UVA - 1543 Telescope——最优三角剖分

最优三角剖分的变形

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;
const double PI = acos(-1.0);
const int maxn = 50;
struct Point {
double x, y;
Point(double xx = 0, double yy = 0) : x(xx), y(yy) {}
};
typedef Point Vector;
int n, m;
double t, dp[maxn][maxn][maxn];
Point p[maxn];
Vector operator - (const Vector A, const Vector B) { return Vector(A.x-B.x, A.y-B.y); }
double Cross(Vector A, Vector B) { return A.x*B.y-A.y*B.x; }
double area(int x, int y, int z) {
return fabs(Cross(p[y] - p[x], p[z] - p[x])) / 2.0;
}
Vector Rotate(Vector A, double rad) {
return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}
int main() {
Vector base; base.x = 1, base.y = 0;
while (~scanf("%d %d", &n, &m) && (n + m)) {
for (int i = 1; i <= n; i++) {
scanf("%lf", &t); p[i] = Rotate(base, t * 2.0 * PI);
}
memset(dp, 0, sizeof(dp));
double ans = 0;
for (int num = 3; num <= m; num++) {
for (int len = 2; len < n; len++) {
for (int i = 1; i + len <= n; i++) {
int j = i + len;
for (int k = i + 1; k < j; k++) {
dp[num][i][j] = max(dp[num][i][j], max(dp[num-1][i][k], dp[num-1][k][j]) + area(i, k, j));
}
ans = max(ans, dp[num][i][j]);
}
}
}
printf("%.6lf\n", ans);
}
return 0;
}