Fibonacci – Normal vs Dynamic programming Huge Time complexity Difference

Dynamic programming, guarantees to find the optimal solution of a problem if the solution exists. It basically follows these steps,

  • Divide the main complex problems into sub-problems
  • Saves the sub-problem result found
  • Apply the saved result rather than re-computing the solution again.

Let’s understand the differences it provides (time complexity difference) with dynamic programming approach,

Fibonacci Program – Normal & Dynamic Programming:

import java.time.LocalDateTime;

public class Fibonacci {

    public static void main(String[] args) {
        // 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
        int n = 10;

        // normal
        long ldtStart =;
        int fibo = nthFibo(n);
        long ldtEnd =;
        System.out.println("Total Execution Time: " + (ldtEnd - ldtStart));

        // with dynamic programming
        long ldtStartDP =;
        int fiboDP = nthFiboDP(n);
        long ldtEndDP =;
        System.out.println("Total Execution Time for DP: " + (ldtEndDP - ldtStartDP));

    private static int nthFibo(int n) {
        if (n <= 1) {
            return n;
        return nthFibo(n - 1) + nthFibo(n - 2);

    private static int nthFiboDP(int n) {
        if (n <= 1) {
            return n;

        int[] dp = new int[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        for (int i = 2; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];
        return dp[n];

If I run the above code, then my output is, (here execution time is very less in both the approaches)

Total Execution Time: 0
Total Execution Time for DP: 0

Now with the n value as = 20,

Total Execution Time: 999700
Total Execution Time for DP: 0

Now with the n value as n =30,

Total Execution Time: 3998800
Total Execution Time for DP: 0

And strange problem here is if the n value is greater than 30 then time complexities getting higher and higher and at n = 100 literly in my machine nothing works for few mins and completely hangs out.

Now, in order to address all these stuff’s in a efficient way, dynamic programming helps really in a greater extend.

Hope this simple program helps you to understand how dynamic programming brings much better improvements from the time complexities perspective.


  • Hello NgDeveloper Team,

    Nice blog! I am editor at Java Code Geeks ( We have the JCG program (see, that I think you’d be perfect for.

    If you’re interested, send me an email to and we can discuss further.

    Best regards,
    Eleftheria Drosopoulou

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