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 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 module Main where 175 176 import Char 177 import IO 178 import System 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 fold1 :: (a->b->b) -> (a->b) -> [a] -> b 216 fold1 f g [a] = g a 217 fold1 f g (a:x) = f a (fold1 f g x) 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 scan1 :: (a->b->b) -> (a->b) -> [a] -> [b] 235 scan1 f g = fold1 f' g' 236 where g' a = [g a] 237 f' a s = f a (head s) : s 238 239 240 241 242 243 244 245 246 tails :: [a] -> [[a]] 247 tails = scan1 (:) (:[]) 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 single :: [a] -> Bool 271 single [a] = True 272 single _ = False 273 274 275 276 277 278 279 280 281 282 283 284 285 286 minWith :: (a->Int) -> [a] -> a 287 minWith f = fold1 choice id 288 where choice a b | f a < f b = a 289 | otherwise = b 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 type Txt = [Word] 307 type Word = String 308 309 310 311 312 313 type Paragraph = [Line] 314 type Line = [Word] 315 316 317 318 319 320 par0 :: Txt -> Paragraph 321 par0 = minWith cost . filter feasible . formats 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 formats :: Txt -> [Paragraph] 340 formats = fold1 next_word last_word 341 where last_word w = [ [[w]] ] 342 next_word w ps = map (new w) ps ++ map (glue w) ps 343 344 new w ls = [w]:ls 345 glue w (l:ls) = (w:l):ls 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 feasible :: Paragraph -> Bool 361 feasible = all fits 362 363 364 365 366 367 368 369 370 maxw :: Int 371 maxw = 70 372 373 374 375 376 377 378 379 380 381 382 fits :: Line -> Bool 383 fits xs = (width xs <= maxw) 384 385 386 387 388 389 390 391 392 393 394 395 396 397 width :: Line -> Int 398 width = fold1 plus length 399 where plus w n = length w + 1 + n 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 optw :: Int 419 optw = 63 420 421 422 423 424 425 426 427 428 429 430 431 432 cost :: Paragraph -> Int 433 cost = fold1 plus (const 0) 434 where plus l n = linc l + n 435 linc l = (optw - width l)^2 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 par1 488 = minWith cost . fold1 step start 489 where 490 step w ps = filter fitH (new w (minWith cost ps):map (glue w) ps) 491 start w = filter fitH [ [[w]] ] 492 fitH = fits . head 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 par1' 516 = the . minWith cost . fold1 step start 517 where 518 step w ps = filter fitH (new w (minWith cost ps):map (glue w) ps) 519 start w = filter fitH [([[w]], length w,0)] 520 new w ([l],n,0) = ([w]:[l], length w, 0) 521 new w p = ([w]:ls , length w, cost p) where (ls,n,m) = p 522 glue w (l:ls,n,m) = ((w:l):ls, length w + 1 + n, m) 523 the (ls,n,m) = ls 524 width_hd (ls,n,m) = n 525 cost_tl (ls,n,m) = m 526 linc_hd p = (optw - width_hd p)^2 527 cost ([_],_,_) = 0 528 cost p = linc_hd p + cost_tl p 529 fitH p = width_hd p <= maxw 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 par2' 661 = minWith cost . fold1 step start 662 where 663 step w ps = trim (filter fitH (new w (minWith cost ps):map (glue w) ps)) 664 start w = filter fitH [ [[w]] ] 665 trim [] = [] 666 trim [p] = [p] 667 trim pspq 668 | cost p <= cost q = trim psp 669 | otherwise = trim psp ++ [q] 670 where q = last pspq 671 psp = init pspq 672 p = last psp 673 ps = init psp 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 par2 924 = last . fold1 step start 925 where 926 step w ps = trim(filter fitH (new w (last ps) `add` map (glue w) ps)) 927 start w = filter fitH [ [[w]] ] 928 add p [] = [p] 929 add p [q] = [p,q] 930 add p (q:r:rs) | bf p q <= bf q r = add p (r:rs) 931 | otherwise = p:q:r:rs 932 bf p q 933 | single q && cost pt == 0 934 = (optw - wph) `min` rqh 935 | single q = rqh 936 | otherwise = ceildiv (cost p - cost q) (2*(wqh-wph)) `min` rqh 937 where ph:pt = p 938 qh:qt = q 939 wph = width ph 940 wqh = width qh 941 rqh = maxw - wqh + 1 942 ceildiv n m = (n+m-1) `div` m 943 trim [] = [] 944 trim [p] = [p] 945 trim pspq | cost p <= cost q = trim psp 946 | otherwise = pspq 947 where q = last pspq 948 psp = init pspq 949 p = last psp 950 ps = init psp 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 par2'' 1052 = last . fold1 step start 1053 where 1054 step w ps = trim(droptail (not.fitH) (new w (last ps) `add` map (glue w) ps)) 1055 start w = droptail (not.fitH) [ [[w]] ] 1056 droptail p [] = [] 1057 droptail p xsx | p x = droptail p xs 1058 | otherwise = xsx 1059 where x = last xsx 1060 xs = init xsx 1061 add p [] = [p] 1062 add p [q] = [p,q] 1063 add p (q:r:rs) | bf p q <= bf q r = add p (r:rs) 1064 | otherwise = p:q:r:rs 1065 bf p q 1066 | single q && cost pt == 0 1067 = (optw - wph) `min` rqh 1068 | single q = rqh 1069 | otherwise = ceildiv (cost p - cost q) (2*(wqh-wph)) `min` rqh 1070 where ph:pt = p 1071 qh:qt = q 1072 wph = width ph 1073 wqh = width qh 1074 rqh = maxw - wqh + 1 1075 ceildiv n m = (n+m-1) `div` m 1076 trim [] = [] 1077 trim [p] = [p] 1078 trim pspq | cost p <= cost q = trim psp 1079 | otherwise = pspq 1080 where q = last pspq 1081 psp = init pspq 1082 p = last psp 1083 ps = init psp 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 type Par = (Width,Cost,Length) 1129 type Width = Int 1130 type Cost = Int 1131 type Length = Int 1132 1133 width_tl = fst3 1134 cost_tl = snd3 1135 len_tl = thd3 1136 1137 1138 1139 1140 1141 1142 fst3 (a,b,c) = a 1143 snd3 (a,b,c) = b 1144 thd3 (a,b,c) = c 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 tile :: Txt -> ([Length],Length) -> Paragraph 1168 tile ws ([],n) = [] 1169 tile ws (m:ms,n) = ws1 : tile ws2 (drop l (m:ms),m) 1170 where l = n - m 1171 (ws1,ws2) = splitAt l ws 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 par3 :: Txt -> Paragraph 1230 par3 ws 1231 = tile ws (map (len_tl.last'.fst3) zs, thd3 (head zs)) 1232 where zs = scan1 stepr startr (map length ws) 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 startr :: Length -> (SymList Par, Width, Length) 1246 startr a | a <= maxw = (cons' (0,0,0) nil',a,1) 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 stepr :: Length -> 1260 (SymList Par, Cost, Length) -> 1261 (SymList Par, Cost, Length) 1262 stepr w (ps,tw,tl) 1263 = (trim (drop_nofit (new (last' ps) `add` ps)), tot_width, tot_len) 1264 where 1265 single p = len_tl p == 0 1266 cost p 1267 | single p = 0 1268 | otherwise = cost_tl p + (optw - width_hd p)^2 1269 width_hd p 1270 | single p = tot_width 1271 | otherwise = tot_width - width_tl p - 1 1272 tot_width = w + 1 + tw 1273 tot_len = 1 + tl 1274 1275 1276 1277 1278 1279 1280 1281 1282 new p | single p = (tw,0,tl) 1283 | otherwise = (tw,cost_tl p + (optw-old_width_hd p)^2,tl) 1284 old_width_hd p | single p = tw 1285 | otherwise = tw - width_tl p - 1 1286 1287 1288 1289 1290 1291 trim ps_pq | null' ps_pq = ps_pq 1292 | single' ps_pq = ps_pq 1293 | cost p <= cost q = trim ps_p 1294 | otherwise = ps_pq 1295 where ps_p = init' ps_pq 1296 q = last' ps_pq 1297 p = last' ps_p 1298 1299 1300 1301 1302 1303 1304 1305 drop_nofit ps_p | null' ps_p = ps_p 1306 | width_hd p > maxw = drop_nofit ps 1307 | otherwise = ps_p 1308 where ps = init' ps_p 1309 p = last' ps_p 