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 planets in space, labeled by to . To his surprise, these planets are all coplanar. So to simplify, Little Q put these planets on a plane coordinate system, and calculated the coordinate of each planet .
Little Q plans to start his journey at the -th planet, and end at the -th planet. When he is at the -th planet, he can next fly to the -th planet only if , which will cost his spaceship 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.
Little Q knows the position of planets in space, labeled by to . To his surprise, these planets are all coplanar. So to simplify, Little Q put these planets on a plane coordinate system, and calculated the coordinate of each planet .
Little Q plans to start his journey at the -th planet, and end at the -th planet. When he is at the -th planet, he can next fly to the -th planet only if , which will cost his spaceship 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
, denoting the number of test cases.
In each test case, there is an integer in the first line, denoting the number of planets.
For the next lines, each line contains integers , denoting the coordinate of the -th planet. Note that different planets may have the same coordinate because they are too close to each other. It is guaranteed that .
In each test case, there is an integer in the first line, denoting the number of planets.
For the next lines, each line contains integers , denoting the coordinate of the -th planet. Note that different planets may have the same coordinate because they are too close to each other. It is guaranteed that .
Output
For each test case, print a single line containing several distinct integers
, denoting the route you chosen is
. Obviously
should be
and
should be
. 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 is lexicographically smaller than a sequence of if there exists such index that for all , but .
A sequence of integers is lexicographically smaller than a sequence of if there exists such index that for all , but .
Sample Input
1
3
0 0
3 0
4 0
Sample Output
1 2 3
Source
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;
}