* Solution to Project Euler problem 99

* By Nayuki Minase

*

* http://nayuki.eigenstate.org/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*/

 

  public static void main(String[] args) {

    System.out.println(new p099().run());

  }

 

 

  public String run() {

    int[] maxVal = DATA[0];

    int maxIndex = 0;

    outer:

    for (int i = 1; i < DATA.length; i++) {

      // Try limited-precision comparisons, retrying with increasing precision

      for (int precision = 16; precision <= 1024; precision *= 2) {

        // Use interval arithmetic for approximate comparisons

        BigFloat curLow  = new BigFloat(DATA[i][0]).power(DATA[i][1], precision, false);

        BigFloat curHigh = new BigFloat(DATA[i][0]).power(DATA[i][1], precision, true );

        BigFloat maxLow  = new BigFloat(maxVal[0] ).power(maxVal [1], precision, false);

        BigFloat maxHigh = new BigFloat(maxVal[0] ).power(maxVal [1], precision, true );

        if (curLow.compareTo(maxHigh) > 0) {

          maxVal = DATA[i];

          maxIndex = i;

          continue outer;

        } else if (curHigh.compareTo(maxLow) < 0)

          continue outer;

      }

     

      // Do full-precision comparison (very slow)

      BigInteger cur = BigInteger.valueOf(DATA[i][0]).pow(DATA[i][1]);

      BigInteger max = BigInteger.valueOf(maxVal [0]).pow(maxVal [1]);

      if (cur.compareTo(max) > 0) {

        maxVal = DATA[i];

        maxIndex = i;

      }

    }

    return Integer.toString(maxIndex + 1);

  }

 

 

  // Represents a strictly positive number equal to mantissa * 2^exponent

   

    private final BigInteger mantissa;

    private final int exponent;

   

   

    public BigFloat(int n) {

      if (n <= 0)

        throw new IllegalArgumentException();

      mantissa = BigInteger.valueOf(n);

      exponent = 0;

    }

   

   

    private BigFloat(BigInteger man, int exp) {

      mantissa = man;

      exponent = exp;

    }

   

   

    public int compareTo(BigFloat other) {

      int minExp = Math.min(exponent, other.exponent);

      BigInteger tempx = mantissa.shiftLeft(exponent - minExp);

      BigInteger tempy = other.mantissa.shiftLeft(other.exponent - minExp);

      return tempx.compareTo(tempy);

    }

   

   

    public String toString() {

      return mantissa + "<<" + exponent;

    }

   

   

    // The output's mantissa will have 'precision' or fewer bits

    public BigFloat multiply(BigFloat other, int precision, boolean roundUp) {

      BigInteger man = mantissa.multiply(other.mantissa);

      int exp = exponent + other.exponent;

      int excess = man.bitLength() - precision;

      if (excess > 0) {

        if (roundUp) {

          BigInteger mask = BigInteger.ONE.shiftLeft(excess).subtract(BigInteger.ONE);

          if (!mask.and(man).equals(BigInteger.ZERO))

            man = man.add(BigInteger.ONE.shiftLeft(excess));

          excess = man.bitLength() - precision;  // In case 'man' is bumped up to the next power of 2

        }

        man = man.shiftRight(excess);

        exp += excess;

      }

      return new BigFloat(man, exp);

    }

   

   

    // Exponentiation by squaring

    public BigFloat power(int y, int precision, boolean roundUp) {

      if (y < 0 || precision <= 0)

        throw new IllegalArgumentException();

     

      BigFloat x = this;

      BigFloat z = new BigFloat(1);

      for (; y != 0; y >>>= 1) {

        if ((y & 1) != 0)

          z = z.multiply(x, precision, roundUp);

        x = x.multiply(x, precision, roundUp);

      }

      return z;

    }

   

  }

 

 

