Digit_canceling_fractions_sol2.ipynb

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        "The fraction  is a curious fraction. An inexperienced mathematician while attempting to simplify it may incorrectly believe that  is obtained by cancelling the s.\n",
        "\n",
        "We shall consider fractions like, , to be trivial examples.\n",
        "\n",
        "Which means fractions where trailing 0's are cancelled are trivial. So we will ignore all the cases where we have to cancel 0's.\n",
        "\n",
        "You will be given 2 integers  and .  represents the number of digits in Numerator and Denominator, and  represents the exact number of digits to be \"cancelled\" from Numerator and Denominator. Find every non-trivial fraction, (1) where numerator is less than denominator, (2) and the value of the reduced fraction is equal to the original fraction.\n",
        "\n",
        "Sum all the Numerators and the Denominators of the original fractions, and print them separated by a space.\n",
        "\n",
        "Input Format\n",
        "\n",
        "Input contains two integers  \n",
        "\n",
        "Constraints\n",
        "\n",
        "\n",
        "\n",
        "Output Format\n",
        "\n",
        "Display 2 space separated integers that denote the sum of the Numerators and the sum of the Denominators respectively of original fractions.\n",
        "Note You do not have to reduce the Numerator and Denominator.\n",
        "\n",
        "https://www.hackerrank.com/contests/projecteuler/challenges/euler033/problem\n",
        "\n",
        "2,1 - 110 322 \n",
        "\n",
        "3,1 - 77262 163829 \n",
        "\n",
        "3,2 - 7429 17305 \n",
        "\n",
        "4,1 - 12999936 28131911 \n",
        "\n",
        "4,2 - 3571225 7153900 \n",
        "\n",
        "4,3 - 255983 467405\n",
        "\n",
        "\n",
        "**What I noticed are the question criteria:**\n",
        "\n",
        "- Never cancel a **\"0\"**, even if it is not on the left.\n",
        "- When the canceled number is left with a zero, after cancellation, the problem considers correct, for example:\n",
        " **15**10 /**1**0**5**7 - After canceling the \"15\" becomes 10/07 and is accepted. The same goes for (**18** 05/**1** 0 **8** 3 canceling 18 -> 5/3).\n",
        "- It is very important to understand that 1015 when canceling 51 can generate 01 or generate 10, we must consider both hypotheses and test to know which of the two can be accepted (3451/1015 -> 34 10/51).\n",
        "- We don't count the same fraction twice, for example 3265/1306 canceling 3 is 265/106 and canceling 6 is 325/130. Even so, the fraction 3265/1306 counts only once."
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            "[9880, 4940] 880 440 9\n",
            "[9880, 5928] 880 528 9\n",
            "[9880, 6916] 880 616 9\n",
            "[9880, 7904] 880 704 9\n",
            "[9882, 4941] 882 441 9\n",
            "[9884, 4942] 884 442 9\n",
            "[9885, 1977] 885 177 9\n",
            "[9885, 3954] 885 354 9\n",
            "[9885, 5931] 885 531 9\n",
            "[9885, 7908] 885 708 9\n",
            "[9886, 4943] 886 443 9\n",
            "[9888, 4944] 888 444 9\n",
            "[9890, 1978] 890 178 9\n",
            "[9890, 2967] 890 267 9\n",
            "[9890, 3956] 890 356 9\n",
            "[9890, 4945] 890 445 9\n",
            "[9890, 5934] 890 534 9\n",
            "[9890, 6923] 890 623 9\n",
            "[9890, 7912] 890 712 9\n",
            "[9890, 8901] 890 801 9\n",
            "[9891, 1099] 981 109 9\n",
            "[9891, 2198] 981 218 9\n",
            "[9891, 3297] 981 327 9\n",
            "[9891, 4396] 981 436 9\n",
            "[9891, 5495] 981 545 9\n",
