Prime Judge

题目描述

众所周知，如果一个正整数只能被1和自身整除，那么该数被称为素数。题目的任务很简单，就是判定一个数是否是一个素数。 只不过可能数的形式与正整数有一些不同，数的形式为a+bi，其中a、b为整数，且ii被定义为-1。如果a+bi能被分解为(a1+b1i)(a2+b2i)的形式，那么该数不是素数；否则，该数是素数。其中a1 、b1、 a2 、b2均为整数，且1，-1，0，i，-i不能作为被分解的因子。 注意，1，-1，0，i，-i均不为素数。

输入格式

输入包括若干组数据，每行包含2个数a、b，表示一个形如a+bi的数。a，b小于10000。

输出格式

对应于输入每行，如果输入的数为素数，则输出“YES”，否则输出“NO”。（不包括引号）

输入样例

-10 2
3 0

输出样例

NO
YES

根据复数的性质可知：a^2+b^2=(a1^2+b1^2)(a2^2+b2^2)。

算算复杂度，由于a,b<10000，令z1=a1^2+b1^2,z2=a2^2+b2^2，枚举z1 ，范围为sqrt（10000^2*2) （大概14320左右）得到z2,再枚举a2^2得到b2^2，在判断b2^2是不是平方数，如果是，则输出NO，否则输出YES。

