UVa 10591 - Happy Number

题意：将给出数各个位上的数字的平方和加起来得到新的数字，依次往下推新数字，直到得到得到数字1（Happy number）或是与之前重复的数字（unhappy number）。

利用哈希表查找判重或是直接打表，因为输入最大是10的9次方的数字，因此得出的数字最大为9*9*9 = 729。

代码一（hash 0.020s）：

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <cmath>

using namespace std;
const int MaxSize  = 850;
int head[MaxSize], next[MaxSize];
int solve(int n)
{
    int t, sum = 0;
    while(n)
    {
        t = n % 10;
        sum += t * t;
        n /= 10;
    }
    return sum;
}
int insert(int s, int h)
{
    int u = head[h];
    while(u)
    {
        if(h == 1)
            return 1;
        if(head[u] == head[s])
            return 2;
        u = next[u];
    }
    next[s] = head[h];
    head[h] = s;
    return 0;
}
int main()
{
#ifdef test
    freopen("sample.txt", "r", stdin);
#endif
    int p, n, flag, cct = 0;
    scanf("%d", &p);
    while(p--)
    {
        int rear = 2;
        scanf("%d", &n);
        printf("Case #%d: %d", ++cct, n);
        memset(head, 0, sizeof(head));
        n = solve(n);
        while(1)
        {
            flag = insert(rear, n);
            if(!flag)
            {
                n = solve(n);
                ++rear;
            }
            else if(flag == 1)
            {
                printf(" is a Happy number.\n");
                break;
            }
            else if(flag == 2)
            {
                printf(" is an Unhappy number.\n");
                break;
            }
        }
    }
}

代码二（直接打表 0.008s）：

#include <iostream> #include <algorithm> #include <cstring> #include <cstdlib> #include <cstdio> #include <cmath> using namespace std; const int MaxSize = 850; int head[MaxSize]; int solve(int n) { int t, sum = 0; while(n) { t = n % 10; sum += t * t; n /= 10; } return sum; } int insert(int n) { int m = n; while(1) { n = solve(n); if(n == 1) return 1; else if(head[n] || n == m) return 0; head[n] = 1; } return 0; } int main() { #ifdef test freopen("sample.txt", "r", stdin); #endif int p, n, cct = 0; scanf("%d", &p); while(p--) { scanf("%d", &n); printf("Case #%d: %d", ++cct, n); memset(head, 0, sizeof(head)); if(insert(n)) printf(" is a Happy number.\n"); else printf(" is an Unhappy number.\n"); } }