BZOJ3315 [Usaco2013 Nov]Pogo-Cow

最新推荐文章于 2021-01-27 17:44:19 发布

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本篇介绍了一个有趣的问题：如何让一头装有弹簧腿的奶牛通过特定的跳跃方式获得最大分数。该问题涉及到算法设计，特别是动态规划与单调队列优化技巧的应用。

[Usaco2013 Nov]Pogo-Cow

Time Limit: 1 Sec Memory Limit: 128 MB
Submit: 17 Solved: 13
[ Submit][ Status]

Description

In an ill-conceived attempt to enhance the mobility of his prize cow Bessie, Farmer John has attached a pogo stick to each of Bessie's legs. Bessie can now hop around quickly throughout the farm, but she has not yet learned how to slow down. To help train Bessie to hop with greater control, Farmer John sets up a practice course for her along a straight one-dimensional path across his farm. At various distinct positions on the path, he places N targets on which Bessie should try to land (1 <= N <= 1000). Target i is located at position x(i), and is worth p(i) points if Bessie lands on it. Bessie starts at the location of any target of her choosing and is allowed to move in only one direction, hopping from target to target. Each hop must cover at least as much distance as the previous hop, and must land on a target. Bessie receives credit for every target she touches (including the initial target on which she starts). Please compute the maximum number of points she can obtain.

一个坐标轴有N个点，每跳到一个点会获得该点的分数，并只能朝同一个方向跳，但是每一次的跳跃的距离必须不小于前一次的跳跃距离，起始点任选，求能获得的最大分数。

Input

* Line 1: The integer N.

* Lines 2..1+N: Line i+1 contains x(i) and p(i), each an integer in the range 0..1,000,000.

Output

* Line 1: The maximum number of points Bessie can receive.

Sample Input

6
5 6
1 1
10 5
7 6
4 8
8 10

INPUT DETAILS: There are 6 targets. The first is at position x=5 and is worth 6 points, and so on.

Sample Output

25
OUTPUT DETAILS: Bessie hops from position x=4 (8 points) to position x=5 (6 points) to position x=7 (6 points) to position x=10 (5 points).

从坐标为4的点，跳到坐标为5的，再到坐标为7和，再到坐标为10的。

HINT

Source

Silver

设f[i][j]表示起点为i，第二步为j

O(n^3)还是很好想的。。。

单调队列优化一下就可以了。。。

#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<iostream>
using namespace std;
const int maxn = 1010;
struct point{
    int x, v;
}a[maxn];
bool cmp1(point a, point b){ return a.x < b.x; }
bool cmp2(point a, point b){ return a.x > b.x; }
int n, f[maxn][maxn];
void init(){
    scanf("%d", &n);
    for (int i = 1; i <= n; i ++) scanf("%d%d",&a[i].x, &a[i].v);
}
int h[maxn][2];
int ans;
void work(){
    for (int i = n; i >= 1; i --){
        f[i][i] = a[i].v;
        int tt = 1, ww = 0;
        for (int j = i + 1; j <= n; j ++){
            while (ww >= tt && f[i][j] >= h[ww][1]) ww --;
            h[++ww][0] = j, h[ww][1] = f[i][j];
        }
        for (int j = i - 1; j >= 1; j --){
            f[j][i] = a[j].v + a[i].v;
            while (ww >= tt && abs(a[h[tt][0]].x - a[i].x) < abs(a[i].x - a[j].x)) tt ++;
            if (ww >= tt) f[j][i] = max(f[j][i], a[j].v + h[tt][1]);
            ans = max(ans, f[j][i]); 
        }
    }
}
int main(){
    init();
    sort(a + 1, a + n + 1, cmp1);
    work();
    sort(a + 1, a + n + 1, cmp2);
    work();
    cout <<ans <<endl;
    return 0;
}