From 8e50ab4c23e044367ee337dea0920b5ce94f524b Mon Sep 17 00:00:00 2001 From: arthur Date: Fri, 19 Dec 2025 07:48:56 -0300 Subject: [PATCH] fix: improved generator --- rod-cutting/input/10 | 4 +- rod-cutting/input/11 | 4 +- rod-cutting/input/12 | 4 +- rod-cutting/input/13 | 4 +- rod-cutting/input/14 | 4 +- rod-cutting/input/15 | 4 +- rod-cutting/input/16 | 4 +- rod-cutting/input/17 | 4 +- rod-cutting/input/18 | 4 +- rod-cutting/input/19 | 4 +- rod-cutting/input/20 | 4 +- rod-cutting/input/21 | 4 +- rod-cutting/input/22 | 4 +- rod-cutting/input/23 | 4 +- rod-cutting/input/24 | 4 +- rod-cutting/input/25 | 4 +- rod-cutting/input/26 | 4 +- rod-cutting/input/27 | 4 +- rod-cutting/input/28 | 4 +- rod-cutting/input/29 | 4 +- rod-cutting/input/30 | 4 +- rod-cutting/input/31 | 4 +- rod-cutting/input/32 | 4 +- rod-cutting/input/33 | 4 +- rod-cutting/input/34 | 4 +- rod-cutting/input/35 | 4 +- rod-cutting/input/36 | 4 +- rod-cutting/input/37 | 4 +- rod-cutting/input/38 | 4 +- rod-cutting/input/39 | 4 +- rod-cutting/input/40 | 4 +- rod-cutting/input/41 | 4 +- rod-cutting/input/42 | 4 +- rod-cutting/input/43 | 4 +- rod-cutting/input/44 | 4 +- rod-cutting/input/5 | 2 +- rod-cutting/input/6 | 4 +- rod-cutting/input/7 | 4 +- rod-cutting/input/8 | 4 +- rod-cutting/input/9 | 4 +- rod-cutting/output/10 | 4 +- rod-cutting/output/11 | 4 +- rod-cutting/output/12 | 4 +- rod-cutting/output/13 | 4 +- rod-cutting/output/14 | 4 +- rod-cutting/output/15 | 4 +- rod-cutting/output/16 | 4 +- rod-cutting/output/17 | 4 +- rod-cutting/output/18 | 4 +- rod-cutting/output/19 | 4 +- rod-cutting/output/20 | 4 +- rod-cutting/output/21 | 4 +- rod-cutting/output/22 | 4 +- rod-cutting/output/23 | 4 +- rod-cutting/output/24 | 4 +- rod-cutting/output/25 | 4 +- rod-cutting/output/26 | 4 +- rod-cutting/output/27 | 4 +- rod-cutting/output/28 | 4 +- rod-cutting/output/29 | 4 +- rod-cutting/output/30 | 4 +- rod-cutting/output/31 | 4 +- rod-cutting/output/32 | 4 +- rod-cutting/output/33 | 4 +- rod-cutting/output/34 | 4 +- rod-cutting/output/35 | 4 +- rod-cutting/output/36 | 4 +- rod-cutting/output/37 | 4 +- rod-cutting/output/38 | 4 +- rod-cutting/output/39 | 4 +- rod-cutting/output/40 | 4 +- rod-cutting/output/41 | 4 +- rod-cutting/output/42 | 4 +- rod-cutting/output/43 | 4 +- rod-cutting/output/44 | 4 +- rod-cutting/output/5 | 4 +- rod-cutting/output/6 | 4 +- rod-cutting/output/7 | 4 +- rod-cutting/output/8 | 4 +- rod-cutting/output/9 | 4 +- rod-cutting/rod-cutting-tutorial.pdf | Bin 0 -> 128064 bytes rod-cutting/rod-cutting-tutorial.tex | 53 +++++++++++++++++++++++++++ rod-cutting/rod-cutting.pdf | Bin 84730 -> 84730 bytes rod-cutting/src/generator.cpp | 21 ++++++++++- rod-cutting/statement/tutorial.tex | 39 ++++++++++++++++++++ 85 files changed, 270 insertions(+), 161 deletions(-) create mode 100644 rod-cutting/rod-cutting-tutorial.pdf create mode 100644 rod-cutting/rod-cutting-tutorial.tex diff --git a/rod-cutting/input/10 b/rod-cutting/input/10 index 5e1d241..096287d 100644 --- a/rod-cutting/input/10 +++ b/rod-cutting/input/10 @@ -1,2 +1,2 @@ -237 -9806 3002 2159 6222 4423 9326 5906 6419 8505 4721 7875 3615 9755 5674 9458 8246 1111 6149 4997 7788 76 1378 2483 3211 7964 2485 9930 8577 5583 6228 7657 5135 6671 2685 8151 5195 1338 7581 9546 9903 8836 7801 8433 2359 1986 7193 7147 8119 2927 1528 5310 9747 9323 8294 6305 7798 9399 3654 1649 5020 714 8688 1088 7735 607 4464 6417 685 6565 5781 5166 4216 5885 8131 258 2437 6528 2337 1376 6454 7143 9580 6618 256 2049 322 2378 8413 3056 1016 6636 7788 7836 2149 114 8828 6254 6741 4767 164 7638 4966 2669 8270 8646 4542 9399 9368 9925 1235 7151 274 4350 9361 8473 1106 4782 4952 8142 6035 7337 2460 8059 4049 8709 6995 4847 4974 2381 3226 2224 3809 4943 3025 1527 8610 8495 2298 4655 5567 5698 5790 8778 9995 9908 9016 2300 2633 3650 2312 5582 8853 6097 8881 8620 6427 3925 9355 5240 5070 7050 4178 8133 6739 319 4533 5388 9299 5558 7720 122 861 7766 5922 1456 7601 8377 144 8882 8966 8046 7104 8009 6149 8696 2327 7585 8555 6413 4859 