CF782B The Meeting Place Cannot Be Changed
题意:
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
思路:
二分,注意控制精度。
实现:
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;
struct node
{
double pos;
double speed;
};
node a[];
int n;
double minn, maxn;
bool check(double t)
{
minn = a[].pos - t * a[].speed;
maxn = a[].pos + t * a[].speed;
for (int i = ; i < n; i++)
{
double tmp_l = a[i].pos - t * a[i].speed;
double tmp_r = a[i].pos + t * a[i].speed;
minn = max(minn, tmp_l);
maxn = min(maxn, tmp_r);
}
return maxn - minn >= 1e-;
} double solve()
{
double l = 0.0, r = , res = ;
for (int i = ; i < ; i++)
{
double mid = (l + r) / 2.0;
if (check(mid))
{
r = mid;
res = mid;
}
else
{
l = mid;
}
}
return res;
} int main()
{
cin >> n;
for (int i = ; i < n; i++)
{
cin >> a[i].pos;
}
for (int i = ; i < n; i++)
{
cin >> a[i].speed;
}
cout << setprecision() << solve() << endl;
return ;
}
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