#include <stdio.h>#include <stdlib.h>

//#define ZEROVALUE 0.00000000000001

#ifndef __max#define __max(a,b)  (((a) > (b)) ? (a) : (b))#endif

#ifndef __min#define __min(a,b)  (((a) < (b)) ? (a) : (b))#endif

typedef struct _LINE{double x1;double y1;double x2;double y2;    _LINE* pNext;} LINE;

//以Pi为原点，从 PiPj 到 PiPk 的方位（返回值的符号表示顺时针 or 逆时针）double Direction(double xi, double yi, //原点                 double xj, double yj, //线段1结束点                 double xk, double yk) //线段2结束点{return (xk - xi) * (yj - yi) - (xj - xi) * (yk - yi);}

//如果点 Pk 位于线段 PiPj 所在直线上，则它是否位于该线段内int OnSegment(double xi, double yi,                 double xj, double yj, //线段1结束点               double xk, double yk) //线段2结束点{if(xk >= __min(xi, xj) && xk <= __max(xi, xj)        && yk >= __min(yi, yj) && yk <= __max(yi, yj))return 1;elsereturn 0;}

//判断两个线段P1P2，P3P4是否相交int intersect(double x1, double y1,double x2, double y2,double x3, double y3,double x4, double y4){double d1 = Direction(x3, y3, x4, y4, x1, y1);double d2 = Direction(x3, y3, x4, y4, x2, y2);double d3 = Direction(x1, y1, x2, y2, x3, y3);double d4 = Direction(x1, y1, x2, y2, x4, y4);

if(    ((d1 > 0 && d2 < 0) || (d1 < 0 && d2 > 0))        && ((d3 > 0 && d4 < 0) || (d3 < 0 && d4 > 0)) )return 1; //相交

else if(d1 == 0 && OnSegment(x3, y3, x4, y4, x1, y1))return 1;else if(d2 == 0 && OnSegment(x3, y3, x4, y4, x2, y2))return 1;else if(d3 == 0 && OnSegment(x1, y1, x2, y2, x3, y3))return 1;else if(d4 == 0 && OnSegment(x1, y1, x2, y2, x4, y4))return 1;elsereturn 0; //绝对不相交}

/* 增加线段到链表尾部 */

void AddLine(LINE** ppHead, LINE** ppTail,double x1, double y1,double x2, double y2){    LINE *pNode = (LINE*)malloc(sizeof(LINE));    pNode->pNext = NULL;    pNode->x1 = x1;    pNode->y1 = y1;    pNode->x2 = x2;    pNode->y2 = y2;

if(*ppTail != NULL)    {        (*ppTail)->pNext = pNode;        }else    {        *ppHead = pNode;    }    *ppTail = pNode;}

void FreeList(LINE** ppHead, LINE** ppTail){    LINE* pNode = (*ppHead);while(pNode != NULL)    {        LINE* tmp = pNode->pNext;        free(pNode);        pNode = tmp;    }    *ppHead = NULL;    *ppTail = NULL;}

/* 检查是否这一系列点围成的多边形是否合法 */

int CheckValid(LINE* pHead){int index = 0; /* 当前正循环到的边的索引 */    LINE* pCur = pHead;    LINE* pTest;

while(pCur != NULL)    {        pTest = NULL;if(pCur->pNext != NULL)            pTest = pCur->pNext->pNext;

while(pTest != NULL)        {//最后一条边(n-1) -- (0)，不与第一条边 (0) -- (1) 检测            if(index == 0 && pTest->pNext == NULL)break;

/* 非相邻边相交？ */if(intersect(pCur->x1, pCur->y1, pCur->x2, pCur->y2,                pTest->x1, pTest->y1, pTest->x2, pTest->y2))            {return 0;            }            pTest = pTest->pNext;        }        pCur = pCur->pNext;        ++index;    }    return 1;}

int main(int argc, char* argv[]){    LINE *pHead = NULL, *pTail = NULL;int i, n = 0, figure = 1;double x0, y0, x1, y1, x2, y2;double area = 0;

//int test = intersect(0, 1, 1, 0, 1, -1, 0, 0.5);

while(1)    {        scanf("%d", &n);if(n <= 0)break;

//打印一个空行        if(figure > 1)            printf("\n");

        area = 0;        scanf("%lf %lf", &x0, &y0);        x1 = x0;        y1 = y0;for(i = 1; i <= n; i++)        {if(i < n)                scanf("%lf %lf", &x2, &y2);else            {                x2 = x0;                y2 = y0;            }            area += (y1 + y2) * (x2 - x1) * 0.5;

            AddLine(&pHead, &pTail, x1, y1, x2, y2);

            x1 = x2;            y1 = y2;        }

if(area < 0)            area *= -1;

if(n < 3)            printf("Figure %d: Impossible\n", figure);else if(!CheckValid(pHead))            printf("Figure %d: Impossible\n", figure);else            printf("Figure %d: %.02lf\n", figure, area);

        FreeList(&pHead, &pTail);

        figure++;    }return 0;}

发信人: dynamic (programming@math), 信区: ACMICPC标  题: Re: 1010里的错误多边形有多少可能性？发信站: 逸仙时空 Yat-sen Channel (Wed Apr  9 20:55:07 2003), 站内信件

我的程序

//zju 1010//by dynamic//on sunday july 28th

#include <stdio.h>

double det(double x1,double y1,double x2,double y2,double x3,double y3){return x1*y2+x2*y3+x3*y1-x2*y1-x3*y2-x1*y3;}

int main(){int n,i,j,count=0,temp;double x[1000],y[1000],area;while(1)        {                scanf("%d",&n);if (n==0) return 0;                count++;if (count>1) printf("\n");                printf("Figure %d: ",count);for(i=0;i<n;i++) scanf("%lf%lf",&x[i],&y[i]);if (n<3){                        printf("Impossible\n");continue;                }for(i=0;i<n;i++)for(j=(i+1)/n;j<i-1;j++){                                temp=(i+1)%n;if (det(x[j],y[j],x[i],y[i],x[j+1],y[j+1])*det(x[j],y[j],x[temp],y[temp],x[j+1],y[j+1])<=0&&                                        det(x[i],y[i],x[j],y[j],x[temp],y[temp])*det(x[i],y[i],x[j+1],y[j+1],x[temp],y[temp])<=0) {                                        printf("Impossible\n");goto quit;                                }                         }                area=0;for(i=0;i<n;i++){                        area+=x[i]*y[(i+1)%n];                        area-=y[i]*x[(i+1)%n];                }if (area<0) area*=-1;                printf("%.2lf\n",area/2);quit:;        }}