5963 8139 3591 4970 8860 7834 5911 6274 4876 145 3677 2214 5545 1743 609 8879 7937 3940 4782 4553 1531 9495 6817 6994 3471 8865 2590 3886 1593 7504 2172 1493 8954 9221 8132 3060 5623 982 4181 9064 3736 4365 2371 7894 4458 3175 1956 +130 +10 20 43 53 63 73 83 93 103 122 132 142 152 162 172 182 192 216 226 232 242 249 259 269 279 289 304 314 324 341 351 361 383 393 394 404 414 424 434 444 454 464 474 484 494 504 514 517 540 544 563 584 586 608 623 633 643 653 663 670 680 690 707 717 738 741 743 753 759 767 777 787 797 807 816 838 848 858 868 878 888 913 923 928 948 954 964 974 984 994 1004 1014 1024 1033 1048 1069 1073 1083 1093 1111 1121 1128 1152 1162 1165 1170 1174 1184 1207 1209 1219 1229 1250 1273 1283 1293 1299 1309 1319 1338 1348 1358 1365 1375 1385 1395 1405 1415 1419 1421 diff --git a/rod-cutting/input/11 b/rod-cutting/input/11 index b7e2b46..a224141 100644 --- a/rod-cutting/input/11 +++ b/rod-cutting/input/11 @@ -1,2 +1,2 @@ -160 -4254 1429 6274 995 7816 126 3883 4364 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728 738 748 754 764 771 781 791 801 811 821 828 838 862 872 896 906 911 921 923 933 943 960 982 992 1002 1012 1014 1021 1031 1041 1044 1053 1063 1079 1094 1104 1114 1124 1134 1149 1159 1161 1171 1177 1197 1207 1217 1227 1233 1243 1248 1258 1268 1291 1301 1311 1336 1346 1356 1366 1376 1386 1401 1405 1415 1425 1442 1446 1456 1466 1476 1486 1511 diff --git a/rod-cutting/input/12 b/rod-cutting/input/12 index 7a0acf4..960d86d 100644 --- a/rod-cutting/input/12 +++ b/rod-cutting/input/12 @@ -1,2 +1,2 @@ -50 -4064 9498 8873 2407 640 6908 6302 9296 789 4581 4980 717 1388 9613 531 8544 1864 7325 4952 1660 5550 9590 3184 2235 56 4664 4352 8520 3443 9019 4112 373 4448 2793 4443 7878 6822 7953 2960 3700 6926 54 2884 6220 8614 2830 3982 2349 2447 7396 +81 +10 20 30 40 58 68 78 85 95 105 115 120 122 124 134 144 154 164 174 182 203 206 216 235 245 246 256 275 299 320 330 340 350 360 361 371 393 403 413 432 442 452 462 487 495 514 524 534 542 550 554 578 588 605 615 619 629 630 640 650 660 670 680 687 697 707 717 727 733 743 753 759 769 779 804 823 833 843 853 863 873 diff --git a/rod-cutting/input/13 b/rod-cutting/input/13 index 114da0c..befc9fb 100644 --- a/rod-cutting/input/13 +++ b/rod-cutting/input/13 @@ -1,2 +1,2 @@ -59 -766 1215 9111 2743 8645 9856 6377 5353 3713 5343 592 4967 5537 1374 6264 4862 1562 18 3774 268 8293 3557 3607 645 2334 5173 8375 210 9222 1923 8635 8637 5762 7430 5088 8423 7179 5574 5721 4387 4780 6673 7356 6920 8727 8569 405 4386 7472 4979 4179 7649 1120 8841 3670 5800 3699 2457 7639 +16 +10 30 47 57 66 76 86 106 116 118 128 138 154 178 188 198 diff --git a/rod-cutting/input/14 b/rod-cutting/input/14 index f3ca5b4..6edc4ab 100644 --- a/rod-cutting/input/14 +++ b/rod-cutting/input/14 @@ -1,2 +1,2 @@ -52 -5723 8933 7408 5138 2539 65 4031 8785 6124 8360 1816 1694 7915 9672 3840 8545 3257 3121 4419 1879 4154 377 5518 1599 9863 2635 9717 8348 6364 707 9039 5526 5706 3396 4597 6600 4614 2562 5239 8755 5688 5736 5894 938 749 6228 4299 8149 2070 8118 4959 3822 +332 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7147 189 8796 5405 9953 1487 6571 4853 9246 7591 3616 8051 2500 5553 2790 8523 2408 3339 7885 3110 5748 152 4008 9664 5526 5902 6015 9594 2575 264 3070 2537 9174 9364 2004 5653 3155 4005 4629 331 7204 4434 6761 5484 7707 4581 2363 7644 1069 4638 3866 2995 4164 398 8251 8783 +35 +10 20 23 31 41 51 61 64 72 95 116 126 136 146 156 166 176 186 195 205 223 233 243 253 263 273 283 292 302 312 336 346 366 376 386 diff --git a/rod-cutting/input/18 b/rod-cutting/input/18 index a75358d..8bf5e7e 100644 --- a/rod-cutting/input/18 +++ b/rod-cutting/input/18 @@ -1,2 +1,2 @@ -419 -8988 9829 5872 4061 2547 835 3499 4630 7970 9734 4520 5810 8427 689 1316 8143 3172 5483 2064 31 4633 1984 8128 8007 536 1473 476 2402 2947 5743 3154 8700 8754 2436 3138 4360 2654 8442 2273 4491 3863 2721 3431 2494 495 2462 8081 2943 5117 1734 3647 6656 9435 8967 7735 1063 9449 6000 6576 525 3879 7828 9032 5071 5151 780 8639 