hdoj 2298 Toxophily(数学推导或三分+二分)

【题目大意】：有一个人站在(0,0)这个点，现在要以初速度为v的飞镖去攻击位于(x,y)的苹果，问飞镖离手是与x轴的夹角。

【解题思路】：高中物理题...直接分解初速度，然后消去t...利用sin^2+cos^2=1进行化简，变形，另tana=x...暴力解一元二次方程...几行而已

第二种做法是以苹果所在的x坐标做直线，三分得到区间(p,q)此时满足当角度在p和q之间的时候可以击中苹果。

再二分区间得到最优值。

【代码】：

//数学做法#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <queue>#include <cmath>#include <string>#include <cctype>#include <map>#include <iomanip>                   using namespace std;                   #define eps 1e-8#define pi acos(-1.0)#define pb push_back#define lc(x) (x << 1)#define rc(x) (x << 1 | 1)#define lowbit(x) (x & (-x))#define ll long long#define g 9.8double x,y,v,a,b,c,tmp,ans1,ans2,tanans1,tanans2;int main() {    int T;    scanf("%d",&T);    while (T--){        scanf("%lf%lf%lf",&x,&y,&v);        a=g*x*x;        b=-2*v*v*x;        c=2*v*v*y+g*x*x;        tmp=b*b-4*a*c;        if (tmp<0) {            printf("-1\n");            continue;        }        else{            tanans1=(-b+sqrt(b*b-4*a*c))/(2*a);            tanans2=(-b-sqrt(b*b-4*a*c))/(2*a);            ans1=atan(tanans1);            ans2=atan(tanans2);            bool flag1=true,flag2=true;            if (ans1<0 || ans1>=pi/2) flag1=false;            if (ans2<0 || ans2>=pi/2) flag2=false;            if (flag1==flag2 && flag1==false) {printf("-1\n");}            else if (flag1==flag2 && flag1==true) {                if (ans1>=ans2) printf("%.6f\n",ans2);                else printf("%.6f\n",ans1);            }            else if (flag1=true) printf("%.6f\n",ans1);            else printf("%.6f\n",ans2);                    }    }    return 0;}

//二分+三分#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <queue>#include <cmath>#include <string>#include <cctype>#include <map>#include <iomanip>                   using namespace std;                   #define eps 1e-8#define pi acos(-1.0)#define pb push_back#define lc(x) (x << 1)#define rc(x) (x << 1 | 1)#define lowbit(x) (x & (-x))#define ll long long#define g 9.8double low,high,mid,mmid,x,y,v;double tmp1,tmp2; double check1(double a){   // double t=x/(v*cos(a));    double ans=tan(a)*x-0.5*g*x*x/v/v/cos(a)/cos(a);    return ans;}void get_extent(){    low=0,high=pi/2;    while (low+eps<high) {            mid=(low+high)/2.0;            mmid=(mid+high)/2.0;         tmp1=check1(mid);        tmp2=check1(mmid);        if (tmp1<tmp2) {                low=mid;           }         else {                high=mmid;                        }        }        return ;    }void get_angle(){    low=0;    while (low+eps<high){        mid=(low+high)/2.0;        tmp1=check1(mid);        if (tmp1>y) high=mid;        else low=mid;    }    printf("%.6f\n",mid);    return ;}int main() {    int T;    scanf("%d",&T);    while (T--){        scanf("%lf%lf%lf",&x,&y,&v);        get_extent();        if (max(tmp1,tmp2)<y) {printf("-1\n"); continue;}        else get_angle();    }     return 0;}