HDU 5303 Delicious Apples（DP + 贪心）

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

题意：有一个长度为L的环，环上有N棵苹果树，有个每次能装K个苹果的篮子，装满后要回到搬到起点，问从起点出发，最少需要多少距离将所有苹果搬到起点

思路：dp[0][i]代表顺时针出发摘掉i个苹果回到起点的最短距离,dp[1][i]相应表示逆时针

从贪心角度考虑，我们每次肯定按照距离顺序拿掉这K个苹果，对于顺逆时针，每次返回起点时都需要考虑是走环还是走半圈进行转移

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <climits>
#include <functional>
#include <deque>
#include <ctime>

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
#pragma comment(linker, "/STACK:102400000,102400000")

using namespace std;

typedef long long ll;

const int maxn = 100100;

struct node
{
int x, v;

bool operator < (const node & rhs) const
{
return x < rhs.x;
}
} a[maxn];

ll sum, dp[2][maxn];

int n, k, l;

int main()
{
int t;
cin >> t;
while (t--)
{
sum = 0;
memset(dp, -1, sizeof(dp));
cin >> l >> n >> k;
for (int i = 0; i < n; i++)
{
scanf("%d%d", &a[i].x, &a[i].v);
sum += a[i].v;
}

sort(a, a + n);
dp[0][0] = dp[1][0] = 0;

ll cnt = 1, p;
for (int i = 0; i < n; i++)
for (int j = 0; j < a[i].v; j++)
{
p = cnt - k > 0 ? cnt - k : 0;

if (dp[0][p] == -1) continue;
dp[0][cnt] = dp[0][p] + min(2 * a[i].x, l);
cnt++;
}

cnt = 1;
for (int i = n - 1; i >= 0; i--)
for (int j = 0; j < a[i].v; j++)
{
p = cnt - k > 0 ? cnt - k : 0;

if (dp[1][p] == -1) continue;
dp[1][cnt] = dp[1][p] + min(2 * l - 2 * a[i].x, l);
cnt++;
}

long long ans = 1e16;
for (int i = 0; i <= sum; i++)
ans = min(ans, dp[0][i] + dp[1][sum - i]);
cout << ans << endl;
}
return 0;
}