Archery UVA - 1421 二分

问题

https://vjudge.net/problem/UVA-1421

分析

参考：https://www.baidu.com/link?url=_97SeoEnptxHUjm7w30zPkV7cwJLuiQoKvbiADlHIWl2-U3imQIzyhtH1rbldN6OXdv3L3eVTvhQfuE2UgVjTK&wd=&eqid=ff3194ad00016a44000000055e6f8f8a
二分法的应用，使用二分来确定应该左移还是右移

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <map>
#include <string>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long LL;
const int maxn=5000+5;
const double eps=1e-6;
struct Target{
    int d,l,r;
    bool operator < (const Target &rhs) const {
        return d<rhs.d;
    }
}tar[maxn];
int T,w,n,s,kase=0,a[maxn],b[maxn];

int judge(double cur){
    //k=1/tan(theta)
    double k1=(tar[0].l-cur)/tar[0].d,k2=(tar[0].r-cur)/tar[0].d,k3,k4;
    for(int i=1;i<n;++i){
        k3=(tar[i].l-cur)/tar[i].d;
        k4=(tar[i].r-cur)/tar[i].d;
        if(k3-k2>eps) return -1;  //点要左移
        else if(k4-k1<-eps) return 1;  //要右移
        k1=max(k1,k3);
        k2=min(k2,k4);
    }
    return 0;
}

bool solve(){
    double L=0,R=w;
    while(R-L>eps){
        double mid=(L+R)/2;
        int t=judge(mid);
        if(t==0) return true;
        else if(t==1){
            L=mid;
        }else{
            R=mid;
        }
    }
    return false;
}

int main(void){
    scanf("%d",&T);
    while(T--){
        scanf("%d%d",&w,&n);
        for(int i=0;i<n;++i){
            scanf("%d%d%d",&tar[i].d,&tar[i].l,&tar[i].r);
        }
        sort(tar,tar+n);
        bool ans=solve();
        printf("%s\n",ans?"YES":"NO");
    }
    return 0;
}