11728 - Alternate Task

由于N的所有因子之和为S, N本身是自己的因子， 所以N不会大于S， S的值小于1000， 直接暴力即可。

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;

const int maxn = 2000;
int prim[maxn], plen;
bool vis[maxn];
void mklist()
{
    memset(vis, 0, sizeof(vis));
    for(int i = 2; i * i < maxn; ++i)
    {
        if(!vis[i])
        {
            for(int j = i; i * j < maxn; ++j) vis[i * j] = true;
        }
    }
    plen = 0;
    for(int i = 2; i < maxn; ++i) if(!vis[i]) prim[plen++] = i;
}

int fac[100][2], flen;
void split(int n)
{
    flen = 0;
    for(int i = 0; i < plen && prim[i] <= n; ++i)
    {
        if(n % prim[i] == 0)
        {
            fac[flen][0] = prim[i];
            fac[flen][1] = 0;
            while(n % prim[i] == 0)
            {
                n /= prim[i];
                fac[flen][1]++;
            }
            ++flen;
        }
    }
}
int sum;
void dfs(int d, int s)
{
    if(d == flen)
    {
        sum += s;
        return;
    }
    int len = fac[d][1];
    int t = 1;
    for(int i = 0; i <= len; ++i)
    {
        dfs(d + 1, s * t);
        t *= fac[d][0];
    }
}
int main()
{
    int n, id = 0;
    mklist();
    while(cin >> n)
    {
        if(n == 0) break;
        if(n == 1)
        {
            cout << "Case " << ++id << ": " << 1 << endl;
            continue;
        }
        int ans = n - 1;
        for(;ans >= 0; --ans)
        {
            split(ans);
            sum = 0;
            dfs(0, 1);
            if(sum == n) break;
        }
        cout << "Case " << ++id << ": " << ans << endl;
    }
    return 0;
}