【 2013 Multi-University Training Contest 7 】

HDU 4666 Hyperspace

曼哈顿距离：|x₁-x₂|+|y₁-y₂|。

最远曼哈顿距离，枚举x₁与x₂的关系以及y₁与y₂的关系，取最大值就是答案。

#include<cstdio>
#include<set>
#define oo 0x7FFFFFFF
#define MAXM 35
#define MAXN 100010
using namespace std;
multiset<int> myset[MAXM];
struct Ask {
    int cmd;
    int arr[MAXM];
} q[MAXN];
int main() {
    int n, m;
    int i, j, k;
    int tmp;
    int res;
    int ans;
    multiset<int>::iterator it1, it2;
    while (~scanf("%d%d", &n, &m)) {
        for (i = 0; i < MAXM; i++) {
            myset[i].clear();
        }
        for (i = 1; i <= n; i++) {
            scanf("%d", &q[i].cmd);
            if (q[i].cmd == 0) {
                for (j = 0; j < m; j++) {
                    scanf("%d", &q[i].arr[j]);
                }
            } else {
                scanf("%d", &tmp);
                q[i].cmd = q[tmp].cmd ^ 1;
                for (j = 0; j < m; j++) {
                    q[i].arr[j] = q[tmp].arr[j];
                }
            }
        }
        for (i = 1; i <= n; i++) {
            if (q[i].cmd == 0) {
                for (j = 0; j < (1 << m); j++) {
                    tmp = j;
                    res = 0;
                    for (k = 0; k < m; tmp >>= 1, k++) {
                        if (tmp & 1) {
                            res -= q[i].arr[k];
                        } else {
                            res += q[i].arr[k];
                        }
                    }
                    myset[j].insert(res);
                }
            } else {
                for (j = 0; j < (1 << m); j++) {
                    tmp = j;
                    res = 0;
                    for (k = 0; k < m; tmp >>= 1, k++) {
                        if (tmp & 1) {
                            res -= q[i].arr[k];
                        } else {
                            res += q[i].arr[k];
                        }
                    }
                    myset[j].erase(myset[j].find(res));
                }
            }
            ans = -oo;
            for (j = 0; j < (1 << m); j++) {
                if (myset[j].size() > 1) {
                    break;
                }
            }
            if (j >= (1 << m)) {
                ans = 0;
            } else {
                for (j = 0; j < (1 << m); j++) {
                    if (myset[j].size() > 1) {
                        it1 = myset[j].end();
                        it1--;
                        it2 = myset[j].begin();
                        ans = max(ans, (*it1 - *it2));
                    }
                }
            }
            printf("%d
", ans);
        }
    }
    return 0;
}

---

HDU 4667 Building Fence

三角形上的点当作普通点。

点与圆的切点可能是凸包上的点。

两圆公切线与圆的交点也可能是凸包上的点。

凸包上两个点属于同一个圆，则长度等于弧长。否则长度就是线段距离。

#include<cstdio>
#include<cmath>
#include<vector>
#include<algorithm>
#define MAXN 500010
#define EPS 1e-8
const double PI = acos(-1.0);
using namespace std;
struct Point {
    double x, y;
    int idx;
    Point(double _x = 0, double _y = 0, int _idx = 0) {
        x = _x;
        y = _y;
        idx = _idx;
    }
};
struct Circle {
    Point o;
    double r;
};
vector<Point> p;
Point st[MAXN];
int top;
Circle c[MAXN];
inline int dbcmp(double x, double y) {
    if (fabs(x - y) < EPS) {
        return 0;
    } else {
        return x > y ? 1 : -1;
    }
}
bool cmp(Point p1, Point p2) {
    if (dbcmp(p1.y, p2.y)) {
        return p1.y < p2.y;
    } else {
        return p1.x < p2.x;
    }
}
Point operator+(Point p1, Point p2) {
    return Point(p1.x + p2.x, p1.y + p2.y);
}
Point operator-(Point p1, Point p2) {
    return Point(p1.x - p2.x, p1.y - p2.y);
}
Point operator*(Point p1, double k) {
    return Point(p1.x * k, p1.y * k);
}
Point Rotate(Point p, double angle) {
    Point res;
    res.x = p.x * cos(angle) - p.y * sin(angle);
    res.y = p.x * sin(angle) + p.y * cos(angle);
    return res;
}
void TangentPoint_PC(Point poi, Point o, double r, Point &result1,
        Point &result2) {
    double line = sqrt(
            (poi.x - o.x) * (poi.x - o.x) + (poi.y - o.y) * (poi.y - o.y));
    double angle = acos(r / line);
    Point unitvector, lin;
    lin.x = poi.x - o.x;
    lin.y = poi.y - o.y;
    unitvector.x = lin.x / sqrt(lin.x * lin.x + lin.y * lin.y) * r;
    unitvector.y = lin.y / sqrt(lin.x * lin.x + lin.y * lin.y) * r;
    result1 = Rotate(unitvector, -angle);
    result2 = Rotate(unitvector, angle);
    result1.x += o.x;
    result1.y += o.y;
    result2.x += o.x;
    result2.y += o.y;
    return;
}
inline double dist(Point p1, Point p2) {
    return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
void TangentPoint_CC(Circle c1, Circle c2) {
    if (dbcmp(c1.r, c2.r) > 0) {
        swap(c1, c2);
    }
    double c2c = dist(c1.o, c2.o);
    double height = c2.r - c1.r;
    double alpha = asin(height / c2c) + PI / 2;
    Point v1, v2, tmp;
    v1 = c2.o - c1.o;
    double len = dist(v1, Point(0, 0));
    v1.x /= len;
    v1.y /= len;