8960 8920 6769 938 85 1252 2742 6496 1191 8787 2828 1040 2053 1582 6283 2762 5583 2045 6032 8833 2940 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b/rod-cutting/input/37 index 3adfbbf..8badc75 100644 --- a/rod-cutting/input/37 +++ b/rod-cutting/input/37 @@ -1,2 +1,2 @@ -92 -9023 3417 6511 6190 6577 4956 5614 289 1294 7405 1101 4917 5406 5207 4335 9869 9837 2086 9274 2706 6524 796 9416 3437 400 9391 7562 3281 6801 5849 2896 3903 8477 6359 8194 2623 2626 6539 9306 4206 4423 4843 2440 4906 5476 2895 1821 3384 7173 5430 1984 6655 2459 7010 2636 843 1099 791 8800 2714 2173 3584 1773 1970 3086 7418 4732 3641 5758 5560 2038 2508 5651 4413 778 1305 7524 2581 6570 2324 7983 8268 7054 8598 6132 9317 4975 3721 3512 356 2621 9565 +856 +10 20 30 40 50 58 79 101 111 121 131 141 151 161 165 174 184 194 204 214 224 234 244 261 268 278 285 289 299 321 337 342 352 362 372 382 404 427 428 438 448 458 468 478 488 495 505 527 537 544 554 564 569 579 601 611 626 634 644 654 672 682 692 716 726 736 742 752 777 783 793 811 821 831 841 851 861 868 878 888 912 922 932 942 966 976 986 996 1002 1012 1022 1032 1033 1043 1053 1059 1069 1079 1089 1093 1103 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5972 5982 5992 6002 6012 6022 6032 6042 6052 6062 6072 6096 6111 6121 6131 6156 6166 6176 6191 6201 6203 6213 6232 6241 6251 6261 6268 6269 6276 6286 6296 6306 6327 6335 6345 6353 6363 6379 6401 6411 6421 6431 6450 6460 6465 6486 6504 6526 6536 6546 6556 6566 6576 6586 6596 6606 6616 6626 6636 6646 6670 6680 6689 6708 6714 6730 6740 6761 6771 6781 6791 6798 6816 6826 6836 6846 6856 6861 6871 6881 6891 6906 6928 6932 6942 6952 6961 6971 6981 6991 7001 7011 7021 7031 7050 7068 7090 7100 7119 7141 7151 7161 7166 7176 7186 7196 7206 7216 7237 7255 7261 7271 7281 7288 7305 7310 7320 7330 7350 7360 7370 7380 7382 7392 7415 7432 7442 7449 7467 7488 7498 7508 7524 7530 7540 7543 7553 7563 7573 7579 7597 7607 7617 7638 7661 7671 7674 7684 7694 7704 7714 7724 7744 7765 7775 7785 7795 7805 7815 7823 7833 7843 7845 7855 7858 7864 7874 7892 7902 7912 7922 7944 7954 7964 7974 7984 7994 8004 8014 8024 8034 8044 8054 8064 8088 8094 8104 8114 8124 8134 8144 8154 8164 8174 8197 8219 8229 8239 8244 8261 8271 8281 8291 8307 8317 8327 8337 8347 8357 8367 8377 8387 8397 8407 8417 8420 8430 8450 8460 8470 8480 8490 8500 8510 8520 8545 8555 8565 8575 8584 8594 8596 8606 8616 8638 8648 8658 8668 8678 8695 8705 8709 8719 8725 8728 8750 8755 8765 8766 8784 8788 8798 8808 8823 8833 8843 8850 8860 8870 8880 8890 8900 8910 8913 8934 8944 8954 8961 8981 9006 9016 9026 9041 9056 9066 9076 9086 9091 9101 9109 9119 9129 9139 9163 9173 9183 9193 9199 9209 9219 9229 9239 9248 9258 9268 9278 9288 9298 9308 9310 9320 9330 9350 9360 9370 9380 9390 9414 9424 9434 9444 9454 9459 9469 9475 9494 9504 9525 9535 9537 9547 9557 9567 9577 9587 9597 9606 9613 9623 9633 9640 9650 9657 9679 9689 9699 9703 9713 9722 9745 9755 diff --git a/rod-cutting/input/44 b/rod-cutting/input/44 index 83fc0a9..a8a0c72 100644 --- a/rod-cutting/input/44 +++ b/rod-cutting/input/44 @@ -1,2 +1,2 @@ -406 -3808 401 2419 7469 6638 2932 62 7120 744 9685 6316 5937 7363 2274 9948 7384 454 7307 1423 3279 5693 4805 6891 9860 3399 3880 6218 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6203 6880 3954 125 9244 6186 6468 8046 6918 8728 1573 6334 3218 4740 5434 6545 7744 623 8572 978 3650 9627 4838 7470 175 9249 3450 7863 8577 6973 188 3362 199 4140 5125 8490 4788 9365 785 4411 9566 3693 9042 6999 3584 8081 8507 9749 8728 2720 7813 6205 1449 5647 6717 1261 9563 6931 8244 6951 4902 2378 7982 9232 9947 67 9940 3987 4955 2209 8274 6364 5965 9788 9449 7086 860 671 590 7421 9479 5515 8329 6949 8864 4595 8983 6609 2302 3486 3353 9028 4714 7033 9763 1956 6933 3922 7277 9370 1265 1614 582 7347 3844 1379 4284 3778 7672 7855 2004 6940 2158 2367 3353 1978 7734 1497 469 9226 344 5299 9065 3487 5086 2185 1947 6813 4471 9291 819 9101 3958 3516 6557 9567 7890 3060 5658 3491 4836 4399 8302 2687 8715 3420 6947 2652 6811 4576 2357 