            "[9891, 6594] 981 654 9\n",
            "[9891, 7693] 981 763 9\n",
            "[9891, 8792] 981 872 9\n",
            "[9892, 4946] 892 446 9\n",
            "[9894, 1649] 984 164 9\n",
            "[9894, 3298] 984 328 9\n",
            "[9894, 4947] 894 447 9\n",
            "[9894, 6596] 984 656 9\n",
            "[9895, 1979] 895 179 9\n",
            "[9895, 3958] 895 358 9\n",
            "[9895, 5937] 895 537 9\n",
            "[9895, 7916] 895 716 9\n",
            "[9896, 4948] 896 448 9\n",
            "[9897, 3299] 987 329 9\n",
            "[9897, 6598] 987 658 9\n",
            "[9898, 4949] 988 494 9\n",
            "[9900, 1980] 900 180 9\n",
            "[9900, 2970] 900 270 9\n",
            "[9900, 3960] 900 360 9\n",
            "[9900, 4950] 900 450 9\n",
            "[9900, 5940] 900 540 9\n",
            "[9900, 6930] 900 630 9\n",
            "[9900, 7920] 900 720 9\n",
            "[9900, 8910] 900 810 9\n",
            "[9902, 4951] 902 451 9\n",
            "[9904, 4952] 904 452 9\n",
            "[9905, 1981] 905 181 9\n",
            "[9905, 3962] 905 362 9\n",
            "[9905, 5943] 905 543 9\n",
            "[9905, 7924] 905 724 9\n",
            "[9906, 4953] 906 453 9\n",
            "[9908, 4954] 908 454 9\n",
            "[9910, 1982] 910 182 9\n",
            "[9910, 2973] 910 273 9\n",
            "[9910, 3964] 910 364 9\n",
            "[9910, 4955] 910 455 9\n",
            "[9910, 5946] 910 546 9\n",
            "[9910, 6937] 910 637 9\n",
            "[9910, 7928] 910 728 9\n",
            "[9910, 8919] 910 819 9\n",
            "[9912, 4956] 912 456 9\n",
            "[9914, 4957] 914 457 9\n",
            "[9915, 1983] 915 183 9\n",
            "[9915, 3966] 915 366 9\n",
            "[9915, 5949] 915 549 9\n",
            "[9915, 7932] 915 732 9\n",
            "[9916, 4958] 916 458 9\n",
            "[9918, 4959] 918 459 9\n",
            "[9920, 1984] 920 184 9\n",
            "[9920, 2976] 920 276 9\n",
            "[9920, 3968] 920 368 9\n",
            "[9920, 4960] 920 460 9\n",
            "[9920, 5952] 920 552 9\n",
            "[9920, 6944] 920 644 9\n",
            "[9920, 7936] 920 736 9\n",
            "[9920, 8928] 920 828 9\n",
            "[9922, 4961] 922 461 9\n",
            "[9924, 4962] 924 462 9\n",
            "[9925, 1191] 925 111 9\n",
            "[9925, 1985] 925 185 9\n",
            "[9925, 3970] 925 370 9\n",
            "[9925, 5955] 925 555 9\n",
            "[9925, 7940] 925 740 9\n",
            "[9926, 4963] 926 463 9\n",
            "[9928, 4964] 928 464 9\n",
            "[9930, 1986] 930 186 9\n",
            "[9930, 2979] 930 279 9\n",
            "[9930, 3972] 930 372 9\n",
            "[9930, 4965] 930 465 9\n",
            "[9930, 5958] 930 558 9\n",
            "[9930, 6951] 930 651 9\n",
            "[9930, 7944] 930 744 9\n",
            "[9930, 8937] 930 837 9\n",
            "[9932, 2483] 992 248 3\n",
            "[9932, 4966] 932 466 9\n",
            "[9934, 4967] 934 467 9\n",
            "[9935, 1987] 935 187 9\n",
            "[9935, 3974] 935 374 9\n",
            "[9935, 5961] 935 561 9\n",
            "[9935, 7948] 935 748 9\n",
            "[9936, 4968] 936 468 9\n",
            "[9938, 4969] 938 469 9\n",
            "[9940, 1491] 940 141 9\n",
            "[9940, 1988] 940 188 9\n",
            "[9940, 2982] 940 282 9\n",
            "[9940, 3976] 940 376 9\n",
            "[9940, 4970] 940 470 9\n",
            "[9940, 5964] 940 564 9\n",
            "[9940, 6958] 940 658 9\n",
            "[9940, 7952] 940 752 9\n",
            "[9940, 8946] 940 846 9\n",
            "[9942, 4971] 942 471 9\n",
            "[9944, 4972] 944 472 9\n",
            "[9945, 1989] 945 189 9\n",