  private static int[][] DATA = {

    {519432,525806},

    {632382,518061},

    {78864,613712},

    {466580,530130},

    {780495,510032},

    {525895,525320},

    {15991,714883},

    {960290,502358},

    {760018,511029},

    {166800,575487},

    {210884,564478},

    {555151,523163},

    {681146,515199},

    {563395,522587},

    {738250,512126},

    {923525,503780},

    {595148,520429},

    {177108,572629},

    {750923,511482},

    {440902,532446},

    {881418,505504},

    {422489,534197},

    {979858,501616},

    {685893,514935},

    {747477,511661},

    {167214,575367},

    {234140,559696},

    {940238,503122},

    {728969,512609},

    {232083,560102},

    {900971,504694},

    {688801,514772},

    {189664,569402},

    {891022,505104},

    {445689,531996},

    {119570,591871},

    {821453,508118},

    {371084,539600},

    {911745,504251},

    {623655,518600},

    {144361,582486},

    {352442,541775},

    {420726,534367},

    {295298,549387},

    {6530,787777},

    {468397,529976},

    {672336,515696},

    {431861,533289},

    {84228,610150},

    {805376,508857},

    {444409,532117},

    {33833,663511},

    {381850,538396},

    {402931,536157},

    {92901,604930},

    {304825,548004},

    {731917,512452},

    {753734,511344},

    {51894,637373},

    {151578,580103},

    {295075,549421},

    {303590,548183},

    {333594,544123},

    {683952,515042},

    {60090,628880},

    {951420,502692},

    {28335,674991},

    {714940,513349},

    {343858,542826},

    {549279,523586},

    {804571,508887},

    {260653,554881},

    {291399,549966},

    {402342,536213},

    {408889,535550},

    {40328,652524},

    {375856,539061},

    {768907,510590},

    {165993,575715},

    {976327,501755},

    {898500,504795},

    {360404,540830},

    {478714,529095},

    {694144,514472},

    {488726,528258},

    {841380,507226},

    {328012,544839},

    {22389,690868},

    {604053,519852},

    {329514,544641},

    {772965,510390},

    {492798,527927},

    {30125,670983},

    {895603,504906},

    {450785,531539},

    {840237,507276},

    {380711,538522},

    {63577,625673},

    {76801,615157},

    {502694,527123},

    {597706,520257},

    {310484,547206},

    {944468,502959},

    {121283,591152},

    {451131,531507},

    {566499,522367},

    {425373,533918},

    {40240,652665},

    {39130,654392},

    {714926,513355},

    {469219,529903},

    {806929,508783},

    {287970,550487},

    {92189,605332},

    {103841,599094},

    {671839,515725},

    {452048,531421},

    {987837,501323},

    {935192,503321},

    {88585,607450},

    {613883,519216},

    {144551,582413},

    {647359,517155},

    {213902,563816},

    {184120,570789},

    {258126,555322},

    {502546,527130},

    {407655,535678},

    {401528,536306},

    {477490,529193},

    {841085,507237},

    {732831,512408},

    {833000,507595},

    {904694,504542},

    {581435,521348},

    {455545,531110},

    {873558,505829},

    {94916,603796},

    {720176,513068},

    {545034,523891},

    {246348,557409},

    {556452,523079},

    {832015,507634},

    {173663,573564},

    {502634,527125},

    {250732,556611},

    {569786,522139},

    {216919,563178},

    {521815,525623},

    {92304,605270},

    {164446,576167},

    {753413,511364},

    {11410,740712},

    {448845,531712},

    {925072,503725},

    {564888,522477},

    {7062,780812},

    {641155,517535},

    {738878,512100},

    {636204,517828},

    {372540,539436},

    {443162,532237},

    {571192,522042},

    {655350,516680},

    {299741,548735},

    {581914,521307},

    {965471,502156},

    {513441,526277},

    {808682,508700},

    {237589,559034},

    {543300,524025},

    {804712,508889},

    {247511,557192},

    {543486,524008},

    {504383,526992},

    {326529,545039},

    {792493,509458},

    {86033,609017},

    {126554,589005},

    {579379,521481},

    {948026,502823},

    {404777,535969},

    {265767,554022},

    {266876,553840},

    {46631,643714},

    {492397,527958},

    {856106,506581},

    {795757,509305},

    {748946,511584},

    {294694,549480},

    {409781,535463},

    {775887,510253},

    {543747,523991},

    {210592,564536},

    {517119,525990},

    {520253,525751},

    {247926,557124},

    {592141,520626},

    {346580,542492},

    {544969,523902},

    {506501,526817},

    {244520,557738},

    {144745,582349},

    {69274,620858},

    {292620,549784},

    {926027,503687},

