POJ 3262 Protecting the Flowers

Protecting the Flowers

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 3290		Accepted: 1332

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 cluster of cows was in his garden eating his beautiful flowers. Wanting to minimize the subsequent damage, FJ decided to take immediate action and transport each cow back to its own barn.

Each cow i is at a location that is T_i minutes (1 ≤ T_i ≤ 2,000,000) away from its own barn. Furthermore, while waiting for transport, she destroys D_i (1 ≤ D_i ≤ 100) flowers per minute. No matter how hard he tries, FJ can only transport one cow at a time back to her barn. Moving cow i to its barn requires 2 × T_i minutes (T_i to get there and T_i to return). FJ starts at the flower patch, transports the cow to its barn, and then walks back to the flowers, taking no extra time to get to the next cow that needs transport.

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.

Input

Line 1: A single integer N  Lines 2..N+1: Each line contains two space-separated integers, T_i and D_i, that describe a single cow's characteristics

Output

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

Sample Input

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

Sample Output

86

Hint

FJ returns the cows in the following order: 6, 2, 3, 4, 1, 5. While he is transporting cow 6 to the barn, the others destroy 24 flowers; next he will take cow 2, losing 28 more of his beautiful flora. For the cows 3, 4, 1 he loses 16, 12, and 6 flowers respectively. When he picks cow 5 there are no more cows damaging the flowers, so the loss for that cow is zero. The total flowers lost this way is 24 + 28 + 16 + 12 + 6 = 86.

 

有一些牛跑到了花园里制造破坏，每分钟造成的破坏是D_i，把它赶回牛棚所用的时间为T_i

求一种将它们赶回牛棚的最佳次序，使造成的总破坏最小

假设有两头牛a和b，

　　若先赶a回去，则b在这段时间里造成的破坏为t_a*d_b

　　若先赶b回去，则a在这段时间里造成的破坏为t_b*d_a

所以要先赶a的条件为t_a*d_b<=t_b*d_a

按照这个规则对所有牛进行排序，然后按顺序赶牛即可

 

#include<iostream>
#include<cstdio>
#include<algorithm>

using namespace std;

typedef struct
{
    int t;
    int d;
} COW;

int n;
int sum[100010];
COW cow[100010];

bool cmp(COW a,COW b)
{
    return a.t*b.d>=a.d*b.t;
}

int main()
{
    while(cin>>n)
    {
        for(int i=0;i<n;i++)
            scanf("%d %d",&cow[i].t,&cow[i].d);
        sort(cow,cow+n,cmp);
        sum[0]=cow[0].d;
        for(int i=1;i<n;i++)
            sum[i]=sum[i-1]+cow[i].d;
        long long ans=0;
        for(int i=n-1;i>0;i--)
            ans+=sum[i-1]*cow[i].t*2;
        cout<<ans<<endl;
    }

    return 0;
}