[LOJ 2039] 「SHOI2015」激光发生器

[LOJ 2039] 「SHOI2015」激光发生器

链接

链接

题解

分为两个部分

第一个是求直线之间的交点找到第一个触碰到的镜面

第二个是求直线经过镜面反射之后的出射光线

第一个很好做，第二个就是将入射光线旋转，注意旋转后在哪一面（可能到镜面背后去）

代码

// Copyright lzt
#include<stdio.h>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<cmath>
#include<iostream>
#include<queue>
#include<string>
#include<ctime>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef long double ld;
typedef unsigned long long ull;
typedef pair<long long, long long> pll;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define rep(i, j, k)  for (register int i = (int)(j); i <= (int)(k); i++)
#define rrep(i, j, k) for (register int i = (int)(j); i >= (int)(k); i--)
#define Debug(...) fprintf(stderr, __VA_ARGS__)

inline ll read() {
  ll x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
  if (ch == '-') f = -1;
  ch = getchar();
  }
  while (ch <= '9' && ch >= '0') {
  x = 10 * x + ch - '0';
  ch = getchar();
  }
  return x * f;
}

const int maxn = 110;
const double eps = 1e-8;
const double pi = acos(-1);

struct Point {
  double x, y;
  Point(double _x = 0, double _y = 0) {
    x = _x; y = _y;
  }
  Point operator + (const Point &b) const {
    return (Point){x + b.x, y + b.y};
  }
  Point operator - (const Point &b) const {
    return (Point){x - b.x, y - b.y};
  }
  Point operator * (const double &b) const {
    return (Point){x * b, y * b};
  }
};
typedef Point Vector;
struct Line {
  Point x; Vector y;
  Line() {}
  Line(Point _x, Vector _y) {
    x = _x; y = _y;
  }
};
struct LLL {
  Point p1, p2;
  double a, b;
} A[maxn];
double Dot(const Vector &a, const Vector &b) {
  return a.x * b.x + a.y * b.y;
}
double Cross(const Vector &a, const Vector &b) {
  return a.x * b.y - a.y * b.x;
}
double Len(const Vector &a) {
  return sqrt(Dot(a, a));
}
int dcmp(double x) {
  return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);
}
Point intersect(const Line &a, const Line &b) {
  Vector v = a.x - b.x;
  double t = Cross(b.y, v) / Cross(a.y, b.y);
  return a.x + a.y * t;
}
double Angle(const Vector &a, const Vector &b) {
  return acos(Dot(a, b) / Len(a) / Len(b));
}
bool onseg(const Point &p, const Point &a, const Point &b) {
  return dcmp(Dot(a - p, b - p)) <= 0 && dcmp(Cross(a - p, a - p)) == 0;
}
Vector rotate(const Vector &a, double b) {
  return (Vector){a.x * cos(b) - a.y * sin(b), a.y * cos(b) + a.x * sin(b)};
}
double X, Y, dx, dy;
int n;

void work() {
  X = read(), Y = read(), dx = read(), dy = read();
  n = read();
  rep(i, 1, n) {
    A[i].p1.x = read(); A[i].p1.y = read();
    A[i].p2.x = read(); A[i].p2.y = read();
    A[i].a = read(), A[i].b = read();
  }
  Point nw = (Point){X, Y};
  Vector v = (Vector){dx, dy};
  rep(_, 1, 10) {
    int ind = 0; double nwdis = 1e9;
    rep(i, 1, n) {
      if (dcmp(Cross(A[i].p1 - A[i].p2, v)) == 0) continue;
      Point p = intersect(Line(A[i].p1, A[i].p2 - A[i].p1), Line(nw, v));
      if (onseg(p, A[i].p1, A[i].p2) && dcmp(Dot(v, p - nw)) > 0) {
        double dis = Len(p - nw);
        if (dis < nwdis) nwdis = dis, ind = i;
      }
    }
    if (!ind) {
      if (_ == 1) puts("NONE");
      break;
    }
    printf("%d ", ind);
    nw = intersect(Line(A[ind].p1, A[ind].p2 - A[ind].p1), Line(nw, v));
    if (dcmp(Dot(A[ind].p1 - A[ind].p2, v)) == 0) v = v * (-1);
    else {
      Vector nwv;
      if (dcmp(Dot(A[ind].p1 - A[ind].p2, v)) > 0) nwv = A[ind].p1 - A[ind].p2;
      else nwv = A[ind].p2 - A[ind].p1;
      double alpha = pi / 2 - Angle(nwv, v);
      if (dcmp(Cross(nwv, v)) > 0) v = rotate(nwv, alpha * A[ind].a / A[ind].b - pi / 2);
      else v = rotate(nwv, pi / 2 - alpha * A[ind].a / A[ind].b);
    }
  }
}

int main() {
  #ifdef LZT
  freopen("in", "r", stdin);
  #endif

  work();

  #ifdef LZT
  Debug("My Time: %.3lfms
", (double)clock() / CLOCKS_PER_SEC);
  #endif
}