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 
     
      #include 
      
       using namespace std;const int MAXN = 1000000;const int ONE_HUNDRED_MILLION = 100000000;int cs[ONE_HUNDRED_MILLION+1];// Collatz sequence countint 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 
     
      using namespace std;//#define DEBUGconst int MAXN = 1000000;// Collatz sequence countint 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;}