Project Euler Problem 92 Square digit chains

Square digit chains

Problem 92

A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.

For example,

44 → 32 → 13 → 10 → 1 → 1
85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89

Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.

How many starting numbers below ten million will arrive at 89?

C++(Faster):

#include <iostream>
#include <cstring>
#include <stack>

using namespace std;

const int MAXN = 10000000;

int arrive[MAXN], chainno[MAXN];
int no;

int nextval(int n)
{
    int sum, v;

    sum = 0;
    while(n) {
        v = n % 10;
        sum += v * v;
        n /= 10;
    }

    return sum;
}

void makechain(int n)
{
    no++;

    while(n != 1 && n != 89) {
        if(chainno[n] > 0) {
            n = arrive[chainno[n]];
            break;
        }
        chainno[n] = no;
        n = nextval(n);
    }

    arrive[no] = n;
}

int main()
{
    int n;

    while(cin >> n && n <= MAXN) {
        memset(arrive, 0, sizeof(arrive));
        memset(chainno, 0, sizeof(chainno));
        chainno[1] = 1;
        arrive[1] = 1;
        chainno[89] = 2;
        arrive[2] = 89;
        no = 2;

        for(int i=1; i<n; i++)
            if(i != 1 && i != 89)
                makechain(i);

        int count = 0;
        for(int i=1; i<n; i++)
            if(arrive[chainno[i]] == 89)
                count++;

        cout << count << endl;
    }

    return 0;
}

C++:

#include <iostream>
#include <cstring>
#include <stack>

using namespace std;

const int MAXN = 10000000;

int arrive[MAXN];

int nextval(int n)
{
    int sum, v;

    sum = 0;
    while(n) {
        v = n % 10;
        sum += v * v;
        n /= 10;
    }

    return sum;
}

void makechain(int n)
{
    stack<int> s;

    while(n != 1 && n != 89) {
        if(arrive[n] > 0) {
            n = arrive[n];
            break;
        }
        s.push(n);
        n = nextval(n);
    }

    while(!s.empty()) {
        int val = s.top();
        s.pop();
        arrive[val] = n;
    }
}

int main()
{
    int n;

    while(cin >> n && n <= MAXN) {
        memset(arrive, 0, sizeof(arrive));
        arrive[1] = 1;
        arrive[89] = 89;

        for(int i=1; i<n; i++)
            makechain(i);

        int count = 0;
        for(int i=1; i<n; i++)
            if(arrive[i] == 89)
                count++;

        cout << count << endl;
    }

    return 0;
}