HDU 5303 Delicious Apples (贪心 枚举 好题)

Delicious Apples

Time Limit: 5000/3000 MS (Java/Others) Memory Limit: 524288/524288 K (Java/Others)

Total Submission(s): 199 Accepted Submission(s): 54

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

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5303

题目大意：有一个长为L的环，n个苹果树，一个篮子最多装k个苹果，装完要回到起点卸下再出发，给出n个苹果树顺时针的位置及苹果的个数，求摘完所有苹果走的最小路程

题目分析：显然，只有在某种特殊条件下，即两侧都还有苹果且可以一次装完且最后的苹果都离起点比较远，这种情况下，我们直接绕圈可能会更优，也就是说整圈最多绕一次，因此我们可以先对两边贪心，题目的数据显示苹果的数量最多就1e5，显然我们可以把苹果“离散”出来，用x[i]记录第i个苹果到起点的位置，然后对位置从小到大排序，先选择路程小的，选择的时候用dis[i]记录单侧装了i个苹果的最小路程，类似背包计数的原理，答案要乘2，因为是来回的，最后在k>=i时，枚举绕整圈的情况，szl－i表示只走左边采的苹果数，szr -
(k - i)表示只走右边采的苹果树，画个图就能看出来了，注意右边这里可能值为负，要和0取最大，然后答案就是（disl[szl－i] + disr[szr - (k - i)]）* 2 ＋L，这里其实画图更加直观。最后取最小即可，注意有几个wa点，一个是要用long long，二是之前说的出现负数和0取大，三是每次要清零

#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
#define ll long long
using namespace std;
int const MAX = 1e5 + 5;
int  L, n, k;
ll x[MAX], disl[MAX], disr[MAX];
vector <ll> l, r;

int main()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        memset(disl, 0, sizeof(disl));
        memset(disr, 0, sizeof(disr));
        l.clear();
        r.clear();
        scanf("%d %d %d", &L, &n, &k);
        int cnt = 1;
        for(int i = 1; i <= n; i++) 
        {
            ll pos, num;
            scanf("%lld %lld", &pos, &num);
            for(int j = 1; j <= num; j++)
                x[cnt ++] = (ll) pos;   //离散操作
        }
        cnt --;
        for(int i = 1; i <= cnt; i++)
        {
            if(2 * x[i] < L)
                l.push_back(x[i]);
            else
                r.push_back(L - x[i]);  //记录位置
        }   
        sort(l.begin(), l.end());
        sort(r.begin(), r.end());
        int szl = l.size(), szr = r.size();
        for(int i = 0; i < szl; i++)
            disl[i + 1] = (i + 1 <= k ? l[i] : disl[i + 1 - k] + l[i]);
        for(int i = 0; i < szr; i++)
            disr[i + 1] = (i + 1 <= k ? r[i] : disr[i + 1 - k] + r[i]);
        ll ans = (disl[szl] + disr[szr]) * 2;
        for(int i = 0; i <= szl && i <= k; i++)
        {
            int p1 = szl - i;
            int p2 = max(0, szr - (k - i));
            ans = min(ans, 2 * (disl[p1] + disr[p2]) + L);
        }
        printf("%I64d\n", ans);
    }
}