Dynamic Fibonacci

If we want to understand the true essence of dynamic programming, we should consider the simple example of fibonacci series. Using the conventional algorithm the time complexity of the solution is O(2^n).

 def fibonacci(n):
    i, a, b = 1, 0, 1
    while(i<=n):
         a, b = b, a+b
         i += 1
    return b

But using the dynamic programming we can reduce the function call, as well as the time complexity to O(n).

class Main {
 int[] f = new int[100];
 
 public int fibonacci(int n) {
       f[0] = f[1] = 1;
       for(int i=2;i<=n;i++) {
            f[i] = f[i-1] + f[i-2];
       }
 return f[n];
 }
}

Author: ashiquechowdhury

A software developer, and a data science enthusiast

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