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