UVa 11626 - Convex Hull

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题目：按逆时针顺序输出凸包上的点，左下角为起点。

分析：计算几何、凸包。题目会给出是够是凸包上的点，不在凸包上的可以忽略。

注意：共线点的处理，如果用int叉乘会溢出。

#include <algorithm> #include <iostream>#include <cstdlib>#include <cstdio>#include <cmath>using namespace std;typedef struct pnode{double x,y,d;}point; point P[ 100001 ];point S[ 100001 ];point MP;double crossproduct( point a, point b, point c )//ab到ac {return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);}double dist( point a, point b ){return sqrt((b.x-a.x)*(b.x-a.x)+(b.y-a.y)*(b.y-a.y));}bool cmp1( point a, point b ){if ( a.x == b.x ) return a.y < b.y;else return a.x < b.x;}bool cmp2( point a, point b ){return crossproduct( P[0], a, b ) > 0;}bool cmp3( point a, point b ){double cp = crossproduct( P[0], a, b );if ( cp == 0.0 ) {if ( !crossproduct( P[0], a, MP ) )//在回边上 return a.d > b.d;else return a.d < b.d;}else return cp > 0;}void Graham( int N ){sort( P+0, P+N, cmp1 );sort( P+1, P+N, cmp2 );//处理共线 for ( int i = 1 ; i < N ; ++ i )P[i].d = dist( P[0], P[i] );MP = P[N-1];sort( P+1, P+N, cmp3 );int top = -1;if ( N > 0 ) S[++ top] = P[0];if ( N > 1 ) S[++ top] = P[1];if ( N > 2 ) {S[++ top] = P[2];for ( int i = 3 ; i < N ; ++ i ) {while ( crossproduct( S[top-1], S[top], P[i] ) < 0 ) -- top;S[++ top] = P[i];}}printf("%d\n",top+1);for ( int i = 0 ; i <= top ; ++ i )printf("%.0lf %.0lf\n",S[i].x,S[i].y);}int main(){int  N,T; char C;while ( scanf("%d",&T) != EOF ) while ( T -- ) {scanf("%d",&N);int count = 0;for ( int i = 0 ; i < N ; ++ i ) {scanf("%lf %lf %c",&P[count].x,&P[count].y,&C);if ( C == 'Y' ) count ++;}Graham( count );}return 0;}