hdu5303Delicious Apples

题意大概就是有n框苹果放在长度为L的环上，每框有ai个苹果。你有一个容量为k的框。要你从0点处出发，随意走。框满了就回到0点把苹果放在那里。继续走直到把苹果都拿完为止。问你最少要走多少路程。

首先贪心的策略，无论往哪边走，碰到苹果就拿，拿满就滚回去。

然后碰到走一个半圈，框还剩下容量的情况，就须要dp了。主要是L为偶数的时候，若L/2的位置有苹果，该算是哪个半圈拿比較好呢？

当然也能够继续贪心，然而太麻烦了。直接dp。

而且由此贪心能够知道若存在须要走一圈的情况。肯定最多走一次一圈。

我们把苹果的位置当作它的权值，所有铺在环上。

dp[0][j]:左半圈拿完j位置的苹果就回去的最小代价

dp[1][j]:右半圈拿完j位置的苹果就回去的最小代价

非常显然，dp[i][j]=dp[i][j-k]+val[j]

最后再枚举走一圈的时候。从左半圈的底部拿走几个苹果，从右半圈的底部拿走几个苹果。不断更新ans就可以。

详细看代码吧。非常easy懂。

#include<map>
#include<string>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<queue>
#include<vector>
#include<iostream>
#include<algorithm>
#include<bitset>
#include<climits>
#include<list>
#include<iomanip>
#include<stack>
#include<set>
using namespace std;
typedef long long ll;
int a[2][100010],len[2];
ll dp[2][100010];
int main()
{
	int T;
	cin>>T;
	while(T--)
	{
		memset(len,0,sizeof(len));
		int l,n,k;
		scanf("%d%d%d",&l,&n,&k);
		int m=l>>1;
		while(n--)
		{
			int x,t;
			scanf("%d%d",&x,&t);
			int i=0;
			if(x>m)
			{
				i=1;
				x=l-x;
			} 
			while(t--)
				a[i][++len[i]]=x;
		}
		for(int i=0;i<2;i++)
			sort(a[i],a[i]+len[i]+1);
		for(int i=0;i<2;i++)
			for(int j=0;j<=len[i];j++)
			{
				dp[i][j]=a[i][j];
				if(j>=k)
					dp[i][j]+=dp[i][j-k];
			}
		ll ans=dp[0][len[0]]+dp[1][len[1]]<<1;
		for(int i=0;i<=k&&i<=len[0];i++)
			ans=min(ans,2*(dp[0][len[0]-i]+dp[1][max(0,len[1]-(k-i))])+l);
		cout<<ans<<endl;
	}
}

Time Limit: 5000/3000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 1078    Accepted Submission(s): 358

Problem Description

There are n apple trees planted along a cyclic road, which is L metres long. Your storehouse is built at position 0 on that cyclic road.
The ith tree is planted at position xi, clockwise from position 0. There are ai delicious apple(s) on the ith tree.

You only have a basket which can contain at most K apple(s). You are to start from your storehouse, pick all the apples and carry them back to your storehouse using your basket. What is your minimum distance travelled?

1≤n,k≤105,ai≥1,a1+a2+...+an≤105
1≤L≤109
0≤x[i]≤L

There are less than 20 huge testcases, and less than 500 small testcases.

 

Input

First line: t, the number of testcases.
Then t testcases follow. In each testcase:
First line contains three integers, L,n,K.
Next n lines, each line contains xi,ai.

 

Output

Output total distance in a line for each testcase.

 

Sample Input

2
10 3 2
2 2
8 2
5 1
10 4 1
2 2
8 2
5 1
0 10000

 

Sample Output

18
26

 

Source

2015 Multi-University Training Contest 2