本文涉及知识点

计算几何

LeetCode 1401. 圆和矩形是否有重叠

给你一个以 (radius, xCenter, yCenter) 表示的圆和一个与坐标轴平行的矩形 (x1, y1, x2, y2) ，其中 (x1, y1) 是矩形左下角的坐标，而 (x2, y2) 是右上角的坐标。
如果圆和矩形有重叠的部分，请你返回 true ，否则返回 false 。
换句话说，请你检测是否 存在 点 (xi, yi) ，它既在圆上也在矩形上（两者都包括点落在边界上的情况）。
示例 1 ：
输入：radius = 1, xCenter = 0, yCenter = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1

输出：true
解释：圆和矩形存在公共点 (1,0) 。
示例 2 ：
输入：radius = 1, xCenter = 1, yCenter = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1

输出：false
示例 3 ：
输入：radius = 1, xCenter = 0, yCenter = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1
输出：true
提示：
1 <= radius <= 2000
-104 <= xCenter, yCenter <= 104
-104 <= x1 < x2 <= 104
-104 <= y1 < y2 <= 104

计算几何

借用LeetCode 龅牙叔的图。

看是否符合以下三种情况之一：
一，圆心在红色矩形内。
二，圆心在绿色矩形内。
三，圆心在原始矩形四个顶点为圆心，Radius为半径的圆内。

代码

核心代码

class Solution {
		public:
			bool checkOverlap(int radius, int xCenter, int yCenter, int x1, int y1, int x2, int y2) {
				auto Dis2 = [](long long x1, long long y1, int x2, int y2){
					return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
				};
				auto IsCycle = [&](int x, int y) {
					return Dis2(x, y, xCenter, yCenter) <= (long long)radius * radius;
				};
				auto IsRect = [&](int x1, int y1, int x2, int y2) {
					return (xCenter >= x1) && (xCenter <= x2) && (yCenter >= y1) && (yCenter <= y2);
				};
				return IsCycle(x1, y1) || IsCycle(x1, y2) || IsCycle(x2, y1) || IsCycle(x2, y2) ||
					IsRect(x1, y1 - radius, x2, y2 + radius) || IsRect(x1 - radius, y1 , x2 + radius, y2 );
			}
		};

单元测试

int radius,  xCenter,  yCenter,  x1,  y1,  x2,  y2;
		TEST_METHOD(TestMethod11)
		{
			radius = 1, xCenter = 0, yCenter = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1;
			auto res = Solution().checkOverlap(radius, xCenter, yCenter, x1, y1, x2, y2);
			AssertEx(true, res);
		}
		TEST_METHOD(TestMethod12)
		{
			radius = 1, xCenter = 1, yCenter = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1;
			auto res = Solution().checkOverlap(radius, xCenter, yCenter, x1, y1, x2, y2);
			AssertEx(false, res);
		}
		TEST_METHOD(TestMethod13)
		{
			radius = 1, xCenter = 0, yCenter = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1;
			auto res = Solution().checkOverlap(radius, xCenter, yCenter, x1, y1, x2, y2);
			AssertEx(true, res);
		}