链接:http://acm.hdu.edu.cn/showproblem.php?pid=6325 Interstellar Travel
Problem DescriptionAfter 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. InputThe 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
. OutputFor 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 Input1
3
0 0
3 0
4 0 Sample Output1 2 3 Source2018 Multi-University Training Contest 3 Recommendchendu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;
}