4377 953 5200 3845 8727 7825 7610 1494 6874 2369 2957 3635 2223 9291 8284 8967 6416 327 1135 7571 3633 8062 9505 3691 +154 +10 13 14 24 27 37 47 57 67 92 102 122 132 142 149 150 165 175 185 207 224 240 265 275 278 288 298 306 328 338 348 354 364 374 384 394 410 414 422 432 442 452 458 468 491 501 511 518 542 552 562 572 582 584 594 604 614 634 657 679 689 699 709 719 729 744 753 772 782 792 816 826 836 837 847 867 877 887 911 935 945 955 957 967 977 987 1012 1037 1042 1050 1060 1070 1072 1082 1092 1102 1112 1122 1132 1142 1145 1165 1175 1185 1186 1204 1212 1232 1242 1250 1260 1268 1287 1297 1307 1327 1343 1360 1370 1380 1390 1400 1407 1417 1421 1431 1452 1462 1467 1474 1480 1490 1494 1504 1509 1519 1529 1550 1560 1561 1571 1589 1599 1620 1630 1640 1662 1672 1689 1699 1717 1727 1731 1740 diff --git a/rod-cutting/input/5 b/rod-cutting/input/5 index 844534a..316727e 100644 --- a/rod-cutting/input/5 +++ b/rod-cutting/input/5 @@ -1,2 +1,2 @@ 8 -4575 6426 9445 8772 81 3447 629 3497 +10 20 30 40 47 54 64 74 diff --git a/rod-cutting/input/6 b/rod-cutting/input/6 index 0596fd2..f065acf 100644 --- a/rod-cutting/input/6 +++ b/rod-cutting/input/6 @@ -1,2 +1,2 @@ -112 -7775 4325 3982 4784 8417 2156 1932 5902 5728 8537 3857 739 6918 9211 9679 8506 3340 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1451 1454 1464 1467 1477 1485 1510 1520 1530 1533 1543 1558 1559 1569 1591 1616 1625 1635 1653 1663 1673 1683 1693 1701 1711 1727 1737 1744 1751 1775 1777 1782 1801 1803 1828 1838 1848 1866 1876 1886 1896 1904 1914 1924 1939 1949 1959 1969 1979 1989 1998 2008 2018 2023 2033 2043 2044 2054 2077 2087 2103 2111 2121 2129 2137 2146 2156 2166 2176 2183 2193 2197 2207 2217 2227 2251 diff --git a/rod-cutting/input/7 b/rod-cutting/input/7 index 050b291..b258dc3 100644 --- a/rod-cutting/input/7 +++ b/rod-cutting/input/7 @@ -1,2 +1,2 @@ -54 -639 9992 9130 6467 8989 7958 2581 6600 7466 1473 1929 9775 2581 9770 9455 3718 4628 6807 9335 1898 1552 6530 5811 9569 4148 3384 6954 8913 114 6315 3686 9334 382 1392 8326 1008 3553 962 4957 4850 8231 2061 1185 1588 4305 2980 7564 1890 52 8747 943 1740 7593 7469 +1 +10 diff --git a/rod-cutting/input/8 b/rod-cutting/input/8 index e98e3ad..de9bead 100644 --- a/rod-cutting/input/8 +++ b/rod-cutting/input/8 @@ -1,2 +1,2 @@ -316 -2516 443 6007 9525 3299 412 7163 6699 3571 8976 7455 2217 3590 9343 4427 3220 1342 4584 4239 4496 5875 2601 1258 1449 3377 40 7428 8238 2455 3517 1653 4433 1768 1957 7307 6456 6878 2977 5368 1999 4882 3541 1826 3764 3269 1401 2098 8698 6763 1515 5413 1495 6523 4571 206 8357 5904 3310 1410 5844 7611 7484 410 3559 9262 1394 8949 1107 8546 2737 7987 4979 2306 4685 9291 5542 6542 9134 1094 2751 2089 898 5729 212 9964 8297 1823 720 5297 2280 4917 4338 7176 8183 7965 5740 3541 9555 3 3316 8256 6013 7611 3974 4931 2024 9609 6176 304 1151 4199 9876 8825 8893 3939 3737 4374 8323 6846 5819 1154 5157 814 6343 1886 1197 3100 1856 1709 3879 5479 2461 3014 9123 9744 5400 7094 9447 9020 9152 3963 9674 7829 8984 9930 5322 6665 2646 9385 9191 1353 7605 7110 4453 3356 243 7694 1854 2297 3075 9831 974 8720 1837 695 9845 7154 1673 5306 7865 5524 952 1231 5329 2353 6331 5692 8027 3413 3081 8438 5063 9858 7358 266 7801 6095 8374 4807 5051 4868 9478 9809 1304 7007 2308 2992 4499 9650 1706 8399 7822 3698 1015 6381 7267 2282 237 7119 6111 9926 3444 9788 9826 9944 3702 1888 6944 5655 3521 4489 6946 1131 6616 2445 1654 4434 3522 4850 2683 2542 5226 741 2486 6101 9661 8532 6961 3568 1903 276 4758 9772 5766 3259 3224 5836 3741 2054 9018 6325 5395 6949 5925 5056 7850 6378 2711 9083 8184 9790 2559 5945 8345 268 2322 7501 555 8772 1785 6675 1312 8665 2321 4920 3696 2516 4857 7149 948 3807 4535 1591 6284 3082 1268 898 3674 841 939 9593 3717 6003 6334 2768 6471 965 1121 1083 9103 2366 1149 5732 5776 7488 2238 3064 2736 6773 8070 2122 1274 6632 1560 7455 4748 +61 +10 20 35 52 62 78 88 98 108 118 128 149 156 162 172 174 192 202 224 234 244 254 262 271 278 288 313 330 340 350 360 370 380 384 394 418 428 438 460 480 498 508 