How to improve the performance of the recursive method?

Question

I'm learning data structures and algorithms, and here is a question that I'm stuck with.

I have to improve the performance of the recursive call by storing the value into memory.

But the problem is that the non-improved version seems faster than this.

Can someone help me out?

Syracuse numbers are a sequence of positive integers defined by the following rules:

syra(1) ≡ 1

syra(n) ≡ n + syra(n/2), if n mod 2 == 0

syra(n) ≡ n + syra((n*3)+1), otherwise

import java.util.HashMap;
import java.util.Map;

public class SyraLengthsEfficient {

    int counter = 0;
    public int syraLength(long n) {
        if (n < 1) {
            throw new IllegalArgumentException();
        }

        if (n < 500 && map.containsKey(n)) {
            counter += map.get(n);
            return map.get(n);
        } else if (n == 1) {
            counter++;
            return 1;
        } else if (n % 2 == 0) {
            counter++;
            return syraLength(n / 2);
        } else {
            counter++;
            return syraLength(n * 3 + 1);
        }
    }

    Map<Integer, Integer> map = new HashMap<Integer, Integer>();

    public int lengths(int n) {
        if (n < 1) {
            throw new IllegalArgumentException();
        }    
        for (int i = 1; i <= n; i++) {
            syraLength(i);
            if (i < 500 && !map.containsKey(i)) {
                map.put(i, counter);
            }
        }    
        return counter;
    }

    public static void main(String[] args) {
        System.out.println(new SyraLengthsEfficient().lengths(5000000));
    }
}

Here is the normal version that i wrote:

 public class SyraLengths{

        int total=1;
        public int syraLength(long n) {
            if (n < 1)
                throw new IllegalArgumentException();
            if (n == 1) {
                int temp=total;
                total=1;
                return temp;
            }
            else if (n % 2 == 0) {
                total++;
                return syraLength(n / 2);
            }
            else {
                total++;
                return syraLength(n * 3 + 1);
            }
        }

        public int lengths(int n){
            if(n<1){
                throw new IllegalArgumentException();
            }
            int total=0;
            for(int i=1;i<=n;i++){
                total+=syraLength(i);
            }

            return total;
        }

        public static void main(String[] args){
            System.out.println(new SyraLengths().lengths(5000000));
        }
       }

EDIT

It is slower than non-enhanced version.

import java.util.HashMap;
import java.util.Map;

public class SyraLengthsEfficient {

    private Map<Long, Long> map = new HashMap<Long, Long>();

    public long syraLength(long n, long count) {

        if (n < 1)
            throw new IllegalArgumentException();

        if (!map.containsKey(n)) {
            if (n == 1) {
                count++;
                map.put(n, count);
            } else if (n % 2 == 0) {
                count++;
                map.put(n, count + syraLength(n / 2, 0));
            } else {
                count++;
                map.put(n, count + syraLength(3 * n + 1, 0));
            }
        }

        return map.get(n);

    }

    public int lengths(int n) {
        if (n < 1) {
            throw new IllegalArgumentException();
        }
        int total = 0;
        for (int i = 1; i <= n; i++) {
            // long temp = syraLength(i, 0);
            // System.out.println(i + " : " + temp);
            total += syraLength(i, 0);

        }
        return total;
    }

    public static void main(String[] args) {
        System.out.println(new SyraLengthsEfficient().lengths(50000000));
    }
}

FINAL SOLUTION (mark as correct by school auto mark system)

public class SyraLengthsEfficient {

private int[] values = new int[10 * 1024 * 1024];

public int syraLength(long n, int count) {

    if (n <= values.length && values[(int) (n - 1)] != 0) {
        return count + values[(int) (n - 1)];
    } else if (n == 1) {
        count++;
        values[(int) (n - 1)] = 1;
        return count;
    } else if (n % 2 == 0) {
        count++;
        if (n <= values.length) {
            values[(int) (n - 1)] = count + syraLength(n / 2, 0);
            return values[(int) (n - 1)];
        } else {
            return count + syraLength(n / 2, 0);
        }
    } else {
        count++;
        if (n <= values.length) {
            values[(int) (n - 1)] = count + syraLength(n * 3 + 1, 0);
            return values[(int) (n - 1)];
        } else {
            return count + syraLength(n * 3 + 1, 0);
        }
    }

}

public int lengths(int n) {
    if (n < 1) {
        throw new IllegalArgumentException();
    }
    int total = 0;
    for (int i = 1; i <= n; i++) {
        total += syraLength(i, 0);
    }
    return total;
}

public static void main(String[] args) {
    SyraLengthsEfficient s = new SyraLengthsEfficient();
    System.out.println(s.lengths(50000000));
}

}

Answer 1

Forget about the answers that say that your code is inefficient because of the use of a Map, that's not the reason why it's going slow - it's the fact that you're limiting the cache of calculated numbers to n < 500. Once you remove that restriction, things start to work pretty fast; here's a proof of concept for you to fill-in the details:

private Map<Long, Long> map = new HashMap<Long, Long>();

public long syraLength(long n) {

    if (!map.containsKey(n)) {
        if (n == 1)
            map.put(n, 1L);
        else if (n % 2 == 0)
            map.put(n, n + syraLength(n/2));
        else
            map.put(n, n + syraLength(3*n+1));
    }

    return map.get(n);

}

If you want to read more about what's happening in the program and why is so fast, take a look at this wikipedia article about Memoization.

Also, I think you're misusing the counter variable, you increment it (++) when a value is calculated the first time, but you accumulate over it (+=) when a value is found in the map. That doesn't seem right to me, and I doubt that it gives the expected result.