Discussion @ 1727. Znaika's Magic Numbers @ Timus Online Judge

Arseniy too easy for 175 [1] // Problem 1727. Znaika's Magic Numbers 1 Mar 2016 01:29

Bazeev Damir`~ plz help wa#3 python3.6 [1] // Problem 1727. Znaika's Magic Numbers 15 Jun 2018 01:04

Michail Yudin plz give me any hint [11] // Problem 1727. Znaika's Magic Numbers 17 Oct 2009 19:50

melkiy Re: plz give me any hint [9] // Problem 1727. Znaika's Magic Numbers 18 Oct 2009 00:15

I compose n from sums of digits of the numbers:
99999 (sum of digits = 45)
99998 (44)
99997
.....
99990 (36)
99989 (44)
.....

until i gain total sum of digits = n.
I take the numbers in such an order because the greatest sums (in average) are in that part of valid range.

I suppose you can start from little numbers but i didn't try.

Partisan Increasing order [5] // Problem 1727. Znaika's Magic Numbers 19 Oct 2009 22:13

Increasing order causes WA#6.

svr Re: Increasing order // Problem 1727. Znaika's Magic Numbers 20 Oct 2009 02:08

More funny solution without WA:
use n for n and so on(recursively)

luckysundog Re: Increasing order [3] // Problem 1727. Znaika's Magic Numbers 27 Oct 2011 05:43

> Increasing order causes WA#6.

But why?!
However, decreasing order is more greedy, but still don't know why it works.

p.s. also got 0.046s AC with 100% solution using map<int,list<int>,greater<int> > container and its lower_bound method.

Edited by author 27.10.2011 05:53

panther.uz Re: Increasing order [1] // Problem 1727. Znaika's Magic Numbers 21 Sep 2012 02:56

thank you for idea that increasing order idea

Andrew Sboev [USU] Re: Increasing order // Problem 1727. Znaika's Magic Numbers 21 Sep 2012 20:16

This problem has simple brutforce solution. Just sum all numbers from 1 , while sum <= n

Pegasus Re: Increasing order // Problem 1727. Znaika's Magic Numbers 7 Nov 2012 19:48

Me too.I use c++ because of it's STL, use multimap can slove it

Edited by author 11.11.2012 18:00

burdakovd Re: plz give me any hint // Problem 1727. Znaika's Magic Numbers 4 Apr 2010 17:00

It is even enough to start from n, not from 99999.

I guess in that case the solution will be more generic, it'll work for any positive n.

Edited by author 04.04.2010 17:06

Roman Rubanenko Re: plz give me any hint [1] // Problem 1727. Znaika's Magic Numbers 4 Apr 2010 23:46

here is my way to solve this problem:
1. count sum of digits for every number from 1 to 99999
2. sort then
3. find some unmarked close number and add it to the answer(with binary search)
4. n=n-a[number] =)
that's all
btw there is no "-1" answer

MarioYC Re: plz give me any hint // Problem 1727. Znaika's Magic Numbers 24 Sep 2011 12:18

Just take n and decrease it by it sum of digits, keep doing this until n = 0

Filip Franik Re: plz give me any hint // Problem 1727. Znaika's Magic Numbers 12 Jul 2016 19:54

First observation we need to make is to see that the highest sum of digits within 10^5 has the number "99999" and it's value is 45. This means that if the input number of digits is more or equal than 45 we can use any number and it will always fit.

We want to make everything quickly so it's best to start from numbers with a lot of nines in them.

99999 (sum = 45)
99998 (sum = 44)
...
96742 (sum = 28)
96741 (sum = 27)

We subtract the sum one by one until we are left with a number of digits that's lower than 45.

Second observation is to see that 9+8+7+6+5+4+3+2+1=45 and that there always is a combination of 9,8,7,6,5,4,3,2,1 that You can sum up to any number lower or equal to 45.

