洛谷 P1080 国王游戏

这是一道贪心题，贪心的策略是将大臣们按左右手金币的乘积升序排列，具体证明过程可以参见洛谷大佬的题解，这里就不再赘述了。

因为本菜鸡之前没有接触过高精度运算，对C++的运算符重载也不太熟练，所以正好借此机会记录一下用到的高精度模版。模版框架参考于：https://blog.csdn.net/Wall_F/article/details/8373395

然而，直接复制该模版会导致TLE，原因在于这道题只需要高精度乘（除）低精度即可，但模版的乘除法运算是支持双高精度的，依赖于高精度的加减法，算法更加复杂，对于这道题来说增加了不必要的时间开销。所以我们需要把乘除法修改一下，删除高精度加减法的部分，得到如下简化版的代码，并顺利AC。

#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>

using namespace std;

const int MAXN = 10010;

struct bign
{
    int len, s[MAXN];
    
    bign ()
    {
        memset(s, 0, sizeof(s));
        len = 1;
    }
    bign (int num) { *this = num; }
    bign (const char *num) { *this = num; }
    
    bign operator = (const int num)
    {
        char s[MAXN];
        sprintf(s, "%d", num);
        *this = s;
        return *this;
    }
    
    bign operator = (const char *num)
    {
        for(int i = 0; num[i] == '0'; num++);
        len = strlen(num);
        for(int i = 0; i < len; i++) s[i] = num[len-i-1] - '0';
        return *this;
    }
    
    void clean()
    {
        while(len > 1 && !s[len-1]) len--;
    }
    
    bign operator * (const int &b)
    {
        bign c;
        c.len = len + 5;
        for(int i = 0; i < len; i++)
            c.s[i] += s[i] * b;
        for(int i = 0; i < c.len; i++)
        {
            c.s[i+1] += c.s[i]/10;
            c.s[i] %= 10;
        }
        c.clean();
        return c;
    }
    
    bign operator *= (const int &b)
    {
        *this = *this * b;
        return *this;
    }
    
    bign operator / (const int &b)
    {
        bign c;
        int f = 0;
        for(int i = len-1; i >= 0; i--)
        {
            f = f*10 + s[i];
            while(f >= b)
            {
                f -= b;
                c.s[i]++;
            }
        }
        c.len = len;
        c.clean();
        return c;
    }
    
    bign operator /= (const int &b)
    {
        *this  = *this / b;
        return *this;
    }
    
    bool operator < (const bign &b)
    {
        if(len != b.len) return len < b.len;
        for(int i = len-1; i != -1; i--)
        {
            if(s[i] != b.s[i]) return s[i] < b.s[i];
        }
        return false;
    }
    
    bool operator > (const bign &b)
    {
        if(len != b.len) return len > b.len;
        for(int i = len-1; i != -1; i--)
        {
            if(s[i] != b.s[i]) return s[i] > b.s[i];
        }
        return false;
    }
    
    bool operator == (const bign &b)
    {
        return !(*this > b) && !(*this < b);
    }
    
    bool operator >= (const bign &b)
    {
        return *this > b || *this == b;
    }
    
    string str() const
    {
        string res = "";
        for(int i = 0; i < len; i++) res = char(s[i]+'0')+res;
        return res;
    }
};

istream& operator >> (istream &in, bign &x)
{
    string s;
    in >> s;
    x = s.c_str();
    return in;
}

ostream& operator << (ostream &out, const bign &x)
{
    out << x.str();
    return out;
}

struct Minister
{
    int left, right;
};

bool cmp(Minister a, Minister b)
{
    return a.left * a.right < b.left * b.right;
}

int main()
{
    int n;
    int kingLeft, kingRight;
    cin >> n;
    cin >> kingLeft >> kingRight;
    
    vector<Minister> queue;
    for (int i = 0; i < n; i++)
    {
        Minister m;
        cin >> m.left >> m.right;
        queue.push_back(m);
    }
    sort(queue.begin(), queue.end(), cmp);
    
    bign reward, maxReward = 0;
    bign product = kingLeft;
    for (int i = 0; i < n; i++)
    {
        reward = product / queue[i].right;
        if (reward >= maxReward)
            maxReward = reward;
        product *= queue[i].left;
    }
    
    cout << maxReward << endl;
    return 0;
}