511 521 531 541 551 561 577 579 597 607 609 619 629 639 649 659 676 686 711 diff --git a/rod-cutting/input/9 b/rod-cutting/input/9 index 3dd6e6f..ea3d226 100644 --- a/rod-cutting/input/9 +++ b/rod-cutting/input/9 @@ -1,2 +1,2 @@ -185 -6061 5889 6954 5320 2034 6733 6345 1090 9640 8212 3717 3135 8211 7037 1483 2144 8668 1778 256 4345 4127 6398 8808 9328 5758 4566 4591 6371 6076 5805 4964 9279 8370 3309 441 8329 8125 3429 661 5241 1166 4870 9394 4314 9513 901 2687 6748 6614 9965 4222 1122 5748 2234 8311 2997 2193 9838 3172 7006 803 3711 2547 9136 5442 8343 3431 7420 2923 5843 3239 6314 7903 8901 2622 8535 5777 8275 3321 2177 1404 6261 2972 4093 8747 1562 8237 1698 4271 4836 504 9420 5101 4743 5433 3897 1277 8110 8645 9487 3324 246 3889 5524 5243 4258 7961 8389 3581 789 4619 4688 6477 3899 4025 9913 6134 1920 3179 1065 8697 4727 1051 7706 763 2500 2471 1068 5652 3266 8850 52 8000 6319 5411 4456 6626 3115 7764 1380 5517 3757 9764 679 3801 8526 9990 2967 3604 475 2416 249 1406 2199 6557 8954 7355 1991 6539 6505 3637 5268 8254 1066 9736 428 4107 6932 5332 6786 2766 2868 8159 5418 9652 9768 1968 9710 9905 6965 1269 475 8460 6802 2638 +11 +10 20 23 33 43 53 72 82 92 102 112 diff --git a/rod-cutting/output/10 b/rod-cutting/output/10 index ade74b7..957b1cb 100644 --- a/rod-cutting/output/10 +++ b/rod-cutting/output/10 @@ -1,2 +1,2 @@ -2324022 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +1859 +4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 diff --git a/rod-cutting/output/11 b/rod-cutting/output/11 index 679f7d2..c62acb0 100644 --- a/rod-cutting/output/11 +++ b/rod-cutting/output/11 @@ -1,2 +1,2 @@ -680640 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +1634 +26 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 diff --git a/rod-cutting/output/12 b/rod-cutting/output/12 index 8b2a9a8..b4e4ba2 100644 --- a/rod-cutting/output/12 +++ b/rod-cutting/output/12 @@ -1,2 +1,2 @@ -237450 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +938 +6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 diff --git a/rod-cutting/output/13 b/rod-cutting/output/13 index e5b30ed..186386e 100644 --- a/rod-cutting/output/13 +++ b/rod-cutting/output/13 @@ -1,2 +1,2 @@ -174641 -3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 3 +248 +3 3 3 3 2 2 diff --git a/rod-cutting/output/14 b/rod-cutting/output/14 index 5b5cbaa..602998f 100644 --- a/rod-cutting/output/14 +++ b/rod-cutting/output/14 @@ -1,2 +1,2 @@ -297596 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +3894 +148 12 12 12 148 diff --git a/rod-cutting/output/15 b/rod-cutting/output/15 index 26b6795..1ee06d6 100644 --- a/rod-cutting/output/15 +++ b/rod-cutting/output/15 @@ -1,2 +1,2 @@ -2099834 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +2740 +57 57 46 57 diff --git a/rod-cutting/output/16 b/rod-cutting/output/16 index f5905c5..bbb911c 100644 --- a/rod-cutting/output/16 +++ b/rod-cutting/output/16 @@ -1,2 +1,2 @@ -59122 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 +3761 +11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 diff --git a/rod-cutting/output/17 b/rod-cutting/output/17 index e8b9553..d72550a 100644 --- a/rod-cutting/output/17 +++ b/rod-cutting/output/17 @@ -1,2 +1,2 @@ -339252 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +386 +35 diff --git a/rod-cutting/output/18 b/rod-cutting/output/18 index 5a28634..6565c67 100644 --- a/rod-cutting/output/18 +++ b/rod-cutting/output/18 @@ -1,2 +1,2 @@ -3765972 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +4717 +156 123 139 diff --git a/rod-cutting/output/19 b/rod-cutting/output/19 index 1caa4f1..5c1adce 100644 --- a/rod-cutting/output/19 +++ b/rod-cutting/output/19 @@ -1,2 +1,2 @@ -356952 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 +1585 +7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 diff --git a/rod-cutting/output/20 b/rod-cutting/output/20 index 83fc85d..3114c80 100644 --- a/rod-cutting/output/20 +++ b/rod-cutting/output/20 @@ -1,2 +1,2 @@ -1120982 -3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 3 +3654 +63 42 42 42 42 42 42 diff --git a/rod-cutting/output/21 b/rod-cutting/output/21 index 1c5802c..a9c527e 100644 --- a/rod-cutting/output/21 +++ b/rod-cutting/output/21 @@ -1,2 +1,2 @@ -2222164 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +758 +4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 diff --git a/rod-cutting/output/22 b/rod-cutting/output/22 index f9e0b9d..ac625fe 100644 --- a/rod-cutting/output/22 +++ b/rod-cutting/output/22 @@ -1,2 +1,2 @@ -367479 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +2670 +3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 diff --git a/rod-cutting/output/23 b/rod-cutting/output/23 index ef7b519..d289f8c 100644 --- a/rod-cutting/output/23 +++ b/rod-cutting/output/23 @@ -1,2 +1,2 @@ -1650135 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +659 +4 4 4 4 4 4 4 4 4 4 1 4 diff --git a/rod-cutting/output/24 b/rod-cutting/output/24 index febb674..4742440 100644 --- a/rod-cutting/output/24 +++ b/rod-cutting/output/24 @@ -1,2 +1,2 @@ -1447444 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +1840 +11 11 11 11 11 11 11 11 11 9 11 diff --git a/rod-cutting/output/25 b/rod-cutting/output/25 index 9cdbed8..a5d7a3a 100644 --- a/rod-cutting/output/25 +++ b/rod-cutting/output/25 @@ -1,2 +1,2 @@ -6814671 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +7208 +5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 diff --git a/rod-cutting/output/26 b/rod-cutting/output/26 index ea6cf2f..0d3ecc6 100644 --- a/rod-cutting/output/26 +++ b/rod-cutting/output/26 @@ -1,2 +1,2 @@ -810060 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +302 +25 diff --git a/rod-cutting/output/27 b/rod-cutting/output/27 index e3c33bb..578b038 100644 --- a/rod-cutting/output/27 +++ b/rod-cutting/output/27 @@ -1,2 +1,2 @@ -3146666 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +9002 +3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 diff --git a/rod-cutting/output/28 b/rod-cutting/output/28 index 4ad6236..c80864e 100644 --- a/rod-cutting/output/28 +++ b/rod-cutting/output/28 @@ -1,2 +1,2 @@ -2997664 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +13253 +14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 9 14 diff --git a/rod-cutting/output/29 b/rod-cutting/output/29 index b55484a..a8cd49c 100644 --- a/rod-cutting/output/29 +++ b/rod-cutting/output/29 @@ -1,2 +1,2 @@ -4535352 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +4171 +40 40 40 40 40 40 40 38 40 diff --git a/rod-cutting/output/30 b/rod-cutting/output/30 index 4d88d61..d7647f3 100644 --- a/rod-cutting/output/30 +++ b/rod-cutting/output/30 @@ -1,2 +1,2 @@ -5823248 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +10401 +56 56 55 55 55 55 55 55 55 55 55 52 52 52 52 52 diff --git a/rod-cutting/output/31 b/rod-cutting/output/31 index 1e3bac7..b79eea9 100644 --- a/rod-cutting/output/31 +++ b/rod-cutting/output/31 @@ -1,2 +1,2 @@ -5803685 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +8365 +2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 diff --git a/rod-cutting/output/32 b/rod-cutting/output/32 index f0809e3..c01ab91 100644 --- a/rod-cutting/output/32 +++ b/rod-cutting/output/32 @@ -1,2 +1,2 @@ -2580804 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +9292 +3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 diff --git a/rod-cutting/output/33 b/rod-cutting/output/33 index d212251..3d1cb7a 100644 --- a/rod-cutting/output/33 +++ b/rod-cutting/output/33 @@ -1,2 +1,2 @@ -4983822 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +2242 +3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 diff --git a/rod-cutting/output/34 b/rod-cutting/output/34 index ed03325..90c8b01 100644 --- a/rod-cutting/output/34 +++ b/rod-cutting/output/34 @@ -1,2 +1,2 @@ -3468096 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +5801 +22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 10 22 diff --git a/rod-cutting/output/35 b/rod-cutting/output/35 