* * * * *
* * * * 4 7 7 * * * *
* * * 5 4 4 8 3 3 4 6 3 * * *
* * 1 4 5 1 1 1 4 5 1 7 1 3 5 * *
* * 4 9 4 9 6 7 5 5 5 8 7 6 6 8 5 * *
* 3 7 2 9 8 3 5 6 7 3 9 1 8 7 5 8 5 *
* * 1 4 7 8 4 2 9 2 7 1 1 8 2 2 7 6 3 * *
* 7 2 1 8 5 5 3 1 1 3 1 3 3 4 2 8 6 1 3 *
* 4 2 6 7 2 5 2 4 2 2 5 4 3 2 8 1 7 7 3 *
* * 4 1 6 5 1 1 1 9 1 4 3 4 4 3 1 9 8 2 7 * *
* 4 3 5 2 3 2 2 3 2 4 2 5 3 5 1 1 3 5 5 3 7 *
* 2 7 1 5 1 1 3 1 5 3(3)2 4 2 3 7 7 5 4 2 7 *
* 2 5 2 2 6 1 2 4 4 6 3 4 1 2 1 2 6 5 1 8 8 *
* * 4 3 7 5 1 9 3 4 4 5 2 9 4 1 9 5 7 4 8 * *
* 4 1 6 7 8 3 4 3 4 1 3 1 2 3 2 3 6 2 4 *
* 7 3 2 6 1 5 3 9 2 3 2 1 5 7 5 8 9 5 4 *
* * 1 6 7 3 4 8 1 2 1 2 1 2 2 8 9 4 1 * *
* 2 5 4 7 8 7 5 6 1 3 5 7 8 7 2 9 3 *
* * 6 5 6 4 6 7 2 5 2 2 6 3 4 7 4 * *
* * 2 3 1 2 3 3 3 2 1 3 2 1 1 * *
* * * 7 4 4 5 7 3 4 4 7 * * *
* * * * 3 3 4 * * * *
* * * * *
Starting from the central cell of this maze (there's a (3) in it), the challenge is to find a path that leads you off the maze, and to a "star" (*).
The number at each cell shows how many steps, in a straight line, you must take. You can travel horizontally, vertically, or diagonally, up or down, left or right.
(In reply to
re(2): computer solution -- by Charlie)
Since the exit is at the lower left, biasing the search towards the upper right can be expected to give longer paths at the beginning, as shown below. However, the algorithm used was such that shorter paths to a given point are preferred to longer ones, so even at the beginning of the search, the first found path is not necessarily the longest with its given bias.
Also, beyond the scope of the algorithm would be to find a path that includes all the nodes in the longest possible path.
But here's a long one with 176 steps (the g7 represents 177, as letters are used to combine two digits, with z0 representing 100; z1, 101; a0, 110; a1, 111; etc.).
804 7 247
/ \
5 4 74> 998 3 < 63 84 6 < 53
v \
1 4 195> 1 1 1 4 205> 1 <187 1 3 215
v
974 779 294 9 476 137> 155> 645 115><768 407 166 <146 <128 g35
v \ \ \ v \ \ /
/ ^
3 337> 2 819 678 3 385> 366> 347> 43 <329 391 <668 <377 < 35 <358 495
\ \ v
^ / / /
1 894 d87 578 4 462 729> 102 <887 311 551><568 2 g22 < 97 736 3
\ v \ v
/ ^ \ \
z57 2 1 938 5 5 <923 861> 871 <913 1 753 633 4 <622 <858 236 1 e63
\ \ v
/ / ^ / / / /
284 2 986 c37 z22 <275 452 a04> 302 542 <265 a14 23 e42 <448 221 a87 <257 3
\ / \ \ /
\ \ / ^ \
4 1 6 5 c21 1 a41> a59 z91 654 3 g44 <z84 3 431 b29 798 2 7
\ / v
^ ^ / / / / / / \
4 z43 5 <z32 c73 z12 <c62 903 532 <z04 c92 5 613 485 1 b11 e53 <605 505 e73 177
\ \ v v
^ / / / / ^
2 7 1 b75 d61 <d51 <b63 1 715 <b53 13 z72 844 422 e33 <707 <b47 <835 4 2 <417
\ v
^ ^ / \ / / / \
2 5 2 d32> d76 d41 2 <d24 f24 g16 a33 <d14 <d01 b02 691 592 <a26 745 1 8 8
\
/ \ \ / ^
g70 4 3 7 d95 1 9 c83 g54 c14 5 <c02 969 784 681 9 5 7 4 e88
\ / /
/ / ^ / / ^
4 1 6 7 8 3 f94 z63 4 1 e23 951 582 823 f52 3 a76 2 4
/ \
/ / ^ \
7 3 2 6 1 5 3 9 b92 a93 c42 941 525 7 5 8 9 <515 4
\
/ \ ^ /
1 6 7 3 4 8 b81 f82 1 e12 f31> f42 2 8 9 f64 1
/
\ ^ \
2 5 g64 7 8 7 f15 6 1 3 5 c57 8 <f07 2 9 3
/ / ^ ^
g06 5 6 4 6 7 e02 5 2 2 6 3 4 b37 a64
2 3 1 2 3 3 3 2 1 3 2 1 1
\
7 4 4 5 7 3 4 f74 7
/
3 3 e94
|
|
Posted by Charlie
on 2005-09-24 19:16:50 |
re(3): computer solution -- longer paths
