2018HDU多校训练-3-Problem G. Interstellar Travel

链接：http://acm.hdu.edu.cn/showproblem.php?pid=6325

Interstellar Travel

Problem Description

After trying hard for many years, Little Q has finally received an astronaut license. To celebrate the fact, he intends to buy himself a spaceship and make an interstellar travel.
Little Q knows the position of n planets in space, labeled by 1 to n . To his surprise, these planets are all coplanar. So to simplify, Little Q put these n planets on a plane coordinate system, and calculated the coordinate of each planet (xi,yi) .
Little Q plans to start his journey at the 1 -th planet, and end at the n -th planet. When he is at the i -th planet, he can next fly to the j -th planet only if xi<xj , which will cost his spaceship xi×yj−xj×yi units of energy. Note that this cost can be negative, it means the flight will supply his spaceship.
Please write a program to help Little Q find the best route with minimum total cost.

Input

The first line of the input contains an integer T(1≤T≤10) , denoting the number of test cases.
In each test case, there is an integer n(2≤n≤200000) in the first line, denoting the number of planets.
For the next n lines, each line contains 2 integers xi,yi(0≤xi,yi≤109) , denoting the coordinate of the i -th planet. Note that different planets may have the same coordinate because they are too close to each other. It is guaranteed that y1=yn=0,0=x1<x2,x3,...,xn−1<xn .

Output

For each test case, print a single line containing several distinct integers p1,p2,...,pm(1≤pi≤n) , denoting the route you chosen is p1→p2→...→pm−1→pm . Obviously p1 should be 1 and pm should be n . You should choose the route with minimum total cost. If there are multiple best routes, please choose the one with the smallest lexicographically.
A sequence of integers a is lexicographically smaller than a sequence of b if there exists such index j that ai=bi for all i<j , but aj<bj .

Sample Input

1 3 0 0 3 0 4 0

Sample Output

1 2 3

Source

2018 Multi-University Training Contest 3

Recommend

chendu

题解：WA了无数发，忘了一句话，“有的星球由于太近可以认为坐标相同，但输出的时候应该输出编号小的”，后来重读了题目，家里个条件就过了；

这个题目可以转化为凸包问题，只求上凸包，求上凸包时注意排除横坐标相同的点，只取纵坐标大的点，重要的一点：对于纵坐标相同而横坐标不同的点，我们需要判断中间点的编号是否比下一个点大，因为按字典序输出，故如果大于则去掉该点，小于等于则保留，注意细节；

参考代码：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn=2e5+10;
LL vis[maxn],T,n;
LL num[maxn];
struct Point{LL x,y;LL id;Point(double xx=0,double yy=0) : x(xx),y(yy) {}
} p[maxn],ch[maxn];
typedef Point Vector;
Vector operator + (Vector a,Vector b) { return Vector(a.x+b.x,a.y+b.y); }
Vector operator - (Vector a,Vector b) { return Vector(a.x-b.x,a.y-b.y); }
Vector operator * (Vector a,Vector b) { return Vector(a.x*b.x,a.y*b.y); }
Vector operator / (Vector a,Vector b) { return Vector(a.x/b.x,a.y/b.y); }
bool operator < (const Point &a,const Point &b){ return a.x==b.x? (a.y==b.y? a.id<b.id : a.y>b.y) : a.x<b.x ; }
LL Cross(Vector a,Vector b) { return a.x*b.y-a.y*b.x; }void ConvexHull()
{LL m=0; memset(vis,0,sizeof vis);for(int i=1;i<=n;i++){if(i>1 && p[i].x == p[i-1].x) continue;while(m>1 && Cross(ch[m]-ch[m-1],p[i]-ch[m])>0) m--;ch[++m]=p[i];}vis[1]=vis[m]=1;for(int i=2;i<m;i++) if(Cross(ch[i+1]-ch[i],ch[i]-ch[i-1])!=0) vis[i]=1;for(int i=m;i>0;i--){if(vis[i]) num[i]=ch[i].id;else num[i]=min(num[i+1],ch[i].id);}for(int i=1;i<m;i++) if(num[i]==ch[i].id) printf("%lld ",num[i]);printf("%lld\n",num[m]);
}int main()
{scanf("%lld",&T);while(T--){scanf("%lld",&n);for(int i=1;i<=n;i++) scanf("%lld%lld",&p[i].x,&p[i].y),p[i].id=i;sort(p+1,p+n+1);ConvexHull();}return 0;
}

转载于:https://www.cnblogs.com/songorz/p/9398507.html

2018HDU多校训练-3-Problem G. Interstellar Travel相关推荐

HDU 6325 Problem G. Interstellar Travel(凸包)
题意: 给你n个点,第一个点一定是(0,0),最后一个点纵坐标yn一定是0,中间的点的横坐标一定都是在(0,xn)之间的然后从第一个点开始飞行,每次飞到下一个点j,你花费的价值就是xi*yj-xj* ...
【杭电多校round3】G Interstellar Travel
题意给定二维平面上的n个点,保证只有一个点(P_1)横坐标最小,一个点横坐标最大(P_n),在坐标轴上其余点无序且可能重合即 y_1=y_n=0, 0=x_1<x_2,x_3,...,x_n ...
2018 Multi-University Training Contest 3: G. Interstellar Travel（凸包）
题意:给你平面上n个点,第一个点一定在(0, 0),第n个点的y坐标一定为0,除此之外中间所有点的x坐标一定大于0且小于最后一个点的x坐标,你从一号点开始出发,中间从第i个点到第j个点必须满足xj&g ...
Western Subregional of NEERC, Minsk, Wednesday, November 4, 2015 Problem G. k-palindrome dp
Problem G. k-palindrome 题目连接: http://opentrains.snarknews.info/~ejudge/team.cgi?SID=c75360ed7f2c7022 ...
Problem G. Pandaria（线段树合并 + Kruskal 重构树）
Problem G. Pandaria 给定一个有nnn条边的无向连通图,每条边有对应的边权,每个点有一个颜色, 问从一个点出发,经过不超过www的边权,所能到达的点中,颜色出现次数做多且颜色编号最小 ...
Problem G: 函数---判断日期（年月日）是否合法
Problem G: 函数---判断日期(年月日)是否合法 Time Limit: 1 Sec Memory Limit: 128 MB Submit: 566 Solved: 240 Descr ...
Problem G: C语言习题医生值班
Problem G: C语言习题医生值班 Time Limit: 3 Sec Memory Limit: 128 MB Submit: 847 Solved: 102 [Submit][Stat ...
“玲珑杯”郑州轻工业学院第八届ACM程序设计大赛Problem G: 蛤玮点菜
Problem G: 蛤玮点菜 Time Limit: 2 Sec Memory Limit: 128 MB Submit: 320 Solved: 31 SubmitWeb Board Desc ...
HDU6578 2019HDU多校训练赛第一场 1001 （dp）
HDU6578 2019HDU多校训练赛第一场 1001 (dp) 传送门:http://acm.hdu.edu.cn/showproblem.php?pid=6578 题意: 你有n个空需要去填,有 ...

2018HDU多校训练-3-Problem G. Interstellar Travel

2018HDU多校训练-3-Problem G. Interstellar Travel相关推荐

最新文章

热门文章