Example of Big O of 2^n

Question

So I can picture what an algorithm is that has a complexity of n^c, just the number of nested for loops.

for (var i = 0; i < dataset.len; i++ {
    for (var         


        

Answer 1

  int Fibonacci(int number)
 {
  if (number <= 1) return number;

  return Fibonacci(number - 2) + Fibonacci(number - 1);
 }

Growth doubles with each additon to the input data set. The growth curve of an O(2N) function is exponential - starting off very shallow, then rising meteorically. My example of big O(2^n), but much better is this:

public void solve(int n, String start, String auxiliary, String end) {
   if (n == 1) {
       System.out.println(start + " -> " + end);
   } else {
       solve(n - 1, start, end, auxiliary);
       System.out.println(start + " -> " + end);
       solve(n - 1, auxiliary, start, end);
   }

In this method program prints all moves to solve "Tower of Hanoi" problem. Both examples are using recursive to solve problem and had big O(2^n) running time.