Recursion vs. Iteration (Fibonacci sequence)
For terseness, Let F(x) be the recursive Fibonacci So your are calling F(8) twice, F(7) 3 times, F(6) 5 times, F(5) 7 times.. and so on So with larger inputs, the tree gets bigger and bigger.
For terseness, Let F(x) be the recursive Fibonacci So your are calling F(8) twice, F(7) 3 times, F(6) 5 times, F(5) 7 times.. and so on So with larger inputs, the tree gets bigger and bigger.
You need to say to allow the name count_help to be used recursively within its definition.
C implementation of your bonus question, in three lines:
this turns the recursion in to a loop:
return factValue * printFactorial(factValue – factCounter); I assume that you should be using the “next” values instead of these. Edit: Also note that the function takes two parameters and is void. Returning factValue times void doesn’t make sense.
Check this: Call the method from main. Let me know if that helps.. 🙂
In fibonacci sequence each item is the sum of the previous two. So, you wrote a recursive algorithm. So, Now you already know fibonacci(1)==1 and fibonacci(0) == 0. So, you can subsequently calculate the other values. Now, And from fibonacci sequence 0,1,1,2,3,5,8,13,21…. we can see that for 5th element the fibonacci sequence returns 5. See here for Recursion Tutorial.
The time complexity, in Big O notation, for each function: This function is being called recursively n times before reaching the base case so its O(n), often called linear. This function is called n-5 for each time, so we deduct five from n before calling the function, but n-5 is also O(n). (Actually called order of n/5 times. … Read more
It is a guard against a stack overflow, yes. Python (or rather, the CPython implementation) doesn’t optimize tail recursion, and unbridled recursion causes stack overflows. You can check the recursion limit with sys.getrecursionlimit: and change the recursion limit with sys.setrecursionlimit: but doing so is dangerous — the standard limit is a little conservative, but Python stackframes can … Read more
Your algorithm is fine. However int is too small for your computations, it fails for this input: At some point integer overflows to negative value and your implementation goes crazy, recursing infinitely. Change int num to long num and you’ll be fine – for some time. Later you’ll need BigInteger. Note that according to Wikipedia on Collatz conjecture (bold mine): The longest progression for … Read more