Order of complexity of fibonacci functions -


i have following 3 algorithms give fibonacci numbers. know how able find out each of order of complexity. know how might able determine this?

method 1 ------------------------------------------------------------------------ long long fibb(long long a, long long b, int n) {     return (--n>0)?(fibb(b, a+b, n)):(a); }  method 2 ------------------------------------------------------------------------ long long int fibb(int n) {     int fnow = 0, fnext = 1, tempf;     while(--n>0){         tempf = fnow + fnext;         fnow = fnext;         fnext = tempf;         }         return fnext;    }  method 3 ------------------------------------------------------------------------ long long unsigned fib(unsigned n) {     return floor( (pow(phi, n) - pow(1 - phi, n))/sqrt(5) ); }

correct me if wrong, guess method 1 o(2^n) since recursive, medtod 2 o(n) , last 1 o(1).

methods 1 , 2 have complexity o(n). reasons straightforward:

  • method 1 recurses n-1 times, each recursion performs simple arithmetic operation.
  • method 2 iterates n-1 times, each iteration has constant time, simple math again.

method 3 has indeed complexity of o(1), may not compute correct value, merely approximation.


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