洛谷 P2983 [USACO10FEB]购买巧克力Chocolate Buying 题解

P2983 [USACO10FEB]购买巧克力Chocolate Buying

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 #1

5 50
5 3
1 1
10 4
7 2
60 1

输出 #1

8

【思路】

贪心
小水题

【题目大意】

很多巧克力，很多奶牛
奶牛都有自己喜欢的巧克力
巧克力都有不同的价格
你有b多的钱
求最多满足的奶牛数
（这是自己总结的意思，和真正的题目大意不太一样，
这样总结的理由在后面）

【题目分析】

可以这样看
每满足一头奶牛都要消耗不同的钱
想要满足最多的奶牛
那一定是要找最便宜的去满足
这就是贪心思想

【最终思路】

知道了怎么贪心
但是题目中给出的是巧克力的价格和喜欢这个巧克力的奶牛的数量
这里的贪心和奶牛的数量没有关系
因为理由可以看成【题目大意】分解之后的题意+【题目分析】里面的解释
然后结构体根据巧克力的价格来排序
从小到大枚举
看看最多能够满足多少奶牛就可以啦

【注意】

一道秒切的小水题
但是需要开unsigned long long
我是一步一步从int->long long -> unsigned long long 变化过来的

【完整代码】

#include<iostream>
#include<cstdio>
#include<algorithm> 
#define int unsigned long long 
using namespace std;
const int Max = 100005;
struct node
{
	int p,c;
}a[Max];

bool cmp(const node x,const node y)
{
	return x.p < y.p;
}

signed main()
{
	int n,b;
	cin >> n >> b;
	for(register int i = 1;i <= n;++ i)
		cin >> a[i].p >> a[i].c;
	sort(a + 1,a + 1 + n,cmp);
	int js = 0;
	for(register int i = 1;i <= n;++ i)
	{
		if(b >= a[i].p * a[i].c)
			b -= a[i].p * a[i].c,js += a[i].c;
		else
		{
			js += b / a[i].p;
			break;
		}
	}
	cout << js << endl;
	return 0;
}