UVA 1543 - Telescope（dp+几何）

#include <stdio.h>
#include <string.h>
#include <math.h>
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
const int N = 45;
int n, m, i, j, k, x;
double p[N], dp[N][N][N];
const double pi = acos(-1.0);

inline double cal(double p1, double p2) {
	double d = pi * (p1 - p2);
	return 2 * sin(d);
}

inline double area(double p1, double p2, double p3) {
	double a = cal(p1, p2);
	double b = cal(p2, p3);
	double c = cal(p3, p1);
	double p = (a + b + c) / 2;
	return sqrt(p * (p - a) * (p - b) * (p - c));
}

int main() {
	while (~scanf("%d%d", &n, &m) && n || m) {
		double ans = 0;
		memset(dp, 0, sizeof(dp));
		for (i = 1; i <= n; i++)
			scanf("%lf", &p[i]);
		for (x = 1; x <= n; x++) {
			int t = min(x, m);
			for (i = 3; i <= t; i++) {
				for (j = 1; j < x; j++) {
					for (k = j + 1; k < x; k++) {
						double s = area(p[x], p[k], p[j]);
						dp[i][j][x] = max(dp[i][j][x], dp[i - 1][j][k] + s);
						if (i == m)
							ans = max(ans, dp[i][j][x]);
					}
				}
			}
		}
		printf("%.6lf\n", ans);
	}
	return 0;
}