[bzoj1007][HNOI2008]水平可见直线 单调栈

1007: [HNOI2008]水平可见直线

Time Limit: 1 Sec  Memory Limit: 162 MB
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Description

　　在xoy直角坐标平面上有n条直线L1,L2,...Ln,若在y值为正无穷大处往下看,能见到Li的某个子线段,则称Li为
可见的,否则Li为被覆盖的.
例如,对于直线:
L1:y=x; L2:y=-x; L3:y=0
则L1和L2是可见的,L3是被覆盖的.
给出n条直线,表示成y=Ax+B的形式(|A|,|B|<=500000),且n条直线两两不重合.求出所有可见的直线.

Input

　　第一行为N(0 < N < 50000),接下来的N行输入Ai,Bi

Output

　　从小到大输出可见直线的编号，两两中间用空格隔开,最后一个数字后面也必须有个空格

Sample Input

3
-1 0
1 0
0 0

Sample Output

1 2

HINT

按斜率排序，维护一个单调栈，如果栈顶元素交点在右边就出栈

#include<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>#define eps 1e-8using namespace std;const int N = 500000 + 5;struct data{int id; double a,b;}l[N],st[N];int n,top; bool is[N];bool cmp(data a,data b){if( fabs(a.a-b.a) < eps ) return a.b < b.b;else return a.a<b.a;}bool cmp2( data a, data b ){ return a.id < b.id; }double x( data y1, data y2 ) {return (y2.b-y1.b)/(y1.a-y2.a);}void insert( data y ){while( top ){if( fabs(st[top].a-y.a) < eps ) top--;else if( top>1 && x(y,st[top-1]) <= x(st[top],st[top-1]) ) top--;else break;}st[++top] = y;}int main(){scanf("%d", &n);for( int i = 1; i <= n; i++ ) scanf("%lf%lf", &l[i].a, &l[i].b), l[i].id = i;sort( l+1, l+n+1, cmp );for( int i = 1; i <= n; i++ ) insert(l[i]);sort( st+1, st+top+1, cmp2 );for( int i = 1; i <= top; i++ ) printf("%d ", st[i].id );return 0;}