hdu 4091

分析一下~只有一种情况背包搜索会超时，那就是当他们的性价比相同的时候，这种情况用数论的知识判断一下就可以了~ac~！最后发现害我wa了那么多次的原因居然是一个a写成了v。。。- -！坑爹。。

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<cmath>
#include<cassert>
#include<cstring>
#include<iomanip>
using namespace std;

#ifdef _WIN32
#define i64 __int64
#define out64 "%I64d\n"
#define in64 "%I64d"
#else
#define i64 long long
#define out64 "%lld\n"
#define in64 "%lld"
#endif

#define FOR(i,a,b)      for( int i = (a) ; i <= (b) ; i ++)
#define FF(i,a)         for( int i = 0 ; i < (a) ; i ++)
#define FFD(i,a)        for( int i = (a)-1 ; i >= 0 ; i --)
#define S64(a)          scanf(in64,&a)
#define SS(a)           scanf("%d",&a)
#define LL(a)           ((a)<<1)
#define RR(a)           (((a)<<1)+1)
#define SZ(a)           ((int)a.size())
#define PP(n,m,a)       puts("---");FF(i,n){FF(j,m)cout << a[i][j] << ' ';puts("");}
#define pb              push_back
#define CL(Q)           while(!Q.empty())Q.pop()
#define MM(name,what)   memset(name,what,sizeof(name))
#define read            freopen("in.txt","r",stdin)
#define write           freopen("out.txt","w",stdout)

const int inf = 0x3f3f3f3f;
const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
const double oo = 1e9;
const double eps = 1e-14;
const double pi = acos(-1.0);

i64 gcd(i64 _a, i64 _b)
{
    if (!_a || !_b)
    {
        return max(_a, _b);
    }
    i64 _t;
    while (_t = _a % _b)
    {
        _a = _b;
        _b = _t;
    }
    return _b;
};

i64 ext_gcd (i64 _a, i64 _b, i64 &_x, i64 &_y)
{
    if (!_b)
    {
        _x = 1;
        _y = 0;
        return _a;
    }
    i64 _d = ext_gcd (_b, _a % _b, _x, _y);
    i64 _t = _x;
    _x = _y;
    _y = _t - _a / _b * _y;
    return _d;
}

i64 invmod (i64 _a, i64 _p)
{
    i64 _ans, _y;
    ext_gcd (_a, _p, _ans, _y);
    _ans < 0 ? _ans += _p : 0;
    return _ans;
}

i64 n,s1,s2,a1,a2;
double w1,w2;

bool yes()
{
    i64 g1 = gcd(s1,a1);
    i64 g2 = gcd(s2,a2);
    s1 /= g1;
    a1 /= g1;
    s2 /= g2;
    a2 /= g2;
    if(a1==a2 && s1==s2)
    {
        s1*=g1;
        a1*=g1;
        a2*=g2;
        s2*=g2;
        return true;
    }
    else
    {
        s1*=g1;
        a1*=g1;
        a2*=g2;
        s2*=g2;
        return false;
    }
}

i64 find()
{
    i64 rest;
    i64 t1 = n/s1;
    rest = n - t1*s1;
    i64 t2 = rest/s2;

    i64 now = t1*a1 + t2*a2;
    double ex;
    i64 temp;

    if(yes())
    {
        i64 gab = gcd(s1,s2);
        s1/=gab;
        s2/=gab;
        n/=gab;

        i64 x1 = invmod(s1,s2);
        i64 x2 = (1-x1*s1)/s2;
        i64 pa = x1*a1 + x2*a2;
        x1*=n;
        x2*=n;
        i64 zx = x1/s2;
        i64 re = n*pa;
        if(x2 + zx*s1<0)
        {
            x1 = n/s1;
            rest = n - x1*s1;
            x2 = rest/s2;
            temp = x1*s1 + x2*s2;
            re = temp;
            while(true)
            {
                x1--;
                if(x1<0) break;
                rest = n - x1*s1;
                x2 = rest/s2;
                temp = x1*s1 + x2*s2;
                if(temp>re)
                {
                    re = temp;
                }
            }
            return re*pa;
        }
        else
        {
            return re;
        }
    }
    else if(s1>s2)
    {
        while(true)
        {
            t1--;
            if(t1<0) break;
            rest = n - t1*s1;
            ex = w1*t1*s1 + rest*w2;
            if(ex < double(now) + eps)
            {
                break;
            }
            t2 = rest/s2;
            temp = t1*a1 + t2*a2;
            if(temp > now)
            {
                now = temp;
            }
        }
    }
    else if(s1<s2)
    {
        while(true)
        {
            t2++;
            rest = n - t2*s2;
            if(rest<0) break;
            ex = w1*rest + t2*s2*w2;
            if(ex < double(now) + eps)
            {
                break;
            }
            t1 = rest/s1;
            temp = t1*a1 + t2*a2;
            if(temp > now)
            {
                now = temp;
            }
        }
    }
    return now;
}

int main()
{
    int T;
    cin>>T;
    for(int tt=1;tt<=T;tt++)
    {
        cin>>n>>s1>>a1>>s2>>a2;
        w1 = double(a1)/double(s1);
        w2 = double(a2)/double(s2);
        if(w2>w1)
        {
            swap(w1,w2);
            swap(a1,a2);
            swap(s1,s2);
        }
        cout<<"Case #"<<tt<<": "<<find()<<endl;
    }
    return 0;
}