1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
| #include <cstdio>
#include <algorithm>
using namespace std;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
flag && (x = ~x + 1);
}
template <class Type>
void write(Type x)
{
x < 0 && (putchar('-'), x = ~x + 1);
x > 9 && (write(x / 10), 0);
putchar(x % 10 + '0');
}
const int N = 1e3 + 10;
double f[N][N], A[N][N];
void Gauss (int n, int d)
{
for (int k = 0; k < n; k++)
{
int t = min(n - 1, k + d);
A[k][n] /= A[k][k];
for (int i = t; i >= k; i--)
A[k][i] /= A[k][k];
for (int i = k + 1; i <= t; i++)
{
A[i][n] -= A[k][n] * A[i][k];
for (int j = t; j >= k; j--)
A[i][j] -= A[k][j] * A[i][k];
}
}
for (int i = n - 1; ~i; i--)
for (int j = i + 1; j < n; j++)
A[i][n] -= A[i][j] * A[j][n];
}
int main ()
{
int n, m, p, q;
read(n), read(m), read(p), read(q);
if (m == 1)
return printf("%.8lf", 2.0 * (n - p)), 0;
for (int i = n - 1; i; i--)
{
A[0][0] = A[m - 1][m - 1] = 2;
A[0][1] = A[m - 1][m - 2] = -1;
A[0][m] = f[i + 1][0] + 3;
A[m - 1][m] = f[i + 1][m - 1] + 3;
for (int j = 1; j + 1 < m; j++)
{
A[j][j] = 3;
A[j][j - 1] = A[j][j + 1] = -1;
A[j][m] = 4 + f[i + 1][j];
}
Gauss(m, 1);
for (int j = 0; j < m; j++)
f[i][j] = A[j][m];
}
printf("%.8lf", f[p][q - 1]);
return 0;
}
|