先求凸包, 最大三角形的三个顶点一定在凸包的点上.
//Rotating Calipers algorithm
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MaxNode 50005
int stack[MaxNode];
int top;
double max;
typedef struct TPoint
{
int x;
int y;
}TPoint;
TPoint point[MaxNode];
void swap(TPoint point[], int i, int j)
{
TPoint tmp;
tmp = point[i];
point[i] = point[j];
point[j] = tmp;
}
double multi(TPoint p1, TPoint p2, TPoint p0)
{
return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}
double distance(TPoint p1, TPoint p2)
{
return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
}
int cmp(const void *a, const void *b)
{
TPoint *c = (TPoint *)a;
TPoint *d = (TPoint *)b;
double k = multi(*c, *d, point[0]);
if(k< 0) return 1;
else if(k == 0 && distance(*c, point[0]) >= distance(*d, point[0]))
return 1;
else return -1;
}
void grahamScan(int n)
{
//Graham扫描求凸包
int i, u;
//将最左下的点调整到p[0]的位置
u = 0;
for(i = 1;i <= n - 1;i++){
if((point[i].y < point[u].y) ||
(point[i].y == point[u].y && point[i].x < point[u].x))
u = i;
}
swap(point, 0, u);
//将平p[1]到p[n - 1]按按极角排序，可采用快速排序
qsort(point + 1, n - 1, sizeof(point[0]), cmp);
for(i = 0;i <= 2;i++) stack[i] = i;
top = 2;
for(i = 3;i <= n - 1;i++){
while(multi(point[i], point[stack[top]], point[stack[top - 1]]) >= 0){
top--;
if(top == 0) break;
}
top++;
stack[top] = i;
}
}
int main()
{
double triangleArea(int i, int j, int k);
void PloygonTriangle();
int i, n;
while(scanf("%d", &n) && n != -1){
for(i = 0;i < n;i++)
scanf("%d%d", &point[i].x, &point[i].y);
if(n <= 2){
printf("0.00\n");
continue;
}
if(n == 3){
printf("%.2lf\n", triangleArea(0, 1, 2));
continue;
}
grahamScan(n);
PloygonTriangle();
printf("%.2lf\n", max);
}
return 0;
}
void PloygonTriangle()
{
double triangleArea(int i, int j, int k);
int i, j , k;
double area, area1;
max = -1;
for(i = 0;i <= top - 2;i++){
k = -1;
for(j = i + 1; j <= top - 1;j++){
if(k <= j) k= j + 1;
area = triangleArea(stack[i], stack[j], stack[k]);
if(area > max) max = area;
while(k + 1 <= top){
area1= triangleArea(stack[i], stack[j], stack[k + 1]);
if(area1 < area) break;
if(area1 > max) max = area1;
area = area1;
k++;
}
}
}
}
double triangleArea(int i, int j, int k)
{
//已知三角形三个顶点的坐标，求三角形的面积
double l = fabs(point[i].x * point[j].y + point[j].x * point[k].y
+ point[k].x * point[i].y - point[j].x * point[i].y
- point[k].x * point[j].y - point[i].x * point[k].y) / 2;
return l;
}
posted on 2011-06-30 20:37
小阮 阅读(2059)
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