POJ 1873 The Fortified Forest 暴力凸包
2013-11-15 11:18
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题意:给出n棵树的坐标,树的高度和树的价值,从这些树中砍掉一些(整棵整棵的)做围栏把剩余的树围起来,使得消耗的树的价值最小。输出应砍掉哪里些树以及剩余的材料的长度。(如果砍掉的价值相同,则取砍掉数目少的)(2 <= n <= 15)。
传说中的WF水题,卡了一晚上,结果发现是周长计算问题orz。。。说明我做题还是要小心点。。。
因为只有15棵树,用位运算枚举砍树情况就行了。
代码:
传说中的WF水题,卡了一晚上,结果发现是周长计算问题orz。。。说明我做题还是要小心点。。。
因为只有15棵树,用位运算枚举砍树情况就行了。
代码:
/* * Author: illuz <iilluzen[at]gmail.com> * Blog: http://blog.csdn.net/hcbbt * File: poj1873.cpp * Create Date: 2013-11-14 19:29:19 * Descripton: convex hull */ #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> using namespace std; #define sqr(a) ((a) * (a)) #define dis(a, b) sqrt(sqr(a.x - b.x) + sqr(a.y - b.y)) const int MAXN = 20; const double PI = acos(-1.0); const int INF = 0x7fffffff; struct Point { double x; double y; int v; int l; Point(double a = 0, double b = 0) : x(a), y(b) {} friend bool operator < (const Point &l, const Point &r) { return l.y < r.y || (l.y == r.y && l.x < r.x); } } p[MAXN], ch[MAXN * 2], tmp[MAXN]; // p, point ch, convex hull double mult(Point a, Point b, Point o) { return (a.x - o.x) * (b.y - o.y) >= (b.x - o.x) * (a.y - o.y); } double Graham(Point p[], int n, Point res[]) { int top = 1; sort(p, p + n); if (n == 0) return 0; res[0] = p[0]; if (n == 1) return 0; res[1] = p[1]; if (n == 2) return dis(p[0], p[1]) * 2; res[2] = p[2]; for (int i = 2; i < n; i++) { while (top && (mult(p[i], res[top], res[top - 1]))) top--; res[++top] = p[i]; } int len = top; res[++top] = p[n - 2]; for (int i = n - 3; i >= 0; i--) { while (top != len && (mult(p[i], res[top], res[top - 1]))) top--; res[++top] = p[i]; } // c double c = dis(res[0], res[top - 1]); for (int i = 0; i < top - 1; i++) c += dis(res[i], res[i + 1]); return c; } int n, cas = 0; int main() { while (scanf("%d", &n) && n) { for (int i = 0; i < n; i++) scanf("%lf%lf%d%d", &p[i].x, &p[i].y, &p[i].v, &p[i].l); int min_cut = INF, min_val = INF, ans = 0; double res_len = 0; for (int bit = 0; bit < (1 << n); bit++) { int res = 0, cut_val = 0; double cut_len = 0; for (int i = 0; i < n; i++) if (bit & (1 << i)) { cut_len += p[i].l; cut_val += p[i].v; } else { tmp[res].x = p[i].x; tmp[res++].y = p[i].y; } if (cut_val > min_val) continue; double c = Graham(tmp, res, ch); if (cut_len >= c) if (cut_val < min_val || (cut_val == min_val && n - res < min_cut)) { ans = bit; min_val = cut_val; min_cut = n - res; res_len = cut_len - c; } } if (cas) puts(""); printf("Forest %d\n", ++cas); printf("Cut these trees:"); for (int i = 0; i < n; i++) if (ans & (1 << i)) printf(" %d", i + 1); printf("\nExtra wood: %.2f\n", res_len); } return 0; }
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