or equal to 0, then 0 is returned as result. Otherwise, if “n” is equal to 1, then 1 is returned. Otherwise, return the sum of the same function with “n-1” as input and still the same function with “n-2” as input.

input=7 a=1 b=1 c=(a+b)

If n=7 a=1 b=1 c=2; n-- (subtract 1) If n=6 a=1 b=2 c=3; n-- If n=5 a=2 b=3 c=5; n-- If n=4 a=3 b=5 c=8; n-- If n=3 a=5 b=8 c=13; then return c output=13

[SeverinJB]

A return statement in a while loop is equal to a break statement. Hence, as soon as n <= 3 the return function is trigged and the while loop stops. Based on this, the while loop stops as soon as n was reduced to 3 by n--. The loop runs a total of 5 times. During the last run, it returned c = 13.

n = 7 —> a = 1, b = 1 —> c = a + b = 2 —> 
a = b = 1, b = c = 2 —> n = 7 - 1 = 6 —> c = a + b = 3 —> 
a = b = 2, b = c = 3 —> n = 6 - 1 = 5 —> c = a + b = 5 —> 
a = b = 3, b = c = 5 —> n = 6 - 1 = 4 —> c = a + b = 8 —> 
a = b = 5, b = c = 8 —> n = 6 - 1 = 3 —> c = a + b = 13 —> c = 13

[Ioanna96]

n=7 a=1 b=1 c=2 n-- n=6 a=1 b=2 c=3 n-- n=5 a=2 b=3 c=5 n-- n=4 a=3 b=5 c=8 n-- n=3 a=5 b=8 c=13 if “n” is less than or equal to “3” then return “c” Output=13

[dafnikitsiki]

Input= 7 Output= (?)

n=7 a=1 b=1 c=2; n-- n= 6 a=1 b=2 c=3; n-- n= 5 a=2 b=3 c=5; n-- n= 4 a=3 b=5 c=8; n-- n=3 (now I can return "c") a= 5 b=8 C= 13;

Output= 13

So, F(3) in Fibonacci's sequence is the key to find the output for any input number!