115 lines
3.5 KiB
C++
115 lines
3.5 KiB
C++
#pragma comment(linker, "/STACK:1024000000,1024000000")
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#include<algorithm>
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#include<iostream>
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#include<cstring>
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#include<cstdio>
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#include<vector>
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#include<string>
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#include<queue>
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#include<cmath>
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#include<stack>
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#include<set>
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#include<map>
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#define FIR first
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#define SEC second
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#define MP make_pair
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#define inf 0x3f3f3f3f
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#define LL long long
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#define CLR(a, b) memset(a, b, sizeof(a))
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using namespace std;
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struct Point
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{
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double x, y;
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Point(double x = 0, double y = 0)
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:x(x), y(y) {}
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};
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double EP = 0;
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double x_mult(Point sp, Point ep, Point op){
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return (sp.x-op.x)*(ep.y-op.y)-(sp.y-op.y)*(ep.x-op.x);
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}
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double cross(Point a,Point b,Point c){
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return (a.x-c.x)*(b.x-c.x)+(a.y-c.y)*(b.y-c.y);
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}
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double dist(Point a,Point b){
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return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
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}
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double cal_area(Point a,Point b,Point c,double r){
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double A,B,C,x,y,tS;
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A=dist(b,c);
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B=dist(a,c);
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C=dist(b,a);
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if(A<r&&B<r)
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return x_mult(a,b,c)/2;
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else if(A<r&&B>=r){
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x=(cross(a,c,b)+sqrt(r*r*C*C-x_mult(a,c,b)*x_mult(a,c,b)))/C;
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tS=x_mult(a,b,c)/2;
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return asin(tS*(1-x/C)*2/r/B*(1-EP))*r*r/2+tS*x/C;
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}
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else if(A>=r&&B<r){
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y=(cross(b,c,a)+sqrt(r*r*C*C-x_mult(b,c,a)*x_mult(b,c,a)))/C;
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tS=x_mult(a,b,c)/2;
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return asin(tS*(1-y/C)*2/r/A*(1-EP))*r*r/2+tS*y/C;
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}
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else if(fabs(x_mult(a,b,c))>=r*C||cross(b,c,a)<=0||cross(a,c,b)<=0){
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if(cross(a,b,c)<0)
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if(x_mult(a,b,c)<0)
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return (-acos(-1.0)-asin(x_mult(a,b,c)/A/B*(1-EP)))*r*r/2;
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else return (acos(-1.0)-asin(x_mult(a,b,c)/A/B*(1-EP)))*r*r/2;
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else return asin(x_mult(a,b,c)/A/B*(1-EP))*r*r/2;
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}
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else{
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x=(cross(a,c,b)+sqrt(r*r*C*C-x_mult(a,c,b)*x_mult(a,c,b)))/C;
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y=(cross(b,c,a)+sqrt(r*r*C*C-x_mult(b,c,a)*x_mult(b,c,a)))/C;
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tS=x_mult(a,b,c)/2;
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return (asin(tS*(1-x/C)*2/r/B*(1-EP))+asin(tS*(1-y/C)*2/r/A*(1-EP)))*r*r/2+tS*((y+x)/C-1);
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}
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}
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double solve(Point p[], int n, Point cir, double r){
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double area=0;
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for(int i=0;i<n;i++){
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area+=cal_area(p[i], p[(i+1)%n], cir, r);
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}
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return area;
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}
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double pi = acos(-1.0);
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int main()
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{
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double v0, v1, D, T;int cas = 1;
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while(cin >> v0 >> v1 >> D >> T)
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{
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printf("Case %d: ", cas ++);
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Point cir = Point(-D, 0);
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double r = v0 * T;
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if(v0 * T <= D)
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{
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printf("%.7f\n", pi * r * r);
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continue;
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}
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double lft = D / v0, rgt = T;
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for(int i = 0; i < 100; i ++)
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{
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double mid = (lft + rgt) / 2;
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double midmid = (mid + rgt) / 2;
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double _mid = sqrt((v0 * mid) * (v0 * mid) - D * D) + v1 * (T - mid);
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double _midmid = sqrt((v0 * midmid) * (v0 * midmid) - D * D) + v1 * (T - midmid);
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if(_mid > _midmid) rgt = midmid;
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else lft = mid;
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}
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double t = (lft + rgt) / 2;
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double y = sqrt((v0 * t) * (v0 * t) - D * D) + v1 * (T - t);
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double x1 = T / t * D, y1 = sqrt(v0 * T * v0 * T - x1 * x1);
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x1 -= D;
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Point p[8];
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p[0] = Point(0, y);
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p[1] = Point(x1, y1);
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p[2] = Point(x1, -y1);
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p[3] = Point(0, -y);
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p[4] = Point(-x1, -y1);
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p[5] = Point(-x1, y1);
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p[6] = p[0];
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double ans = solve(p, 6, cir, r);
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ans = pi * r * r + x1 * y1 * 4 + x1 * (y - y1) * 2 - fabs(ans);
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printf("%.7f\n", ans);
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}
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}
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