Problem E
Problem E
Minimal pour out of vessels
We can use a set of vessels to fill a tank with a precisely
stated amount of fluid. The problem is to use them in an
optimal way to avoid too much labour and inadequacy. For
simplicity we assume that we have a tank of capacity more than
10000 litres and a set of vessels with precise capacity in
litres. We can use vessels to fill the tank (using tap to fill
a vessel first), and we can also use vessels to empty it
(using sink to empty a vessel next). We should minimize the
number of the fill and pour away operations of the tank to
obtain the given amount of fluid inside.
Your program has to read the capacity of each vessel (we will
have no more than 1000 vessels) and the amount of fluid the
tank should be filled with.
The program should compute the minimal number of the fills and
pours away to obtain a given amount of fluid inside in an
efficient manner.
Suggestion
Algorithm of exponential-time complexity will probably not be
accepted, because it can exceed the execution time limit.
Input
* the input contains as many lines as problems to solve,
plus one line with a single 0 (zero) to denote the end;
* each problem line is a sequence of positive integers each
not greater than 5000, describing the amount of fluid the tank
should be filled with and the capacities of available vessels;
0 (zero) denotes the end of the line.
Output
a separate line for each, set of vessels containing the
minimal number of add and pour away operations or the string
"Impossible" in the case the solution does not exist.
EXAMPLE
Input
8 3 7 0
5 3 7 0
5000 2 4 12 11 34 0
17 2 4 8 0
0
Output
4
5
148
Impossible
Solution
Test
input
1 70 101 0
5000 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
172 173 174 175 176 177 178 179 180 181 182 183
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
209 210 211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230 231 232
233 234 235 236 237 238 239 240 241 242 243 244
245 246 247 248 249 250 251 252 253 254 255 256 257
258 259 260 261 262 263 264 265 266 267 268 269
270 271 272 273 274 275 276 277 278 279 280 281
282 283 284 285 286 287 288 289 290 291 292 293
294 295 296 297 298 299 300 301 302 303 304 305 306
307 308 309 310 311 312 313 314 315 316 317 318
319 320 321 322 323 324 325 326 327 328 329 330
331 332 333 334 335 336 337 338 339 340 341 342
343 344 345 346 347 348 349 350 351 352 353 354 355
356 357 358 359 360 361 362 363 364 365 366 367
368 369 370 371 372 373 374 375 376 377 378 379
380 381 382 383 384 385 386 387 388 389 390 391
392 393 394 395 396 397 398 399 400 401 402 403 404
405 406 407 408 409 410 411 412 413 414 415 416
417 418 419 420 421 422 423 424 425 426 427 428
429 430 431 432 433 434 435 436 437 438 439 440
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
477 478 479 480 481 482 483 484 485 486 487 488
489 490 491 492 493 494 495 496 497 498 499 500
501 502 503 504 505 506 507 508 509 510 511 512
513 514 515 516 517 518 519 520 521 522 523 524
525 526 527 528 529 530 531 532 533 534 535 536
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
657 658 659 660 661 662 663 664 665 666 667 668
669 670 671 672 673 674 675 676 677 678 679 680
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
921 922 923 924 925 926 927 928 929 930 931 932
933 934 935 936 937 938 939 940 941 942 943 944
945 946 947 948 949 950 951 952 953 954 955 956
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 0
1111 200 250 300 0
0
output
35
5
Impossible
Listing
© zwir, wierzej,
Mon Oct 28 23:01:26 MET DST 1996