    {736320,512225},

    {515528,526113},

    {407549,535688},

    {848089,506927},

    {24141,685711},

    {9224,757964},

    {980684,501586},

    {175259,573121},

    {489160,528216},

    {878970,505604},

    {969546,502002},

    {525207,525365},

    {690461,514675},

    {156510,578551},

    {659778,516426},

    {468739,529945},

    {765252,510770},

    {76703,615230},

    {165151,575959},

    {29779,671736},

    {928865,503569},

    {577538,521605},

    {927555,503618},

    {185377,570477},

    {974756,501809},

    {800130,509093},

    {217016,563153},

    {365709,540216},

    {774508,510320},

    {588716,520851},

    {631673,518104},

    {954076,502590},

    {777828,510161},

    {990659,501222},

    {597799,520254},

    {786905,509727},

    {512547,526348},

    {756449,511212},

    {869787,505988},

    {653747,516779},

    {84623,609900},

    {839698,507295},

    {30159,670909},

    {797275,509234},

    {678136,515373},

    {897144,504851},

    {989554,501263},

    {413292,535106},

    {55297,633667},

    {788650,509637},

    {486748,528417},

    {150724,580377},

    {56434,632490},

    {77207,614869},

    {588631,520859},

    {611619,519367},

    {100006,601055},

    {528924,525093},

    {190225,569257},

    {851155,506789},

    {682593,515114},

    {613043,519275},

    {514673,526183},

    {877634,505655},

    {878905,505602},

    {1926,914951},

    {613245,519259},

    {152481,579816},

    {841774,507203},

    {71060,619442},

    {865335,506175},

    {90244,606469},

    {302156,548388},

    {399059,536557},

    {478465,529113},

    {558601,522925},

    {69132,620966},

    {267663,553700},

    {988276,501310},

    {378354,538787},

    {529909,525014},

    {161733,576968},

    {758541,511109},

    {823425,508024},

    {149821,580667},

    {269258,553438},

    {481152,528891},

    {120871,591322},

    {972322,501901},

    {981350,501567},

    {676129,515483},

    {950860,502717},

    {119000,592114},

    {392252,537272},

    {191618,568919},

    {946699,502874},

    {289555,550247},

    {799322,509139},

    {703886,513942},

    {194812,568143},

    {261823,554685},

    {203052,566221},

    {217330,563093},

    {734748,512313},

    {391759,537328},

    {807052,508777},

    {564467,522510},

    {59186,629748},

    {113447,594545},

    {518063,525916},

    {905944,504492},

    {613922,519213},

    {439093,532607},

    {445946,531981},

    {230530,560399},

    {297887,549007},

    {459029,530797},

    {403692,536075},

    {855118,506616},

    {963127,502245},

    {841711,507208},

    {407411,535699},

    {924729,503735},

    {914823,504132},

    {333725,544101},

    {176345,572832},

    {912507,504225},

    {411273,535308},

    {259774,555036},

    {632853,518038},

    {119723,591801},

    {163902,576321},

    {22691,689944},

    {402427,536212},

    {175769,572988},

    {837260,507402},

    {603432,519893},

    {313679,546767},

    {538165,524394},

    {549026,523608},

    {61083,627945},

    {898345,504798},

    {992556,501153},

    {369999,539727},

    {32847,665404},

    {891292,505088},

    {152715,579732},

    {824104,507997},

    {234057,559711},

    {730507,512532},

    {960529,502340},

    {388395,537687},

    {958170,502437},

    {57105,631806},

    {186025,570311},

    {993043,501133},

    {576770,521664},

    {215319,563513},

    {927342,503628},

    {521353,525666},

    {39563,653705},

    {752516,511408},

    {110755,595770},

    {309749,547305},

    {374379,539224},

    {919184,503952},

    {990652,501226},

    {647780,517135},

    {187177,570017},

    {168938,574877},

    {649558,517023},

    {278126,552016},

    {162039,576868},

    {658512,516499},

    {498115,527486},

    {896583,504868},

    {561170,522740},

    {747772,511647},

    {775093,510294},

    {652081,516882},

    {724905,512824},

    {499707,527365},

    {47388,642755},

    {646668,517204},

    {571700,522007},

    {180430,571747},

    {710015,513617},

    {435522,532941},

    {98137,602041},

    {759176,511070},

    {486124,528467},

    {526942,525236},

    {878921,505604},

    {408313,535602},

    {926980,503640},

    {882353,505459},

    {566887,522345},

    {3326,853312},

    {911981,504248},

    {416309,534800},

    {392991,537199},

    {622829,518651},

    {148647,581055},

    {496483,527624},

    {666314,516044},

    {48562,641293},

    {672618,515684},

    {443676,532187},

    {274065,552661},

