P2983 [USACO10FEB]购买巧克力Chocolate Buying

最优巧克力购买策略

最新推荐文章于 2025-05-01 14:13:07 发布

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最新推荐文章于 2025-05-01 14:13:07 发布

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原文链接：http://www.cnblogs.com/planche/p/8650449.html

本文介绍了一个关于如何在有限预算内为最多数量的奶牛购买巧克力的问题。通过算法优化选择最经济的巧克力种类来满足最大数量的需求。

题目描述

Bessie and the herd love chocolate so Farmer John is buying them some.

The Bovine Chocolate Store features N (1 <= N <= 100,000) kinds of chocolate in essentially unlimited quantities. Each type i of chocolate has price P_i (1 <= P_i <= 10^18) per piece and there are C_i (1 <= C_i <= 10^18) cows that want that type of chocolate.

Farmer John has a budget of B (1 <= B <= 10^18) that he can spend on chocolates for the cows. What is the maximum number of cows that he can satisfy? All cows only want one type of chocolate, and will be satisfied only by that type.

Consider an example where FJ has 50 to spend on 5 different types of chocolate. A total of eleven cows have various chocolate preferences:

Chocolate_Type Per_Chocolate_Cost Cows_preferring_this_type 1 5 3

2 1 1

3 10 4

4 7 2

5 60 1

Obviously, FJ can't purchase chocolate type 5, since he doesn't have enough money. Even if it cost only 50, it's a counterproductive purchase since only one cow would be satisfied.

Looking at the chocolates start at the less expensive ones, he can * purchase 1 chocolate of type #2 for 1 x 1 leaving 50- 1=49, then * purchase 3 chocolate of type #1 for 3 x 5 leaving 49-15=34, then * purchase 2 chocolate of type #4 for 2 x 7 leaving 34-14=20, then * purchase 2 chocolate of type #3 for 2 x 10 leaving 20-20= 0.

He would thus satisfy 1 + 3 + 2 + 2 = 8 cows.

贝西和其他奶牛们都喜欢巧克力，所以约翰准备买一些送给她们。奶牛巧克力专卖店里

有N种巧克力，每种巧克力的数量都是无限多的。每头奶牛只喜欢一种巧克力，调查显示，

有Ci头奶牛喜欢第i种巧克力，这种巧克力的售价是P。

约翰手上有B元预算，怎样用这些钱让尽量多的奶牛高兴呢？

输入输出格式

输入格式：

* Line 1: Two space separated integers: N and B

* Lines 2..N+1: Line i contains two space separated integers defining chocolate type i: P_i and C_i

输出格式：

* Line 1: A single integer that is the maximum number of cows that Farmer John can satisfy

输入输出样例

输入样例#1：复制

输出样例#1：复制

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define inf 2147483647
const ll INF = 0x3f3f3f3f3f3f3f3fll;
#define ri register int
template <class T> inline T min(T a, T b, T c)
{
    return min(min(a, b), c);
}
template <class T> inline T max(T a, T b, T c)
{
    return max(max(a, b), c);
}
template <class T> inline T min(T a, T b, T c, T d)
{
    return min(min(a, b), min(c, d));
}
template <class T> inline T max(T a, T b, T c, T d)
{
    return max(max(a, b), max(c, d));
}
#define scanf1(x) scanf("%d", &x)
#define scanf2(x, y) scanf("%d%d", &x, &y)
#define scanf3(x, y, z) scanf("%d%d%d", &x, &y, &z)
#define scanf4(x, y, z, X) scanf("%d%d%d%d", &x, &y, &z, &X)
#define pi acos(-1)
#define me(x, y) memset(x, y, sizeof(x));
#define For(i, a, b) for (int i = a; i <= b; i++)
#define FFor(i, a, b) for (int i = a; i >= b; i--)
#define bug printf("***********\n");
#define mp make_pair
#define pb push_back
const int maxn = 100005;
// name*******************************
ll n,b;
ll ans=0;
struct pp{
ll c,p;
}a[maxn];
bool cmp(pp a,pp b){
return a.p<b.p;
}
// function******************************



//***************************************
int main()
{
//    ios::sync_with_stdio(0);
//    cin.tie(0);
//    freopen("test.txt", "r", stdin);
    //  freopen("outout.txt","w",stdout);
    cin>>n>>b;
    For(i,1,n)
    {
        cin>>a[i].p>>a[i].c;
    }
    sort(a+1,a+1+n,cmp);
    For(i,1,n)
    {
        ll t=b/a[i].p;
        if(t>a[i].c)
        {
            b-=a[i].p*a[i].c;
            ans+=a[i].c;
        }
        else
        {
            ans+=t;
            break;
        }
//        cout<<i<<":"<<ans<<" "<<b<<endl;
    }
    cout<<ans;

    return 0;
}