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 add p qr_rs | single' qr_rs || null' qr_rs = cons' p qr_rs 1323 | bf p q <= bf q r = add p r_rs 1324 | otherwise = cons' p qr_rs 1325 where r_rs = tail' qr_rs 1326 q = head' qr_rs 1327 r = head' r_rs 1328 1329 1330 1331 1332 1333 bf p q 1334 | single q && cost_tl p == 0 = (optw - wph) `min` rqh 1335 | single q = rqh 1336 | otherwise = ceildiv (cost p-cost q) 1337 (2*(wqh-wph)) `min` rqh 1338 where 1339 wph = width_hd p 1340 wqh = width_hd q 1341 rqh = maxw - wqh + 1 1342 1343 ceildiv n m = (n+m-1) `div` m 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 fmt = unparse . map (par3 . concat) . parse 1373 1374 1375 1376 1377 1378 fmtWith par = unparse . map (par . concat) . parse 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 type SymList a = ([a],[a]) 1665 1666 single' (x,y) = (null x && single y) || (single x && null y) 1667 1668 null' ([],[]) = True 1669 null' _ = False 1670 1671 nil' = ([],[]) 1672 1673 head' (x,y) | not (null x) = head x 1674 | otherwise = head y 1675 1676 last' (y,x) | not (null x) = head x 1677 | otherwise = head y 1678 1679 cons' a (x,y) | not (null y) = (a:x,y) 1680 | otherwise = ([a],x) 1681 1682 snoc' a (y,x) | not (null y) = (y,a:x) 1683 | otherwise = (x,[a]) 1684 1685 tail' (x,y) | null x = ([],[]) 1686 | single x = (reverse y1, y0) 1687 | otherwise = (tail x, y) 1688 where (y0,y1) = splitAt (length y `div` 2) y 1689 1690 init' (y,x) | null x = ([],[]) 1691 | single x = (y0, reverse y1) 1692 | otherwise = (y, tail x) 1693 where (y0,y1) = splitAt (length y `div` 2) y 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 unformat :: a -> [[a]] -> [a] 1711 unformat a = fold1 insert id 1712 where insert xs ys = xs ++ [a] ++ ys 1713 1714 format :: Eq a => a -> [a] -> [[a]] 1715 format a [] = [[]] 1716 format a x = fold1 (break a) (start a) x 1717 where break a b xs | a == b = []:xs 1718 | otherwise = (b:head xs):tail xs 1719 start a b = break a b [[]] 1720 1721 1722 1723 1724 1725 1726 1727 unparas :: [[[String]]] -> [[String]] 1728 unparas = unformat [] 1729 1730 paras :: [[String]] -> [[[String]]] 1731 paras = filter (/=[]) . format [] 1732 1733 parse = paras . map words . lines 1734 unparse = unlines . map unwords . unparas 1735 1736 1737 1738 1739 1740 1741 1742 parg :: Txt -> Paragraph 1743 parg = foldl nextword [[]] 1744 where 1745 nextword p w | fits (last p++[w]) = init p ++ [last p ++ [w]] 1746 | otherwise = p ++ [[w]] 1747 fmtg = fmtWith parg 1748 1749 1750 1751 1752 1753 fmt1 = fmtWith par1 1754 1755 1756 1757 1758 test = 1759 "In the constructive programming community it is commonplace to see " ++ 1760 "formal developments of textbook algorithms. In the algorithm design " ++ 1761 "community, on the other hand, it may be well known that the textbook " ++ 1762 "solution to a problem is not the most efficient possible. However, in " ++ 1763 "presenting the more efficient solution, the algorithm designer will " ++ 1764 "usually omit some of the implementation details, this creating an " ++ 1765 "algorithm gap between the abstract algorithm and its concrete " ++ 1766 "implementation. This is in contrast to the formal development, which " ++ 1767 "usually presents the complete concrete implementation of the less " ++ 1768 "efficient solution. \n \n" 1769 1770 tests = concat (repeat test) 1771 1772 main = getArgs >>= (\as -> 1773 if length as /= 1 1774 then putStr "usage: para <file name>" 1775 else openFile (head as) ReadMode >>= (\h -> 1776 hGetContents h >>= (\ws -> 1777 putStr (if null ws then [] else (fmt ws))))) 1778 1779 1780 1781