CodeForces 782B The Meeting Place Cannot Be Changed (二分)

题意：题意:给出n个人的在x轴的位置和最大速度,求n个人相遇的最短时间。

析：二分时间，然后求并集，注意精度，不然会超时。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#include <sstream>
#define debug() puts("++++");
#define gcd(a, b) __gcd(a, b)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const LL LNF = 1e17;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-7;
const int maxn = 60000 + 5;
const int mod = 1000000007;
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, 1, 0, -1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline bool is_in(int r, int c){
  return r >= 0 && r < n && c >= 0 && c < m;
}

struct Node{
  double x, v;
};
Node a[maxn];


bool judge(double m){
  double l = a[0].x-a[0].v*m, r = a[0].x+a[0].v*m;
  for(int i = 1; i < n; ++i){
    l = max(l, a[i].x-a[i].v*m);
    r = min(r, a[i].x+a[i].v*m);
    if(r < l)  return false;
  }
  return r >= l;
}

int main(){
  scanf("%d", &n);
  for(int i = 0; i < n; ++i){
    scanf("%lf", &a[i].x);
  }
  for(int i = 0; i < n; ++i){
    scanf("%lf", &a[i].v);
  }
  double l = 0.0, r = 1e9;
  while(r - l > eps){
    double m = (l + r) / 2.0;
    if(judge(m))  r = m;
    else  l = m;
  }
  printf("%.6f\n", l);
  return 0;
}