Question

I’m trying implement simple solution for rod cutting problem. Below is the code for naive and dynamic programming solutions,

public static int rodCutNaive(int[] a, int n) {
    if (n == 1) {
        return a[0];
    }
    int q = 0;
    for (int i = 1; i <= n; i++) {
        int optimalCut = a[i - 1] + rodCutNaive(a, n - i);
        if (q < optimalCut) {
            q = optimalCut;
        }
    }
    return q;
}

public static int rodCutDPBottomUp(int[] a, int n) {
    if (n == 1) {
        return a[0];
    }
    int[] s = new int[a.length];
    s[0] = a[0];

    for (int i = 2; i <= n; i++) {
        s[i - 1] = a[i - 1];
        for (int j = 1; j <= i - 1; j++) {
            int optimalCut = a[j - 1] + s[i - j - 1];
            if (s[i - 1] < optimalCut) {
                s[i - 1] = optimalCut;
            }
        }
    }

    return s[n - 1];
}

And I tested with below method,

public void testRodCutEfficiency() {
    int[] a = { 1, 5, 8, 9, 10, 17, 17, 20, 22, 25, 26, 29, 34, 35, 39, 45,
            46, 47, 50, 51 };

    long t1 = System.nanoTime();
    for (int i = 0; i < 1000; i++)
        Rod.rodCutNaive(a, a.length);
    long t2 = System.nanoTime();
    for (int i = 0; i < 1000; i++)
        Rod.rodCutDPBottomUp(a, a.length);
    long t3 = System.nanoTime();

    System.out.println("Problem size = " + a.length);
    System.out.println("Naive = " + (t2 - t1));
    System.out.println("DP    = " + (t3 - t2));
}

Output:

Problem size = 20
Naive = 7989627046
DP    = 7913165707

May be compiler doing some kind of tail recursion optimization with naive version or is it possible that JVM remebers solutions to previous calls of methods?

Oh, Sorry guys. It’s a copy paste mistake. I called same method both the times. Now I’ve changed it and new output is,

Problem size = 20
Naive = 7764056945
DP    = 1324966

I tried to delete the question but it already has answers.

Answer 1

You’re calling rodCutNaive both times.