That way we end up with something like this:
Input: 55
3
99999 9 1

Edited by author 12.07.2016 19:56

Andrew Shirshov [YSPU] Wa #3 [5] // Problem 1727. Znaika's Magic Numbers 17 Oct 2009 19:28

Pegasus I want some test [1] // Problem 1727. Znaika's Magic Numbers 8 Nov 2012 21:00

Илья Зиновьев WA 5 [1] // Problem 1727. Znaika's Magic Numbers 16 Nov 2009 21:32

Hrayr AC 0.031s,196 kb! [1] // Problem 1727. Znaika's Magic Numbers 25 Jun 2011 17:48

Tigran92[RAU_902] Brute force with some optimization get AC in 0.375!!! [1] // Problem 1727. Znaika's Magic Numbers 1 Dec 2010 23:47

Qafqaz_Ferhad Cebiyev Is there more than one answer for same n? [10] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 13:23

For example:

Input
17

Output
2
9 80

Edited by author 29.06.2010 14:01

UNKNOWN_LAMER Re: Is there more than one answer for same n? [9] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 19:23

Yes. This answer is correct too. Any generating set with
different positive integers strictly less than 10^5 will be OK.

Qafqaz_Ferhad Cebiyev Is it also true?.....Look at it. [8] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 21:14

Input
17

Output
6
1 2 3 4 5 200

UNKNOWN_LAMER Re: Is it also true?.....Look at it. [7] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 21:15

Yes. This one is correct too.

Qafqaz_Ferhad Cebiyev But what is problem here. [6] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 21:19

#include <cstdlib>
#include <iostream>

using namespace std;

int a[10000];
int main(int argc, char *argv[])
{
    int n, s, c , sum=0, y, i, l=1,x=0,ferq;
    cin >> n;

      for( i=1;i<=800;i++)
   {sum=0;
   y=i;
       while(y!=0)
       {
            c= y%10;
            sum = sum +c;
         y/=10; }
   a[l]=i;
   l++;
        x=x+sum;

         if(x==n) {y=2;break;}
    else if(x>n) {l=l-1; x=x-sum;ferq = n-x;     y=1;break;}

    }
    if((ferq*100)>a[l-1]) cout << l<<endl;
    else cout << l-1<<endl;
    for(i=1;i<=l-2;i++) cout << a[i]<<" ";
    if(y==2)
    cout << a[l-1];
    else
    {
        if((ferq*100)>a[l-1])
     cout << a[l-1]<<" "<<ferq<<0<<0<<" ";
     else cout << a[l-1]<<ferq ;
    }
    system("PAUSE");
    return EXIT_SUCCESS;
}

Sfesw I have WA#3 [5] // Problem 1727. Znaika's Magic Numbers 29 Jun 2010 21:52

Vladimir Yakovlev (USU) Did you try maximal test? [4] // Problem 1727. Znaika's Magic Numbers 1 Jul 2010 21:20

Qafqaz_Ferhad Cebiyev Re: Did you try maximal test? [3] // Problem 1727. Znaika's Magic Numbers 5 Jul 2010 12:04

Yes I tried.

Qafqaz_Ferhad Cebiyev Re: Did you try maximal test? [2] // Problem 1727. Znaika's Magic Numbers 5 Jul 2010 12:07

9999
779
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
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
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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 8497

UNKNOWN_LAMER Re: Did you try maximal test? [1] // Problem 1727. Znaika's Magic Numbers 5 Jul 2010 13:42

But maximal test is 10^5-1, not 10^4-1.
:D

Qafqaz_Ferhad Cebiyev Thank you Unknown Lamer. // Problem 1727. Znaika's Magic Numbers 5 Jul 2010 13:44

It is unbeliavable. How I can't see it?.
I am really very sorry.

zsyzgu What's meaning? // Problem 1727. Znaika's Magic Numbers 5 Apr 2010 14:54

nikenny Why WA21?? [1] // Problem 1727. Znaika's Magic Numbers 2 Jan 2010 17:13

ahmedov(NUUz_2) Please, help.Where is my mistake? [2] // Problem 1727. Znaika's Magic Numbers 6 Nov 2009 02:18

FlashKa WA6 [1] // Problem 1727. Znaika's Magic Numbers 17 Oct 2009 17:49

data lapiashvili cifiri [1] // Problem 1727. Znaika's Magic Numbers 17 Oct 2009 15:17

Discussion of Problem 1727. Znaika's Magic Numbers