codeforces 782B - The Meeting Place Cannot Be Changed
5 seconds
256 megabytes
standard input
standard output
The main road in Bytecity is a straight line from south to north. Conveniently, there are coordinates measured in meters from the southernmost building in north direction.
At some points on the road there are n friends, and i-th of them is standing at the point xi meters and can move with any speed no greater than vi meters per second in any of the two directions along the road: south or north.
You are to compute the minimum time needed to gather all the n friends at some point on the road. Note that the point they meet at doesn't need to have integer coordinate.
The first line contains single integer n (2 ≤ n ≤ 60 000) — the number of friends.
The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 109) — the current coordinates of the friends, in meters.
The third line contains n integers v1, v2, ..., vn (1 ≤ vi ≤ 109) — the maximum speeds of the friends, in meters per second.
Print the minimum time (in seconds) needed for all the n friends to meet at some point on the road.
Your answer will be considered correct, if its absolute or relative error isn't greater than 10 - 6. Formally, let your answer be a, while jury's answer be b. Your answer will be considered correct if holds.
3
7 1 3
1 2 1
2.000000000000
4
5 10 3 2
2 3 2 4
1.400000000000
#include<cstdio>
struct type{
int x;
int v;
}p[+];
int n;
bool check(double time)
{
//遍历每个人在time个单位时间后能走到的位置,不断更新重叠的区间[l,r],只要到最后这个区间一人不为空,就return true
double l=p[].x-time*p[].v;
double r=p[].x+time*p[].v;
for(int i=;i<=n;i++){
if(p[i].x-time*p[i].v > l) l=p[i].x-time*p[i].v;
if(p[i].x+time*p[i].v < r) r=p[i].x+time*p[i].v;
if(l>r) return false;
}
return true;
}
int main()
{
scanf("%d",&n);
for(int i=;i<=n;i++) scanf("%d",&p[i].x);
for(int i=;i<=n;i++) scanf("%d",&p[i].v);
double st=,ed=;
while(ed-st>1e-){
double mid=st+(ed-st)/;
if(check(mid)) ed=mid;
else st=mid;
}
printf("%.12lf\n",ed);
}
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