1# Towers of Hanoi in sed. 2# 3# @(#)hanoi.sed 8.1 (Berkeley) 06/06/93 4# 5# 6# Ex: 7# Run "sed -f hanoi.sed", and enter: 8# 9# :abcd: : :<CR><CR> 10# 11# note -- TWO carriage returns, a peculiarity of sed), this will output the 12# sequence of states involved in moving 4 rings, the largest called "a" and 13# the smallest called "d", from the first to the second of three towers, so 14# that the rings on any tower at any time are in descending order of size. 15# You can start with a different arrangement and a different number of rings, 16# say :ce:b:ax: and it will give the shortest procedure for moving them all 17# to the middle tower. The rules are: the names of the rings must all be 18# lower-case letters, they must be input within 3 fields (representing the 19# towers) and delimited by 4 colons, such that the letters within each field 20# are in alphabetical order (i.e. rings are in descending order of size). 21# 22# For the benefit of anyone who wants to figure out the script, an "internal" 23# line of the form 24# b:0abx:1a2b3 :2 :3x2 25# has the following meaning: the material after the three markers :1, :2, 26# and :3 represents the three towers; in this case the current set-up is 27# ":ab : :x :". The numbers after a, b and x in these fields indicate 28# that the next time it gets a chance, it will move a to tower 2, move b 29# to tower 3, and move x to tower 2. The string after :0 just keeps track 30# of the alphabetical order of the names of the rings. The b at the 31# beginning means that it is now dealing with ring b (either about to move 32# it, or re-evaluating where it should next be moved to). 33# 34# Although this version is "limited" to 26 rings because of the size of the 35# alphabet, one could write a script using the same idea in which the rings 36# were represented by arbitrary [strings][within][brackets], and in place of 37# the built-in line of the script giving the order of the letters of the 38# alphabet, it would accept from the user a line giving the ordering to be 39# assumed, e.g. [ucbvax][decvax][hplabs][foo][bar]. 40# 41# George Bergman 42# Math, UC Berkeley 94720 USA 43 44# cleaning, diagnostics 45s/ *//g 46/^$/d 47/[^a-z:]/{a\ 48Illegal characters: use only a-z and ":". Try again. 49d 50} 51/^:[a-z]*:[a-z]*:[a-z]*:$/!{a\ 52Incorrect format: use\ 53\ : string1 : string2 : string3 :<CR><CR>\ 54Try again. 55d 56} 57/\([a-z]\).*\1/{a\ 58Repeated letters not allowed. Try again. 59d 60} 61# initial formatting 62h 63s/[a-z]/ /g 64G 65s/^:\( *\):\( *\):\( *\):\n:\([a-z]*\):\([a-z]*\):\([a-z]*\):$/:1\4\2\3:2\5\1\3:3\6\1\2:0/ 66s/[a-z]/&2/g 67s/^/abcdefghijklmnopqrstuvwxyz/ 68:a 69s/^\(.\).*\1.*/&\1/ 70s/.// 71/^[^:]/ba 72s/\([^0]*\)\(:0.*\)/\2\1:/ 73s/^[^0]*0\(.\)/\1&/ 74:b 75# outputting current state without markers 76h 77s/.*:1/:/ 78s/[123]//gp 79g 80:c 81# establishing destinations 82/^\(.\).*\1:1/td 83/^\(.\).*:1[^:]*\11/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\31/ 84/^\(.\).*:1[^:]*\12/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\33/ 85/^\(.\).*:1[^:]*\13/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\32/ 86/^\(.\).*:2[^:]*\11/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\33/ 87/^\(.\).*:2[^:]*\12/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\32/ 88/^\(.\).*:2[^:]*\13/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\31/ 89/^\(.\).*:3[^:]*\11/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\32/ 90/^\(.\).*:3[^:]*\12/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\31/ 91/^\(.\).*:3[^:]*\13/s/^\(.\)\(.*\1\([a-z]\).*\)\3./\3\2\33/ 92bc 93# iterate back to find smallest out-of-place ring 94:d 95s/^\(.\)\(:0[^:]*\([^:]\)\1.*:\([123]\)[^:]*\1\)\4/\3\2\4/ 96td 97# move said ring (right, resp. left) 98s/^\(.\)\(.*\)\1\([23]\)\(.*:\3[^ ]*\) /\1\2 \4\1\3/ 99s/^\(.\)\(.*:\([12]\)[^ ]*\) \(.*\)\1\3/\1\2\1\3\4 / 100tb 101s/.*/Done! Try another, or end with ^D./p 102d 103