HDU 1798 Tell me the area

最新推荐文章于 2025-08-18 20:10:55 发布

转载最新推荐文章于 2025-08-18 20:10:55 发布 · 64 阅读

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原文链接：http://www.cnblogs.com/zlrrrr/p/9688159.html

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本文介绍了一种计算平面上两个圆之间的公共区域面积的方法。通过解析输入的圆心坐标和半径，利用数学公式计算并输出精确到小数点后三位的交叠面积。

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http://acm.hdu.edu.cn/showproblem.php?pid=1798

Problem Description

There are two circles in the plane (shown in the below picture), there is a common area between the two circles. The problem is easy that you just tell me the common area.

Input

There are many cases. In each case, there are two lines. Each line has three numbers: the coordinates (X and Y) of the centre of a circle, and the radius of the circle.

Output

For each case, you just print the common area which is rounded to three digits after the decimal point. For more details, just look at the sample.

Sample Input

0 0 2

2 2 1

Sample Output

0.108

代码：

#include <bits/stdc++.h>
using namespace std;

int main() {
    double x1, y1, r1, x2, y2, r2, minr, maxr, d, ans;
    while(~scanf("%lf%lf%lf", &x1, &y1, &r1)) {
        scanf("%lf%lf%lf", &x2, &y2, &r2);
        d = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
        minr = min(r1, r2);
        maxr = max(r1, r2);
        if(d <= maxr - minr)
            ans = acos(-1.0) * minr * minr;
        else if(d >= r1 + r2)
            ans = 0;
        else {
            double a1, a2;
            double p;
            p = (r1 + r2 + d) / 2;
            a1 = acos((r1 * r1 + d * d - r2 * r2) / (2 * r1 * d));
            a2 = acos((r2 * r2 + d * d - r1 * r1) / (2 * r2 * d));
            ans = a1 * r1 * r1 + a2 * r2 * r2 - 2 * sqrt(p * (p - r1) * (p - r2) * (p - d));
        }
        printf("%.3f\n", ans);
    }
    return 0;
}

转载于:https://www.cnblogs.com/zlrrrr/p/9688159.html