97 lines
2.8 KiB
C++
97 lines
2.8 KiB
C++
#include <cstdio>
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#include <cstring>
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#include <cstdlib>
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#include <ctime>
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#include <climits>
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#include <cmath>
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#include <iostream>
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#include <string>
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#include <vector>
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#include <set>
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#include <map>
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#include <list>
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#include <queue>
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#include <stack>
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#include <deque>
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#include <algorithm>
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using namespace std;
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const int maxn = 20005;
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const double eps = 1e-8;
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int n, a, b, c, l, r;
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int x[maxn], y[maxn];
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double p[maxn*2];
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int tot;
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int dcmp(double x) {if (fabs(x) < eps) return 0; return x > 0 ? 1 : -1;}
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double func(double x)
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{
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return (a * x + b) * x + c;
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}
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bool between(double a, double b, double c) {return dcmp(a - b) > 0 && dcmp(c - a) > 0;}
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bool solve(double a, double b, double c, double &x1, double &x2)
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{
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double d = b*b - 4*a*c;
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if (dcmp(d) <= 0) return 0;
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d = sqrt(d);
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x1 = (-b - d) / a * 0.5;
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x2 = (-b + d) / a * 0.5;
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return 1;
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}
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void get(int x1, int y1, int x2, int y2)
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{
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if (x1 == x2)
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{
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double y = func(x1);
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if (y1 > y2) swap(y1, y2);
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if (between(y, y1, y2)) p[tot++] = x1;
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}
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else
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{
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double k = (double)(y2 - y1) / (x2 - x1), r1, r2;
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if (solve(a, b - k, c + k * x1 - y1, r1, r2))
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{
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if (x1 > x2) swap(x1, x2);
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if (between(r1, x1, x2)) p[tot++] = r1;
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if (between(r2, x1, x2)) p[tot++] = r2;
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}
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}
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}
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double sqr(double x) {return x * x;}
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double f(double x)
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{
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return sqrt(sqr(2*a*x + b) + 1);
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}
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double simpson(double p1, double p2)
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{
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double mid = (p1 + p2) / 2, mid1 = (p1 + mid) / 2, mid2 = (mid + p2) / 2;
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double f1 = f(p1), f2 = f(p2), fm = f(mid), fm1 = f(mid1), fm2 = f(mid2);
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double tmp = (f1 + fm * 4 + f2) * (p2 - p1) / 6;
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if (dcmp(tmp - (f1 + fm1 * 4 + fm) * (mid - p1) / 6 - (fm + fm2 * 4 + f2) * (p2 - mid) / 6) == 0) return tmp;
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return simpson(p1, mid) + simpson(mid, p2);
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}
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int main()
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{
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int nr;
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double r1, r2;
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while (scanf("%d", &n) == 1)
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{
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scanf("%d%d%d%d%d", &a, &b, &c, &l, &r);
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for (int i=0;i<n;i++) scanf("%d%d", &x[i], &y[i]);
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x[n] = x[0]; y[n] = y[0]; x[n+1] = x[1]; y[n+1] = y[1];
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tot = 0;
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for (int i=0;i<n;i++) get(x[i], y[i], x[i+1], y[i+1]);
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for (int i=1;i<=n;i++)
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{
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double x1 = (x[i-1] - x[i]) * 1e-3 + x[i], y1 = (y[i-1] - y[i]) * 1e-3 + y[i];
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double x2 = (x[i+1] - x[i]) * 1e-3 + x[i], y2 = (y[i+1] - y[i]) * 1e-3 + y[i];
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if (dcmp(func(x1) - y1) * dcmp(func(x2) - y2) < 0) p[tot++] = x[i];
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}
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sort(p, p+tot);
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double ans = 0;
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tot--;
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for (int i=0;i<tot;i++)
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if (!(i&1)) ans += simpson(max((double)l, p[i]), min((double)r, p[i+1]));
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printf("%.2lf\n", ans);
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}
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return 0;
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}
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