index d6568c0..698312e 100644 --- a/rod-cutting/output/35 +++ b/rod-cutting/output/35 @@ -1,2 +1,2 @@ -3047352 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +4543 +12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 4 4 12 diff --git a/rod-cutting/output/36 b/rod-cutting/output/36 index c8cef3e..531f53b 100644 --- a/rod-cutting/output/36 +++ b/rod-cutting/output/36 @@ -1,2 +1,2 @@ -1236570 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +1726 +40 39 37 37 diff --git a/rod-cutting/output/37 b/rod-cutting/output/37 index f03d141..75c3828 100644 --- a/rod-cutting/output/37 +++ b/rod-cutting/output/37 @@ -1,2 +1,2 @@ -830116 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +10807 +8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 diff --git a/rod-cutting/output/38 b/rod-cutting/output/38 index c17baef..bf6ce5b 100644 --- a/rod-cutting/output/38 +++ b/rod-cutting/output/38 @@ -1,2 +1,2 @@ -2879100 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +11480 +39 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 6 6 38 diff --git a/rod-cutting/output/39 b/rod-cutting/output/39 index 418bc53..bf9b476 100644 --- a/rod-cutting/output/39 +++ b/rod-cutting/output/39 @@ -1,2 +1,2 @@ -6355176 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +8463 +304 96 3 3 3 3 3 3 3 3 3 3 3 3 3 3 304 diff --git a/rod-cutting/output/40 b/rod-cutting/output/40 index 4e71349..e78003f 100644 --- a/rod-cutting/output/40 +++ b/rod-cutting/output/40 @@ -1,2 +1,2 @@ -3956784 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +5908 +44 44 44 44 44 44 44 44 44 44 44 1 1 1 1 44 diff --git a/rod-cutting/output/41 b/rod-cutting/output/41 index a6aff22..3868a46 100644 --- a/rod-cutting/output/41 +++ b/rod-cutting/output/41 @@ -1,2 +1,2 @@ -1069300 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +2840 +12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 4 12 diff --git a/rod-cutting/output/42 b/rod-cutting/output/42 index ea2a235..fd3cf79 100644 --- a/rod-cutting/output/42 +++ b/rod-cutting/output/42 @@ -1,2 +1,2 @@ -2794441 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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a/rod-cutting/rod-cutting-tutorial.tex b/rod-cutting/rod-cutting-tutorial.tex new file mode 100644 index 0000000..64d4ccc --- /dev/null +++ b/rod-cutting/rod-cutting-tutorial.tex @@ -0,0 +1,53 @@ +\documentclass[10pt]{article} +\usepackage[utf8]{inputenc} +\usepackage{amsmath,amsthm,amssymb} +\usepackage{fullpage} +\usepackage{url} +\pagenumbering{gobble} +\usepackage{hyperref} + +\title{ Tutorial: Barras e Barras} +\author{} +\date{} +\begin{document} +\maketitle +\section{Solução do Problema} + +O problema do corte de barras (\textit{Rod Cutting}) pode ser resolvido de forma eficiente por meio de \textbf{programação dinâmica}. +A ideia é decompor o problema em subproblemas menores: para cada comprimento \(L\) queremos saber qual é a melhor receita máxima que podemos obter cortando (ou não cortando) uma barra de comprimento \(L\). + +\subsection{Definição do Subproblema} + +Seja \(p[1 \dots n]\) o vetor de preços onde \(p[i]\) é o preço de vender um pedaço de comprimento \(i\). +Definimos: + +\[ +dp[L] = \text{o maior receita obtida cortando uma barra de comprimento } L. +\] + +Assim, \(dp[L]\) representa a resposta ótima para uma barra de tamanho \(L\). + +\subsection{Função de Transição} + +Para determinar \(dp[L]\) consideramos a primeira peça que retiramos da barra: se escolhemos cortar uma peça de tamanho \(x\) (com \(1 \le x \le L\)), obtemos imediatamente o preço \(p[x]\) e ficamos com o subproblema da barra restante de tamanho \(L-x\), cujo melhor valor é \(dp[L-x]\). Logo: + +\[ +dp[L] = \max_{1 \le x \le L} \big( p[x] + dp[L-x] \big). +\] + +Em particular, se não fizermos cortes (i.e., vendermos a barra inteira), isso corresponde ao caso \(x=L\) e é coberto pela fórmula acima. + +\subsection{Casos Base} + +O caso base é natural: + +\[ +dp[0] = 0, +\] + +isto é, uma barra de comprimento