codeforces - 257c View Angle 【数学】
2016-10-17 21:00
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C. View Angle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Flatland has recently introduced a new type of an eye check for the driver's licence. The check goes like that: there is a plane with mannequins standing on it. You should tell the value of the minimum angle with the vertex at the origin of coordinates and
with all mannequins standing inside or on the boarder of this angle.
As you spend lots of time "glued to the screen", your vision is impaired. So you have to write a program that will pass the check for you.
Input
The first line contains a single integer n (1 ≤ n ≤ 105) —
the number of mannequins.
Next n lines contain two space-separated integers each: xi, yi (|xi|, |yi| ≤ 1000) —
the coordinates of the i-th mannequin. It is guaranteed that the origin of the coordinates has no mannequin. It is guaranteed that
no two mannequins are located in the same point on the plane.
Output
Print a single real number — the value of the sought angle in degrees. The answer will be considered valid if the relative or absolute error doesn't exceed 10 - 6.
Examples
input
output
input
output
input
output
input
output
Note
Solution for the first sample test is shown below:
Solution for the second sample test is shown below:
Solution for the third sample test is shown below:
Solution for the fourth sample test is shown below:
思路:
要想使最小的角度包含所有的点,必定会有两个相邻点所夹得角没有被覆盖,而且只有一个。现在,把这个角找出来就可以了。
#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
const int MAXN = 1e5 + 10;
double ang[MAXN];
bool cmp(double x, double y) {return x > y;}
int main () {
int n; double a, b;
while (scanf("%d", &n) != EOF) {
for (int i = 0; i < n; i++) {
scanf("%lf%lf", &a, &b);
ang[i] = atan(b/a)/PI*180;
if (ang[i] < 0) ang[i] += 180;
if (b < 0 || a < 0 && b == 0) ang[i] += 180;
}
sort(ang, ang + n, cmp);
double ans = 360 - ang[0] + ang[n - 1]; //用最后一个减去第一个,从而形成一个环。
for (int i = 0; i < n - 1; i++) {
ans = max(ans, ang[i] - ang[i + 1]);
}
printf("%.8lf\n", 360 - ans);
}
return 0;
}
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Flatland has recently introduced a new type of an eye check for the driver's licence. The check goes like that: there is a plane with mannequins standing on it. You should tell the value of the minimum angle with the vertex at the origin of coordinates and
with all mannequins standing inside or on the boarder of this angle.
As you spend lots of time "glued to the screen", your vision is impaired. So you have to write a program that will pass the check for you.
Input
The first line contains a single integer n (1 ≤ n ≤ 105) —
the number of mannequins.
Next n lines contain two space-separated integers each: xi, yi (|xi|, |yi| ≤ 1000) —
the coordinates of the i-th mannequin. It is guaranteed that the origin of the coordinates has no mannequin. It is guaranteed that
no two mannequins are located in the same point on the plane.
Output
Print a single real number — the value of the sought angle in degrees. The answer will be considered valid if the relative or absolute error doesn't exceed 10 - 6.
Examples
input
2 2 0 0 2
output
90.0000000000
input
3 2 0 0 2 -2 2
output
135.0000000000
input
4 2 0 0 2 -2 0 0 -2
output
270.0000000000
input
2 2 1 1 2
output
36.8698976458
Note
Solution for the first sample test is shown below:
Solution for the second sample test is shown below:
Solution for the third sample test is shown below:
Solution for the fourth sample test is shown below:
思路:
要想使最小的角度包含所有的点,必定会有两个相邻点所夹得角没有被覆盖,而且只有一个。现在,把这个角找出来就可以了。
#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
const int MAXN = 1e5 + 10;
double ang[MAXN];
bool cmp(double x, double y) {return x > y;}
int main () {
int n; double a, b;
while (scanf("%d", &n) != EOF) {
for (int i = 0; i < n; i++) {
scanf("%lf%lf", &a, &b);
ang[i] = atan(b/a)/PI*180;
if (ang[i] < 0) ang[i] += 180;
if (b < 0 || a < 0 && b == 0) ang[i] += 180;
}
sort(ang, ang + n, cmp);
double ans = 360 - ang[0] + ang[n - 1]; //用最后一个减去第一个,从而形成一个环。
for (int i = 0; i < n - 1; i++) {
ans = max(ans, ang[i] - ang[i + 1]);
}
printf("%.8lf\n", 360 - ans);
}
return 0;
}
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