    {265386,554079},

    {347668,542358},

    {31816,667448},

    {181575,571446},

    {961289,502320},

    {365689,540214},

    {987950,501317},

    {932299,503440},

    {27388,677243},

    {746701,511701},

    {492258,527969},

    {147823,581323},

    {57918,630985},

    {838849,507333},

    {678038,515375},

    {27852,676130},

    {850241,506828},

    {818403,508253},

    {131717,587014},

    {850216,506834},

    {904848,504529},

    {189758,569380},

    {392845,537217},

    {470876,529761},

    {925353,503711},

    {285431,550877},

    {454098,531234},

    {823910,508003},

    {318493,546112},

    {766067,510730},

    {261277,554775},

    {421530,534289},

    {694130,514478},

    {120439,591498},

    {213308,563949},

    {854063,506662},

    {365255,540263},

    {165437,575872},

    {662240,516281},

    {289970,550181},

    {847977,506933},

    {546083,523816},

    {413252,535113},

    {975829,501767},

    {361540,540701},

    {235522,559435},

    {224643,561577},

    {736350,512229},

    {328303,544808},

    {35022,661330},

    {307838,547578},

    {474366,529458},

    {873755,505819},

    {73978,617220},

    {827387,507845},

    {670830,515791},

    {326511,545034},

    {309909,547285},

    {400970,536363},

    {884827,505352},

    {718307,513175},

    {28462,674699},

    {599384,520150},

    {253565,556111},

    {284009,551093},

    {343403,542876},

    {446557,531921},

    {992372,501160},

    {961601,502308},

    {696629,514342},

    {919537,503945},

    {894709,504944},

    {892201,505051},

    {358160,541097},

    {448503,531745},

    {832156,507636},

    {920045,503924},

    {926137,503675},

    {416754,534757},

    {254422,555966},

    {92498,605151},

    {826833,507873},

    {660716,516371},

    {689335,514746},

    {160045,577467},

    {814642,508425},

    {969939,501993},

    {242856,558047},

    {76302,615517},

    {472083,529653},

    {587101,520964},

    {99066,601543},

    {498005,527503},

    {709800,513624},

    {708000,513716},

    {20171,698134},

    {285020,550936},

    {266564,553891},

    {981563,501557},

    {846502,506991},

    {334,1190800},

    {209268,564829},

    {9844,752610},

    {996519,501007},

    {410059,535426},

    {432931,533188},

    {848012,506929},

    {966803,502110},

    {983434,501486},

    {160700,577267},

    {504374,526989},

    {832061,507640},

    {392825,537214},

    {443842,532165},

    {440352,532492},

    {745125,511776},

    {13718,726392},

    {661753,516312},

    {70500,619875},

    {436952,532814},

    {424724,533973},

    {21954,692224},

    {262490,554567},

    {716622,513264},

    {907584,504425},

    {60086,628882},

    {837123,507412},

    {971345,501940},

    {947162,502855},

    {139920,584021},

    {68330,621624},

    {666452,516038},

    {731446,512481},

    {953350,502619},

    {183157,571042},

    {845400,507045},

    {651548,516910},

    {20399,697344},

    {861779,506331},

    {629771,518229},

    {801706,509026},

    {189207,569512},

    {737501,512168},

    {719272,513115},

    {479285,529045},

    {136046,585401},

    {896746,504860},

    {891735,505067},

    {684771,514999},

    {865309,506184},

    {379066,538702},

    {503117,527090},

    {621780,518717},

    {209518,564775},

    {677135,515423},

    {987500,501340},

    {197049,567613},

    {329315,544673},

    {236756,559196},

    {357092,541226},

    {520440,525733},

    {213471,563911},

    {956852,502490},

    {702223,514032},

    {404943,535955},

    {178880,572152},

    {689477,514734},

    {691351,514630},

    {866669,506128},

    {370561,539656},

    {739805,512051},

    {71060,619441},

    {624861,518534},

    {261660,554714},

    {366137,540160},

    {166054,575698},

    {601878,519990},

    {153445,579501},

    {279899,551729},

    {379166,538691},

    {423209,534125},

    {675310,515526},

    {145641,582050},

    {691353,514627},

    {917468,504026},

    {284778,550976},

    {81040,612235},

    {161699,576978},

    {616394,519057},

    {767490,510661},

    {156896,578431},

    {427408,533714},

    {254849,555884},

    {737217,512182},

    {897133,504851},

    {203815,566051},

    {270822,553189},

    {135854,585475},

    {778805,510111},

    {784373,509847},

    {305426,547921},

    {733418,512375},

    {732087,512448},

    {540668,524215},

    {702898,513996},

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