            "[9945, 3978] 945 378 9\n",
            "[9945, 5967] 945 567 9\n",
            "[9945, 7956] 945 756 9\n",
            "[9946, 4973] 946 473 9\n",
            "[9948, 4974] 948 474 9\n",
            "[9950, 1194] 950 114 9\n",
            "[9950, 1393] 950 133 9\n",
            "[9950, 1592] 950 152 9\n",
            "[9950, 1791] 950 171 9\n",
            "[9950, 1990] 950 190 9\n",
            "[9950, 2985] 950 285 9\n",
            "[9950, 3980] 950 380 9\n",
            "[9950, 4975] 950 475 9\n",
            "[9950, 5970] 950 570 9\n",
            "[9950, 6965] 950 665 9\n",
            "[9950, 7960] 950 760 9\n",
            "[9950, 8955] 950 855 9\n",
            "[9952, 1555] 992 155 5\n",
            "[9952, 4354] 992 434 5\n",
            "[9952, 4976] 952 476 9\n",
            "[9952, 7153] 992 713 5\n",
            "[9954, 3555] 994 355 5\n",
            "[9954, 4977] 954 477 9\n",
            "[9955, 1991] 955 191 9\n",
            "[9955, 3982] 955 382 9\n",
            "[9955, 5973] 955 573 9\n",
            "[9955, 7964] 955 764 9\n",
            "[9956, 4978] 956 478 9\n",
            "[9958, 4979] 958 479 9\n",
            "[9960, 1494] 960 144 9\n",
            "[9960, 1992] 960 192 9\n",
            "[9960, 2490] 960 240 9\n",
            "[9960, 2988] 960 288 9\n",
            "[9960, 3984] 960 384 9\n",
            "[9960, 4980] 960 480 9\n",
            "[9960, 5976] 960 576 9\n",
            "[9960, 6972] 960 672 9\n",
            "[9960, 7968] 960 768 9\n",
            "[9960, 8964] 960 864 9\n",
            "[9962, 4981] 962 481 9\n",
            "[9964, 2491] 964 241 9\n",
            "[9964, 4982] 964 482 9\n",
            "[9965, 1993] 965 193 9\n",
            "[9965, 3986] 965 386 9\n",
            "[9965, 5979] 965 579 9\n",
            "[9965, 7972] 965 772 9\n",
            "[9966, 4983] 966 483 9\n",
            "[9968, 2492] 968 242 9\n",
            "[9968, 4984] 968 484 9\n",
            "[9970, 1994] 970 194 9\n",
            "[9970, 2991] 970 291 9\n",
            "[9970, 3988] 970 388 9\n",
            "[9970, 4985] 970 485 9\n",
            "[9970, 5982] 970 582 9\n",
            "[9970, 6979] 970 679 9\n",
            "[9970, 7976] 970 776 9\n",
            "[9970, 8973] 970 873 9\n",
            "[9972, 2493] 972 243 9\n",
            "[9972, 4986] 972 486 9\n",
            "[9974, 4987] 974 487 9\n",
            "[9975, 1197] 975 117 9\n",
            "[9975, 1596] 975 156 9\n",
            "[9975, 1995] 975 195 9\n",
            "[9975, 2394] 975 234 9\n",
            "[9975, 2793] 975 273 9\n",
            "[9975, 3192] 975 312 9\n",
            "[9975, 3591] 975 351 9\n",
            "[9975, 3990] 975 390 9\n",
            "[9975, 5985] 975 585 9\n",
            "[9975, 7980] 975 780 9\n",
            "[9976, 2494] 976 244 9\n",
            "[9976, 4988] 976 488 9\n",
            "[9978, 4989] 978 489 9\n",
            "[9980, 1497] 980 147 9\n",
            "[9980, 1996] 980 196 9\n",
            "[9980, 2495] 980 245 9\n",
            "[9980, 2994] 980 294 9\n",
            "[9980, 3493] 980 343 9\n",
            "[9980, 3992] 980 392 9\n",
            "[9980, 4491] 980 441 9\n",
            "[9980, 4990] 980 490 9\n",
            "[9980, 5988] 980 588 9\n",
            "[9980, 6986] 980 686 9\n",
            "[9980, 7984] 980 784 9\n",
            "[9980, 8982] 980 882 9\n",
            "[9982, 1288] 992 128 8\n",
            "[9982, 4186] 992 416 8\n",
            "[9982, 4991] 982 491 9\n",
            "[9982, 7084] 992 704 8\n",
            "[9984, 2496] 984 246 9\n",
            "[9984, 4992] 984 492 9\n",
            "[9985, 1997] 985 197 9\n",
            "[9985, 3994] 985 394 9\n",
