hihoCoder#1040 矩形判断

原题地址

 

一开始写了一个求交点然后算角度的，特别复杂不说，还很容易出错，WA了很久也不知道错在哪

 

后来想想，应该用向量做

四条直线能围成一个矩形 <=> 四条直线两两之间有4个平行关系，8个垂直关系

注意，直线重合并不算平行

 

代码清晰明了，一遍AC，这酸爽。

 

代码：

 1 #include <iostream>

 2 #include <vector>

 3 

 4 using namespace std;

 5 

 6 struct Line {

 7   int x[2];

 8   int y[2];

 9   Line(int x1, int y1, int x2, int y2) {

10     x[0] = x1;

11     x[1] = x2;

12     y[0] = y1;

13     y[1] = y2;

14   }

15   int vx() {return x[0] - x[1];}

16   int vy() {return y[0] - y[1];}

17 };

18 

19 bool parallelp(Line &a, Line &b) {

20   return a.vx() * b.vy() - b.vx() * a.vy() == 0;

21 }

22 

23 bool samep(Line &a, Line &b) {

24   Line c(a.x[0], a.y[0], b.x[0], b.y[0]);

25   return parallelp(a, c);

26 }

27 

28 bool verticalp(Line &a, Line &b) {

29   return a.vx() * b.vx() + a.vy() * b.vy() == 0;

30 }

31 

32 int parallel_count(vector<Line> &lines) {

33   int res = 0;

34 

35   for (int i = 0; i < 4; i++) {

36     for (int j = 0; j < 4; j++) {

37       if (i == j)

38         continue;

39       if (parallelp(lines[i], lines[j]) && !samep(lines[i], lines[j]))

40         res++;

41     }

42   }

43 

44   return res;

45 }

46 

47 int vertical_count(vector<Line> &lines) {

48   int res = 0;

49 

50   for (int i = 0; i < 4; i++) {

51     for (int j = 0; j < 4; j++) {

52       if (i == j)

53         continue;

54       if (verticalp(lines[i], lines[j]))

55         res++;

56     }

57   }

58 

59   return res;

60 }

61 

62 bool rectanglep(vector<Line> &lines) {

63   int p_count = parallel_count(lines);

64   int v_count = vertical_count(lines);

65   return p_count == 4 && v_count == 8;

66 }

67 

68 int main() {

69   int n;

70   double x1, y1, x2, y2;

71 

72   cin >> n;

73   while (n--) {

74     vector<Line> lines;

75     for (int i = 0; i < 4; i++) {

76       cin >> x1 >> y1 >> x2 >> y2;

77       lines.push_back(Line(x1, y1, x2, y2));

78     }

79 

80     if (rectanglep(lines))

81       cout << "YES" << endl;

82     else

83       cout << "NO" << endl;

84   }

85   return 0;

86 }