hdu 5298 Solid Geometry Homework

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http://acm.hdu.edu.cn/showproblem.php?pid=5298

用red和yellow给空间染色，使得相邻区域颜色不同，且指定点所在区域颜色为yellow，问是否存在解和指定点颜色？

立体几何，其实是道水题，将点带入方程判断是在面的哪一侧，保证球面内外，平面上下都是反的，然后再判断一下合法性就ok了！

其实给我的感觉也就是这种成功染色的方法蛮奇妙的！哈哈，还好啦，你就两个点两个点想，这种方法，刚开始颜色是一样的，然后中间经过各种取反，肯定能保证最后相邻两个点的颜色是不相等的！因此就肯定是合法的染色！

#include <cstdio>#include <cstring>#include <vector>#include <algorithm>using namespace std;const int maxn = 3000;typedef long long ll;struct Point {    int type;    ll x, y, z;    Point (int type = 0, ll x = 0, ll y = 0, ll z = 0) {        this->type = type;        this->x = x;        this->y = y;        this->z = z;    }};struct Shape {    int type;    ll a, b, c, d;    Shape (int type = 0, ll a = 0, ll b = 0, ll c = 0, ll d = 0) {        this->type = type;        this->a = a;        this->b = b;        this->c = c;        this->d = d;    }    bool judge (Point u) {        if (type) {            ll ta = u.x - a, tb = u.y - b, tc = u.z - c;            return ta * ta + tb * tb + tc * tc - d * d > 0;        }        return a * u.x + b * u.y + c * u.z + d > 0;    }};int M, N, P, Q, V[maxn];vector<Shape> s;vector<Point> p;void init () {    s.clear();    p.clear();    memset(V, 0, sizeof(V));    ll a, b, c, d;    scanf("%d%d%d%d", &M, &N, &P, &Q);    for (int i = 0; i < M; i++) {        scanf("%lld%lld%lld%lld", &a, &b, &c, &d);        s.push_back(Shape(0, a, b, c, d));    }    for (int i = 0; i < N; i++) {        scanf("%lld%lld%lld%lld", &a, &b, &c, &d);        s.push_back(Shape(1, a, b, c, d));    }    for (int i = 0; i < P; i++) {        scanf("%lld%lld%lld", &a, &b, &c);        p.push_back(Point(0, a, b, c));    }    for (int i = 0; i < Q; i++) {        scanf("%lld%lld%lld", &a, &b, &c);        p.push_back(Point(1, a, b, c));    }}void solve () {    if (P == 0) {        for (int i = 0; i < Q; i++)            printf("Both\n");        return;    }    for (int i = 0; i < s.size(); i++) {        for (int j = 0; j < p.size(); j++) {            if (s[i].judge(p[j]))                V[j] ^= 1;        }    }    int yellow = -1;    for (int i = 0; i < p.size(); i++) {        if (p[i].type == 0) {            if (yellow == -1)                yellow = V[i];            else if (yellow != V[i]) {                printf("Impossible\n");                return;            }        }    }    for (int i = 0; i < p.size(); i++) {        if (p[i].type) {            printf("%s\n", V[i] == yellow ? "Y" : "R");        }    }}int main () {    int cas;    scanf("%d", &cas);    while (cas--) {        init();        solve();        if (cas)            printf("\n");    }    return 0;}

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