ural 1143. Electric Path

  1 /**
  2 Create By yzx - stupidboy
  3 */
  4 #include <cstdio>
  5 #include <cstring>
  6 #include <cstdlib>
  7 #include <cmath>
  8 #include <deque>
  9 #include <vector>
 10 #include <queue>
 11 #include <iostream>
 12 #include <algorithm>
 13 #include <map>
 14 #include <set>
 15 #include <ctime>
 16 #include <iomanip>
 17 using namespace std;
 18 typedef long long LL;
 19 typedef double DB;
 20 #define MIT (2147483647)
 21 #define INF (1000000001)
 22 #define MLL (1000000000000000001LL)
 23 #define sz(x) ((int) (x).size())
 24 #define clr(x, y) memset(x, y, sizeof(x))
 25 #define puf push_front
 26 #define pub push_back
 27 #define pof pop_front
 28 #define pob pop_back
 29 #define ft first
 30 #define sd second
 31 #define mk make_pair
 32 
 33 inline int Getint()
 34 {
 35     int Ret = 0;
 36     char Ch = ‘ ‘;
 37     bool Flag = 0;
 38     while(!(Ch >= ‘0‘ && Ch <= ‘9‘))
 39     {
 40         if(Ch == ‘-‘) Flag ^= 1;
 41         Ch = getchar();
 42     }
 43     while(Ch >= ‘0‘ && Ch <= ‘9‘)
 44     {
 45         Ret = Ret * 10 + Ch - ‘0‘;
 46         Ch = getchar();
 47     }
 48     return Flag ? -Ret : Ret;
 49 }
 50 
 51 const int N = 410;
 52 struct Point
 53 {
 54     DB x, y;
 55 
 56     inline void Read()
 57     {
 58         scanf("%lf%lf", &x, &y);
 59     }
 60 } arr[N];
 61 int n;
 62 DB dp[N][N][2];
 63 bool visit[N][N][2];
 64 
 65 inline void Input()
 66 {
 67     scanf("%d", &n);
 68     for(int i = 1; i <= n; i++) arr[i].Read();
 69 }
 70 
 71 inline DB Sqr(DB x)
 72 {
 73     return x * x;
 74 }
 75 
 76 inline DB Dist(const Point &A, const Point &B)
 77 {
 78     return sqrt(Sqr(A.x - B.x) + Sqr(A.y - B.y));
 79 }
 80 
 81 inline DB Work(int left, int right, bool type)
 82 {
 83     if(left >= right) return 0;
 84     if(visit[left][right][type])
 85         return dp[left][right][type];
 86     visit[left][right][type] = 1;
 87     DB ret = 1.0 * INF, cnt;
 88     if(type == 0)
 89     {
 90         cnt = Dist(arr[left], arr[left + 1]);
 91         cnt += Work(left + 1, right, 0);
 92         ret = min(ret, cnt);
 93 
 94         cnt = Dist(arr[left], arr[right]);
 95         cnt += Work(left + 1, right, 1);
 96         ret = min(ret, cnt);
 97     }
 98     else
 99     {
100         cnt = Dist(arr[right], arr[right - 1]);
101         cnt += Work(left, right - 1, 1);
102         ret = min(ret, cnt);
103 
104         cnt = Dist(arr[right], arr[left]);
105         cnt += Work(left, right - 1, 0);
106         ret = min(ret, cnt);
107     }
108 
109     return dp[left][right][type] = ret;
110 }
111 
112 inline void Solve()
113 {
114     for(int i = n + 1; i <= 2 * n; i++)
115         arr[i] = arr[i - n];
116 
117     DB ans = 1.0 * INF, cnt;
118     for(int i = 1; i <= n; i++)
119     {
120         cnt = Work(i, i + n - 1, 0);
121         ans = min(ans, cnt);
122         cnt = Work(i, i + n - 1, 1);
123         ans = min(ans, cnt);
124     }
125 
126     printf("%.3lf\n", ans);
127 }
128 
129 int main()
130 {
131     freopen("a.in", "r", stdin);
132     Input();
133     Solve();
134     return 0;
135 }