            "[9985, 5991] 985 591 9\n",
            "[9985, 7988] 985 788 9\n",
            "[9986, 4993] 986 493 9\n",
            "[9988, 2497] 988 247 9\n",
            "[9988, 4994] 988 494 9\n",
            "[9988, 7491] 988 741 9\n",
            "[9990, 1998] 990 198 9\n",
            "[9990, 2997] 990 297 9\n",
            "[9990, 3996] 990 396 9\n",
            "[9990, 4995] 990 495 9\n",
            "[9990, 5994] 990 594 9\n",
            "[9990, 6993] 990 693 9\n",
            "[9990, 7992] 990 792 9\n",
            "[9990, 8991] 990 891 9\n",
            "[9992, 1249] 992 124 9\n",
            "[9992, 2498] 992 248 9\n",
            "[9992, 4996] 992 496 9\n",
            "[9992, 7494] 992 744 9\n",
            "[9994, 4997] 994 497 9\n",
            "[9995, 1999] 995 199 9\n",
            "[9995, 3998] 995 398 9\n",
            "[9995, 5997] 995 597 9\n",
            "[9995, 7996] 995 796 9\n",
            "[9996, 2499] 996 249 9\n",
            "[9996, 4998] 996 498 9\n",
            "[9996, 7497] 996 747 9\n",
            "[9998, 4999] 998 499 9\n",
            "12999936 28131911\n"
          ]
        }
      ],
      "source": [
        "from itertools import combinations\n",
        "\n",
        "def int_ab(a,b):\n",
        "    '''\n",
        "    Intersection of two lists including duplicates\n",
        "    '''\n",
        "    a = list(a)\n",
        "    b = list(b)\n",
        "    c = []\n",
        "    for x in a:\n",
        "        if x in b and x != '0':\n",
        "            b.remove(x)\n",
        "            c.append(x)\n",
        "    return c\n",
        "\n",
        "\n",
        "def remol(l1,l2):\n",
        "    '''\n",
        "    recebe duas strings e as subtrai elemento a elemento\n",
        "    # '1511','11' - > '#15'\\11 :15 or \\1'#5'\\1'#1:51\n",
        "    '''\n",
        "    l1t = list(l1)\n",
        "    l2t = l1t[::-1]\n",
        "    for k in l2:\n",
        "        if k in l1t:\n",
        "            l1t.remove(k)\n",
        "        if k in l2t:\n",
        "            l2t.remove(k)\n",
        "\n",
        "    l2t.reverse()\n",
        "    return set([\"\".join(l1t), \"\".join(l2t)])\n",
        "\n",
        "n = 4\n",
        "k = 1\n",
        "\n",
        "\n",
        "start = 10**(n-1)\n",
        "end = start*10\n",
        "\n",
        "lista = []\n",
        "\n",
        "for num in range(start + 1, end):\n",
        "    st_num = str(num)\n",
        "\n",
        "    st_den = [j for j in range(start,num) if len(int_ab(st_num,str(j))) >= k]\n",
        "\n",
        "    for i in st_den:\n",
        "        frac_found = False\n",
        "        com = int_ab(st_num,str(i))\n",
        "        if k > 1:\n",
        "            com = list(set([''.join(j) for j in combinations(com, k)]))\n",
        "\n",
        "        for j in com:\n",
        "            lj = j\n",
        "            set_newd = remol(str(i),j)\n",
        "            set_newn = remol(st_num,j)\n",
        "            if frac_found:\n",
        "                break\n",
        "\n",
        "            for newd in set_newd:\n",
        "                if frac_found:\n",
        "                    break                \n",
        "                for newn in set_newn:\n",
        "                    if (newn and (int(newd) * num == int(newn) * i)\n",
        "                        and int(newd) != 0):\n",
        "                        lista.append([num, i])\n",
        "                        print([num, i],newn,newd,j)\n",
        "                        frac_found = True\n",
        "                        break\n",
        "\n",
        "print(sum([k[1] for k in lista]),sum([k[0] for k in lista]))"
      ]
    }
  ]
}