Project Euler Problem 14 Longest Collatz sequence

Longest Collatz sequence

Problem 14

The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even)
n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.

C++:

#include <iostream>
#include <cstring>

using namespace std;

const int MAXN = 1000000;
const int ONE_HUNDRED_MILLION = 100000000;

int cs[ONE_HUNDRED_MILLION+1];

// Collatz sequence count
int cscount(long long x)
{
    if(x <= ONE_HUNDRED_MILLION && cs[x])
        return cs[x];

    int count;
    if(x % 2 == 0)
        count = 1 + cscount(x / 2);
    else
        count =  1 + cscount(x * 3 + 1);

    if(x <= ONE_HUNDRED_MILLION)
        cs[x] = count;

    return count;
}

int main()
{
    memset(cs, 0, sizeof(cs));
    cs[1] = 1;

    int n, ans;
    while(cin >> n && n <= MAXN) {
        ans = 1;
        for(int i=1; i<=n; i++) {
            cs[i] = cscount(i);
            if(cs[i] > cs[ans])
                ans = i;
        }
        cout << ans << endl;
    }

    return 0;
}

Input data:

999999

C++(Too slow):

#include <iostream>

using namespace std;

//#define DEBUG

const int MAXN = 1000000;

// Collatz sequence count
int cscount(int start)
{
#ifdef DEBUG
        cout << start << ": ";
#endif

    int count = 0;
    for(;;) {
#ifdef DEBUG
        cout << start << " ";
#endif

        count++;
        if(start == 1)
            break;
        if(start & 1)
            start = 3 * start + 1;
        else
            start >>= 1;
    }

#ifdef DEBUG
    cout << endl;
#endif

    return count;
}

int main()
{
    int n, ans, maxcount=0, temp;
    while(cin >> n && n <= MAXN) {
        for(int i=1; i<=n; i++) {
            temp = cscount(i);
            if(temp > maxcount) {
                maxcount = temp;
                ans = i;
            }
        }
        cout << ans << endl;
    }

    return 0;
}