【每日一题】蓝桥杯历年真题题解 -荒岛探测

import java.util.*;
public class Main {    private static final double eps = 1e-6;    private static double xa;    private static double ya;    private static double xb;    private static double yb;    private static double L;    private static double A;    private static double ans;    private static double[] x = new double[6];    private static double[] y = new double[6];    private static double[] Y = new double[6];
    private static double dist(double a, double b, double c, double d) {        return Math.sqrt((c - a) * (c - a) + (d - b) * (d - b));    }
    private static double get(double now, int pos1, int pos2) {        if (Math.abs(x[pos1] - x[pos2]) <= eps && Math.abs(x[pos1] - now) <= eps) {            return 1002;        }        if (now <= Math.min(x[pos1], x[pos2]) || now >= Math.max(x[pos1], x[pos2])) {            return 1002;        }        return (y[pos2] - y[pos1]) / (x[pos2] - x[pos1]) * (now - x[pos2]) + y[pos2];    }
    private static boolean ok1(double now) {        double xx = (xa + xb) / 2;        double yy = (ya + yb) / 2;        double a = L / 2;        double c = dist(xa, ya, xb, yb) / 2;        double b = Math.sqrt(a * a - c * c);        double mid = 1.0 - (now - xx) * (now - xx) / (a * a);        if (mid <= 0) {            return false;        }        mid = Math.sqrt(mid) * b;        Y[1] = yy - mid;        Y[2] = yy + mid;        return true;    }
    private static boolean ok2(double now) {        int cnt = 2;        for (int i = 1; i <= 3; i++) {            int nex = i + 1 == 4 ? 1 : i + 1;            double mid = get(now, i, nex);            if (mid - 1000 > eps) {                continue;            }            if (cnt == 3 && Math.abs(mid - Y[cnt]) <= eps) {                continue;            }            Y[++cnt] = mid;        }        if (cnt != 4) {            return false;        }        return true;    }
    private static double get_angle(double a, double b, double c, double d) {        double now = Math.acos((c - a) / dist(a, b, c, d));        if (d - b < 0) {            return 2 * Math.acos(-1) - now;        }        return now;    }
    private static void init() {        A = get_angle(xa, ya, xb, yb);        double dis1 = dist(0, 0, xa, ya);        double dis2 = dist(0, 0, xb, yb);        double S1 = get_angle(0, 0, xa, ya) - A;        double S2 = get_angle(0, 0, xb, yb) - A;        xa = dis1 * Math.cos(S1);        ya = dis1 * Math.sin(S1);        xb = dis2 * Math.cos(S2);        yb = dis2 * Math.sin(S2);    }
    private static void change(int pos) {        double dis = dist(0, 0, x[pos], y[pos]);        double S = get_angle(0, 0, x[pos], y[pos]) - A;        x[pos] = dis * Math.cos(S);        y[pos] = dis * Math.sin(S);    }
    private static double calc(double now) {        if (!ok1(now)) {            return 0;        }        if (!ok2(now)) {            return 0;        }        double ma = Math.max(Math.min(Y[1], Y[2]), Math.min(Y[3], Y[4]));        double mi = Math.min(Math.max(Y[1], Y[2]), Math.max(Y[3], Y[4]));        if (mi - ma <= eps) {            return 0;        }        return mi - ma;    }
    public static void main(String[] args) {        Scanner cin = new Scanner(System.in);        xa = cin.nextDouble();        ya = cin.nextDouble();        xb = cin.nextDouble();        yb = cin.nextDouble();        L = cin.nextDouble();        init();        for (int i = 1; i <= 3; i++) {            x[i] = cin.nextDouble();            y[i] = cin.nextDouble();            change(i);        }        if (L <= eps || dist(xa, ya, xb, yb) >= L) {            System.out.print("0.00n");            return;        }        for (double i = -1000; i <= 1000; i += 0.001) {            ans += calc(i) * 0.001;        }        System.out.printf("%.2fn", ans);    }}

#include <bits/stdc++.h>using namespace std;const double eps = 1e-6;const int inf = 0x3f3f3f3f;double xa, ya, xb, yb, L, A, ans;double x[6], y[6], Y[6];double dist(double a, double b, double c, double d){    return sqrt((c - a) * (c - a) + (d - b) * (d - b));}double get(double now, int pos1, int pos2){    if(fabs(x[pos1] - x[pos2]) <= eps && fabs(x[pos1] - now) <= eps) return inf;    if(now <= min(x[pos1], x[pos2]) || now >= max(x[pos1], x[pos2])) return inf;    return (y[pos2] - y[pos1]) / (x[pos2] - x[pos1]) * (now - x[pos2]) + y[pos2];}bool ok1(double now){    double xx = (xa + xb) / 2, yy = (ya + yb) / 2;    double a = L / 2 , c = dist(xa, ya, xb, yb) / 2;    double b = sqrt(a * a - c * c);    double mid = 1.0 - (now - xx) * (now - xx) / (a * a);    if(mid <= 0) return false;    mid = sqrt(mid) * b;    Y[1] = yy - mid, Y[2] = yy + mid;    return true;}bool ok2(double now){    int cnt = 2;    for(int i = 1; i <= 3; i++){        int nex = i + 1 == 4 ? 1 : i + 1;        double mid = get(now, i, nex);        if(mid - 1000 > eps) continue;        if(cnt == 3 && fabs(mid - Y[cnt]) <= eps) continue;        Y[++cnt] = mid;    }    if(cnt != 4) return false;    return true;}double get_angle(double a, double b, double c, double d){    double now = acos((c - a) / dist(a, b, c, d));    if(d - b < 0) return 2 * acos(-1) - now;    return now;}void init(){    A = get_angle(xa , ya , xb , yb);    double dis1 = dist(0, 0, xa, ya), dis2 = dist(0, 0, xb, yb);    double S1 = get_angle(0, 0, xa, ya) - A, S2 = get_angle(0, 0, xb, yb) - A;    xa = dis1 * cos(S1) , ya = dis1 * sin(S1);    xb = dis2 * cos(S2) , yb = dis2 * sin(S2);}void change(int pos){    double dis = dist(0, 0, x[pos], y[pos]);    double S = get_angle(0, 0, x[pos], y[pos]) - A;    x[pos] = dis * cos(S) , y[pos] = dis * sin(S);}double calc(double now){    if(!ok1(now)) return 0;    if(!ok2(now)) return 0;    double ma = max(min(Y[1], Y[2]), min(Y[3], Y[4]));    double mi = min(max(Y[1], Y[2]), max(Y[3], Y[4]));    if(mi - ma <= eps) return 0;    return mi - ma;}signed main(){    ios::sync_with_stdio(false);    cin.tie(0) , cout.tie(0);    cin >> xa >> ya >> xb >> yb >> L;    init();    for (int i = 1 ; i <= 3 ; i ++) cin >> x[i] >> y[i] , change(i);    if(L <= eps || dist(xa, ya, xb, yb) >= L) return cout << "0.00n" , 0;    for(double i = -1000 ; i <= 1000 ; i += 0.001) ans += calc(i) * 0.001;    cout << setprecision(2) << fixed << ans << 'n';    return 0;}