BZOJ 1634: [Usaco2007 Jan]Protecting the Flowers 护花-优快云博客

本文介绍了一种解决农民约翰如何最高效地将牛群送回牛棚，以最小化花园中花朵被破坏的问题。通过比较相邻牛在运输过程中对其他牛的影响，提出了一种排序算法，使得总花朵损失最小。

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题目

1634: [Usaco2007 Jan]Protecting the Flowers 护花

Time Limit: 5 Sec Memory Limit: 64 MB
Submit: 487 Solved: 307
[ Submit][ Status]

Description

Farmer John went to cut some wood and left N (2 <= N <= 100,000) cows eating the grass, as usual. When he returned, he found to his horror that the cows were in his garden eating his beautiful flowers. Wanting to minimize the subsequent damage, FJ decided to take immediate action and transport the cows back to their barn. Each cow i is at a location that is Ti minutes (1 <= Ti <= 2,000,000) away from the barn. Furthermore, while waiting for transport, she destroys Di (1 <= Di <= 100) flowers per minute. No matter how hard he tries,FJ can only transport one cow at a time back to the barn. Moving cow i to the barn requires 2*Ti minutes (Ti to get there and Ti to return). Write a program to determine the order in which FJ should pick up the cows so that the total number of flowers destroyed is minimized.

约翰留下他的N只奶牛上山采木．他离开的时候，她们像往常一样悠闲地在草场里吃草．可是，当他回来的时候，他看到了一幕惨剧：牛们正躲在他的花园里，啃食着他心爱的美丽花朵！为了使接下来花朵的损失最小，约翰赶紧采取行动，把牛们送回牛棚．牛们从1到N编号．第i只牛所在的位置距离牛棚Ti(1≤Ti《2000000)分钟的路程，而在约翰开始送她回牛棚之前，她每分钟会啃食Di(1≤Di≤100)朵鲜花．无论多么努力，约翰一次只能送一只牛回棚．而运送第第i只牛事实上需要2Ti分钟，因为来回都需要时间．写一个程序来决定约翰运送奶牛的顺序，使最终被吞食的花朵数量最小．

Input

* Line 1: A single integer

N * Lines 2..N+1: Each line contains two space-separated integers, Ti and Di, that describe a single cow's characteristics

第1行输入N，之后N行每行输入两个整数Ti和Di．

Output

* Line 1: A single integer that is the minimum number of destroyed flowers

一个整数，表示最小数量的花朵被吞食．

Sample Input

6
3 1
2 5
2 3
3 2
4 1
1 6

Sample Output

HINT

约翰用6，2，3，4，1，5的顺序来运送他的奶牛．

题解

这里我们看相邻的两头牛a,b不会改变其他牛的答案，唯一有区别的就是a牛运送的时间里b吃的花的数量和b牛运送时间里a牛吃的花的数量，所以很明显可以比出优劣，这样的性质我们可以应用到所有牛的身上，所以写个cmp，直接排序就好啦！

代码

 1 /*Author:WNJXYK*/
 2 #include<cstdio>
 3 #include<algorithm>
 4 using namespace std;
 5 struct Cow{
 6     int eat;
 7     int tim;
 8 }; 
 9 Cow cow[100010];
10 int n;
11 bool cmp(Cow a,Cow b){
12     if (a.eat*b.tim>b.eat*a.tim) return true;
13     return false;
14 }
15 int main(){
16     scanf("%d",&n);
17     for (int i=1;i<=n;i++) scanf("%d%d",&cow[i].tim,&cow[i].eat);
18     sort(cow+1,cow+n+1,cmp);
19     long long ans=0;
20     long long tim=0;
21     for (int i=1;i<=n;i++){
22         ans+=tim*cow[i].eat;
23         tim+=cow[i].tim*2;
24     }
25     printf("%lld\n",ans);
26     return 0;
27 }