zero tem receita zero. + +\subsection{Recuperação da Decomposição (pedaços)} + +Para além do valor máximo \(dp[n]\), frequentemente queremos também uma decomposição concreta (lista de comprimentos dos pedaços) que atinja esse valor. Para isso mantemos, durante a computação de \(dp\), um vetor auxiliar \texttt{cut[L]} que armazena o tamanho \(x\) do primeiro pedaço que produz o ótimo para \(dp[L]\). Após preencher \(dp\) e \texttt{cut}, reconstruímos os pedaços repetindo a operação: tomar \(x=\texttt{cut}[L]\), imprimir \(x\), e reduzir \(L \leftarrow L - x\), até \(L=0\). +\end{document} diff --git a/rod-cutting/rod-cutting.pdf b/rod-cutting/rod-cutting.pdf index a5a5974a1d1ba5c6162cb1f36d159433545268cd..c0c85021018845c646b2872feb60867f534fd9d4 100644 GIT binary patch delta 140 zcmex0mG#$D)`l&Nvn&`bx6ig<3}n)>G%z=@FgDONFjhA(P}k(r_svgnNi0cK&~ULb zGB7eVG%|!L*)C?y_=CsM$=K1=$kf@w)Y8<_&Dq4!$->ms)X>e%)X2ox(A7@C#@PtJ LlI{K;jH{UdXe%SE delta 140 zcmex0mG#$D)`l&Nvn&`5x6ig<3}n(WG%_$XHZjsQFjhA(P}k(r_svgnNi0cK&~ULb zGB7eVG%|!L*)C?y_=CsM#LU9X!r9f#(Z$W&(A3$?z}3jn$;8Cc(AC-0!rV^5#@PtJ LlI{K;jH{UdSo0&4 diff --git a/rod-cutting/src/generator.cpp b/rod-cutting/src/generator.cpp index 6352376..12b776f 100644 --- a/rod-cutting/src/generator.cpp +++ b/rod-cutting/src/generator.cpp @@ -62,9 +62,26 @@ string rnd_test(int i) int n = rnd.next(min_n, max_n); vector nums(n); - for (int i = 0; i < n; i++) + + nums[0] = 10; + for (int j = 1; j < n; j++) { - nums[i] = rnd.next(MIN_NI, MAX_NI); + int length = j + 1; + + int choice = rnd.next(0, 100); + + if (choice < 20) { + nums[j] = nums[j-1] + rnd.next(1, nums[0] - 1); + } + else if (choice < 80) { + int offset = rnd.next(-2, 3); + nums[j] = nums[j-1] + nums[0]; + } + else { + nums[j] = nums[j-1] + nums[0] + rnd.next(5, 15); + } + + nums[j] = min(nums[j], MAX_NI); } return (output_tc(nums)); } diff --git a/rod-cutting/statement/tutorial.tex b/rod-cutting/statement/tutorial.tex index e69de29..38b8fb2 100644 --- a/rod-cutting/statement/tutorial.tex +++ b/rod-cutting/statement/tutorial.tex @@ -0,0 +1,39 @@ +\section{Solução do Problema} + +O problema do corte de barras (\textit{Rod Cutting}) pode ser resolvido de forma eficiente por meio de \textbf{programação dinâmica}. +A ideia é decompor o problema em subproblemas menores: para cada comprimento \(L\) queremos saber qual é a melhor receita máxima que podemos obter cortando (ou não cortando) uma barra de comprimento \(L\). + +\subsection{Definição do Subproblema} + +Seja \(p[1 \dots n]\) o vetor de preços onde \(p[i]\) é o preço de vender um pedaço de comprimento \(i\). +Definimos: + +\[ +dp[L] = \text{o maior receita obtida cortando uma barra de comprimento } L. +\] + +Assim, \(dp[L]\) representa a resposta ótima para uma barra de tamanho \(L\). + +\subsection{Função de Transição} + +Para determinar \(dp[L]\) consideramos a primeira peça que retiramos da barra: se escolhemos cortar uma peça de tamanho \(x\) (com \(1 \le x \le L\)), obtemos imediatamente o preço \(p[x]\) e ficamos com o subproblema da barra restante de tamanho \(L-x\), cujo melhor valor é \(dp[L-x]\). Logo: + +\[ +dp[L] = \max_{1 \le x \le L} \big( p[x] + dp[L-x] \big). +\] + +Em particular, se não fizermos cortes (i.e., vendermos a barra inteira), isso corresponde ao caso \(x=L\) e é coberto pela fórmula acima. + +\subsection{Casos Base} + +O caso base é natural: + +\[ +dp[0] = 0, +\] + +isto é, uma barra de comprimento zero tem receita zero. + +\subsection{Recuperação da Decomposição (pedaços)} + +Para além do valor máximo \(dp[n]\), frequentemente queremos também uma decomposição concreta (lista de comprimentos dos pedaços) que atinja esse valor. Para isso mantemos, durante a computação de \(dp\), um vetor auxiliar \texttt{cut[L]} que armazena o tamanho \(x\) do primeiro pedaço que produz o ótimo para \(dp[L]\). Após preencher \(dp\) e \texttt{cut}, reconstruímos os pedaços repetindo a operação: tomar \(x=\texttt{cut}[L]\), imprimir \(x\), e reduzir \(L \leftarrow L - x\), até \(L=0\).