UVa 10002 Center of Masses (凸包重心)

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http://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=943

重心=(多边形三角剖分的各个三角形的重心*各个三角形的有向面积/多边形面积)/3

完整代码：

/*0.095s*/#include<bits/stdc++.h>using namespace std;const int mx = 105;const double eps = 1e-8;struct P{double x, y;P(double x = 0, double y = 0): x(x), y(y) {}void read(){scanf("%lf%lf", &x, &y);}bool operator < (const P& p) const ///加cosnt以便sort调用，其他函数不加const对速度没有影响{return x < p.x || x == p.x && y < p.y;}P operator + (P p){return P(x + p.x, y + p.y);}P operator - (P p){return P(x - p.x, y - p.y);}P operator * (double d){return P(x * d, y * d);}P operator / (double d){return P(x / d, y / d);}double dot(P p){return x * p.x + y * p.y;}double det(P p){return x * p.y - y * p.x;}} a[mx], ans[mx];int n, len;///求凸包void convex_hull(){sort(a, a + n);len = 0;int i;for (i = 0; i < n; ++i){while (len >= 2 && (ans[len - 1] - ans[len - 2]).det(a[i] - ans[len - 1]) < eps)--len;ans[len++] = a[i];}int tmp = len;for (i = n - 2; i >= 0; --i){while (len > tmp && (ans[len - 1] - ans[len - 2]).det(a[i] - ans[len - 1]) < eps)--len;ans[len++] = a[i];}--len;}double area(){double sum = 0.0;ans[n] = ans[0];for (int i = 0; i < len; ++i)sum += ans[i].det(ans[i + 1]);return sum / 2.0;}P masscenter(){P res = P(0, 0);double s = area();if (s < eps) return res;ans[n] = ans[0];for (int i = 0; i < len; ++i)res = res + (ans[i] + ans[i + 1]) * (ans[i].det(ans[i + 1]));return res / s / 6.0; ///((res/2)/s)/3}int main(){int i;P res;while (scanf("%d", &n), n >= 3){for (i = 0; i < n; ++i) a[i].read();convex_hull();res = masscenter();printf("%.3f %.3f\n", res.x, res.y);}return 0;}

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