题目:平面上给定n条线段,找出一个点,使这个点到这n条线段的距离和最小。
源码如下:
1 #include <iostream>
2 #include <string.h>
3 #include <stdlib.h>
4 #include <stdio.h>
5 #include <time.h>
6 #include <math.h>
7
8 #define N 1005
9 #define eps 1e-8 //搜索停止条件阀值
10 #define INF 1e99
11 #define delta 0.98 //温度下降速度
12 #define T 100 //初始温度
13
14 using namespace std;
15
16 int dx[4] = {0, 0, -1, 1};
17 int dy[4] = {-1, 1, 0, 0}; //上下左右四个方向
18
19 struct Point
20 {
21 double x, y;
22 };
23
24 Point s[N], t[N];
25
26 double cross(Point A, Point B, Point C)
27 {
28 return (B.x - A.x) * (C.y - A.y) - (B.y - A.y) * (C.x - A.x);
29 }
30
31 double multi(Point A, Point B, Point C)
32 {
33 return (B.x - A.x) * (C.x - A.x) + (B.y - A.y) * (C.y - A.y);
34 }
35
36 double dist(Point A, Point B)
37 {
38 return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
39 }
40
41 double GetDist(Point A, Point B, Point C)
42 {
43 if(dist(A, B) < eps) return dist(B, C);
44 if(multi(A, B, C) < -eps) return dist(A, C);
45 if(multi(B, A, C) < -eps) return dist(B, C);
46 return fabs(cross(A, B, C) / dist(A, B));
47 }
48
49 double GetSum(Point s[], Point t[], int n, Point o)
50 {
51 double ans = 0;
52 while(n--)
53 ans += GetDist(s[n], t[n], o);
54 return ans;
55 }
56
57 double Search(Point s[], Point t[], int n, Point &o)
58 {
59 o = s[0];
60 double tem = T;
61 double ans = INF;
62 while(tem > eps)
63 {
64 bool flag = 1;
65 while(flag)
66 {
67 flag = 0;
68 for(int i = 0; i < 4; i++) //上下左右四个方向
69 {
70 Point z;
71 z.x = o.x + dx[i] * tem;
72 z.y = o.y + dy[i] * tem;
73 double tp = GetSum(s, t, n, z);
74 if(ans > tp)
75 {
76 ans = tp;
77 o = z;
78 flag = 1;
79 }
80 }
81 }
82 tem *= delta;
83 }
84 return ans;
85 }
86
87 int main()
88 {
89 int n;
90 while(scanf("%d", &n) != EOF)
91 {
92 for(int i = 0; i < n; i++)
93 scanf("%lf %lf %lf %lf", &s[i].x, &s[i].y, &t[i].x, &t[i].y);
94 Point o;
95 double ans = Search(s, t, n, o);
96 printf("%.1lf %.1lf %.1lf\n", o.x, o.y, ans);
97 }
98 return 0;
99 }