    v2 = Rotate(v1, alpha);
    tmp = v2 * c1.r + c1.o;
    tmp.idx = c1.o.idx;
    p.push_back(tmp);
    tmp = v2 * c2.r + c2.o;
    tmp.idx = c2.o.idx;
    p.push_back(tmp);

    v2 = Rotate(v1, -alpha);
    tmp = v2 * c1.r + c1.o;
    tmp.idx = c1.o.idx;
    p.push_back(tmp);
    tmp = v2 * c2.r + c2.o;
    tmp.idx = c2.o.idx;
    p.push_back(tmp);
}
inline double xmult(Point p0, Point p1, Point p2) {
    return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}
double dot(Point a, Point b) {
    return a.x * b.x + a.y * b.y;
}
double cross(Point a, Point b) {
    return a.x * b.y - a.y * b.x;
}
double len(Point a) {
    return sqrt(a.x * a.x + a.y * a.y);
}
double angle(Point a, Point b) {
    double ret = acos(dot(a, b) / (len(a) * len(b)));
    if (cross(a, b) > 0) {
        return ret;
    } else {
        return 2 * PI - ret;
    }
}
int main() {
    int n, m;
    int i, j;
    double x, y;
    int tmp;
    Point p1, p2;
    double ans;
    while (~scanf("%d%d", &n, &m)) {
        p.clear();
        for (i = 0; i < n; i++) {
            scanf("%lf%lf%lf", &x, &y, &c[i].r);
            c[i].o = Point(x, y, i);
        }
        for (i = 0; i < m; i++) {
            for (j = 0; j < 3; j++) {
                scanf("%lf%lf", &x, &y);
                p.push_back(Point(x, y, -1));
            }
        }
        for (i = 0; i < n; i++) {
            for (j = 0; j < 3 * m; j++) {
                TangentPoint_PC(p[j], c[i].o, c[i].r, p1, p2);
                p1.idx = p2.idx = c[i].o.idx;
                p.push_back(p1);
                p.push_back(p2);
            }
        }
        for (i = 0; i < n; i++) {
            for (j = i + 1; j < n; j++) {
                TangentPoint_CC(c[i], c[j]);
            }
        }
        sort(p.begin(), p.end(), cmp);
        top = -1;
        for (i = 0; i < (int) p.size(); i++) {
            while (top > 0 && dbcmp(xmult(st[top - 1], st[top], p[i]), 0) <= 0) {
                top--;
            }
            st[++top] = p[i];
        }
        tmp = top;
        for (i = p.size() - 2; i >= 0; i--) {
            while (top > tmp && dbcmp(xmult(st[top - 1], st[top], p[i]), 0) <= 0) {
                top--;
            }
            st[++top] = p[i];
        }
        if (n == 1 && m == 0) {
            ans = 2 * PI * c[0].r;
        } else {
            ans = 0;
            for (i = 0; i < top; i++) {
                if (st[i].idx < 0 || st[i + 1].idx < 0
                        || st[i].idx != st[i + 1].idx) {
                    ans += dist(st[i], st[i + 1]);
                } else {
                    ans += c[st[i].idx].r
                            * angle(st[i] - c[st[i].idx].o,
                                    st[i + 1] - c[st[i].idx].o);
                }
            }
        }
        printf("%.5lf
", ans);
    }
    return 0;
}