2016 ICPC大连赛区 hdu5974 Convex

最新推荐文章于 2024-10-12 07:46:51 发布

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本篇博客介绍了一道关于计算特殊凸包面积的问题。题目中给出一个距离原点固定距离的凸包及其各边间的夹角，需要计算该凸包的总面积。通过将凸包分解为多个三角形并运用三角函数公式进行计算。

Convex

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 170 Accepted Submission(s): 145

Problem Description

We have a special convex that all points have the same distance to origin point.
As you know we can get N segments after linking the origin point and the points on the convex. We can also get N angles between each pair of the neighbor segments.
Now give you the data about the angle, please calculate the area of the convex

Input

There are multiple test cases.
The first line contains two integer N and D indicating the number of the points and their distance to origin. (3 <= N <= 10, 1 <= D <= 10)
The next lines contain N integers indicating the angles. The sum of the N numbers is always 360.

Output

For each test case output one float numbers indicating the area of the convex. The printed values should have 3 digits after the decimal point.

Sample Input

  
   4 1
90 90 90 90
6 1
60 60 60 60 60 60

Sample Output

  
   2.000
2.598

Source

2016ACM/ICPC亚洲区大连站-重现赛（感谢大连海事大学）

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wange2014 | We have carefully selected several similar problems for you: 5981 5977 5976 5975 5973

讲道理，大连的题目质量怎么这么低，水题也太多了吧。

题意：已知一个凸包，每个点距离原点的距离为定值d，然后给你两两边的夹角，求凸包面积。

思路：将凸包拆成n个三角形，然后套公式就得了。下面给代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
typedef long long LL;
using namespace std;
#define maxn 1005
#define ll l,mid,now<<1
#define rr mid+1,r,now<<1|1
#define lson l1,mid,l2,r2,now<<1
#define rson mid+1,r1,l2,r2,now<<1|1
#define pi 3.14159
int main(){
    int n,d;
    while(~scanf("%d%d",&n,&d)){
        double sum=0;
        while(n--){
            int num;
            scanf("%d",&num);
            sum+=sin(num*pi/180);
        }
        printf("%.3lf\n",d*d*sum/2);
    }
}