我事先打了平方和表（14320之内）

代码如下：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#define N 10000
using namespace std;
long long  a,b,a1,a2,b1,b2;
long long  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00,7402,7405,7412,7417,7418,7421,7424,7432,7433,7442,7444,7445,7450,7453,7456,7457,7460,7461,7465,7466,7474,7477,7481,7488,7489,7492,7496,7497,7501,7508,7514,7517,7522,7528,7529,7537,7538,7540,7541,7549,7556,7561,7565,7569,7570,7573,7577,7578,7585,7586,7589,7592,7594,7604,7605,7610,7618,7621,7624,7625,7632,7633,7642,7649,7650,7652,7666,7669,7673,7677,7681,7684,7685,7688,7690,7693,7696,7706,7709,7712,7713,7717,7720,7730,7732,7738,7741,7744,7745,7748,7753,7754,7757,7760,7762,7765,7769,7778,7780,7785,7786,7789,7793,7794,7796,7801,7808,7813,7816,7817,7825,7829,7834,7837,7840,7841,7844,7848,7850,7853,7857,7858,7865,7873,7877,7880,7888,7892,7893,7897,7901,7913,7921,7922,7925,7929,7930,7933,7937,7938,7940,7946,7949,7954,7956,7957,7969,7970,7972,7976,7978,7985,7988,7993,8000,8002,8005,8009,8010,8017,8020,8021,8026,8033,8036,8042,8045,8053,8065,8066,8068,8069,8072,8077,8080,8081,8082,8089,8090,8093,8098,8100,8101,8104,8105,8109,8114,8116,8117,8125,8136,8138,8144,8145,8146,8149,8161,8164,8168,8177,8180,8181,8185,8186,8192,8194,8200,8209,8210,8212,8221,8224,8226,8228,8233,8237,8242,8244,8245,8249,8258,8264,8266,8269,8273,8276,8281,8282,8285,8290,8293,8296,8297,8298,8306,8314,8317,8320,8321,8324,8325,8329,8330,8333,8336,8345,8352,8353,8354,8356,8357,8361,8362,8369,8377,8381,8388,8389,8392,8402,8405,8410,8420,8424,8425,8429,8433,8434,8450,8452,8458,8461,8464,8465,8468,8469,8473,8477,8480,8482,8485,8488,8489,8497,8500,8501,8506,8513,8516,8521,8522,8528,8530,8537,8541,8545,8546,8548,8552,8564,8570,8573,8577,8578,8581,8584,8585,8586,8593,8594,8597,8605,8608,8609,8612,8621,8629,8633,8641,8642,8644,8649,8650,8653,8656,8658,8660,8665,8669,8674,8676,8677,8681,8685,8689,8692,8693,8698,8704,8705,8712,8713,8714,8720,8722,8725,8730,8737,8738,8741,8744,8746,8749,8753,8761,8762,8765,8768,8770,8776,8784,8788,8793,8794,8801,8810,8818,8820,8821,8825,8829,8833,8836,8837,8840,8842,8845,8849,8852,8857,8861,8864,8865,8869,8872,8874,8882,8884,8885,8893,8900,8905,8906,8912,8914,8917,8929,8933,8936,8938,8941,8945,8948,8954,8957,8962,8969,8973,8978,8980,8986,8989,8992,8993,8996,9000,9001,9005,9010,9013,9025,9026,9028,9029,9032,9034,9040,9041,9049,9050,9061,9065,9074,9076,9077,9081,9089,9090,9092,9098,9104,9106,9109,9113,9117,9122,9124,9125,9133,9137,9140,9146,9153,9157,9160,9161,9162,9169,9172,9173,9178,9181,9188,9189,9193,9194,9197,9209,9216,9217,9220,9221,9224,9225,9232,9236,9241,9242,9245,9248,9250,9252,9256,9257,9265,9266,9274,9277,9280,9281,9290,9293,9297,9298,9305,9314,9316,9320,9325,9332,9333,9337,9341,9344,9346,9349,9360,9364,9365,9370,9376,9377,9378,9385,9386,9389,9396,9397,9409,9410,9412,9413,9418,9421,9425,9428,9433,9434,9437,9441,9442,9445,9448,9457,9458,9461,9466,9469,9472,9473,9477,9488,9490,9497,9505,9506,9508,9509,9512,9521,9522,9524,9529,9530,9533,9536,9540,9544,9549,9553,9554,9556,9565,9572,9577,9578,9586,9593,9594,9601,9602,9604,9605,9608,9610,9613,9616,9620,9621,9626,9629,9634,9640,9649,9650,9653,9657,9661,9665,9668,9673,9677,9680,9684,9685,9689,9697,9698,9700,9701,9704,9721,9722,9725,9733,9736,9738,9745,9748,9749,9754,9760,9764,9769,9770,9773,9778,9781,9792,9797,9800,9801,9802,9805,9808,9809,9810,9817,9818,9826,9829,9832,9833,9837,9841,9850,9857,9860,9864,9865,9866,9872,9873,9874,9881,9882,9892,9893,9896,9898,9901,9908,9914,9922,9925,9928,9929,9938,9941,9945,9946,9949,9953,9962,9965,9970,9972,9973,9981,9985,9986,9992,9997,10000,10001,10004,10009,10016,10018,10025,10026,10034,10036,10037,10042,10045,10048,10049,10053,10057,10061,10064,10069,10081,10082,10084,10085,10088,10090,10093,10100,10114,10116,10121,10125,10130,10132,10133,10138,10141,10144,10145,10154,10161,10162,10169,10170,10177,10180,10181,10192,10193,10196,10201,10202,10205,10210,10216,10217,10225,10226,10228,10229,10237,10240,10242,10244,10249,10250,10253,10256,10265,10273,10280,10282,10285,10289,10301,10305,10306,10309,10312,10313,10321,10322,10324,10330,10333,10337,10345,10357,10361,10368,10369,10370,10372,10376,10377,10378,10386,10388,10394,10397,10400,10404,10405,10408,10413,10418,10420,10421,10426,10429,10433,10436,10440,10441,10445,10448,10453,10457,10466,10468,10469,10474,10477,10484,10485,10489,10490,10496,10498,10501,10504,10512,10513,10517,10522,10525,10529,10530,10532,10537,10546,10548,10553,10562,10565,10568,10573,10576,10580,10585,10589,10594,10597,10600,10601,10609,10610,10613,10618,10625,10628,10629,10634,10642,10645,10656,10657,10658,10660,10666,10673,10674,10676,10682,10685,10690,10693,10701,10705,10706,10708,10709,10728,10729,10730,10733,10737,10753,10756,10760,10762,10765,10768,10769,10772,10777,10778,10781,10784,10786,10789,10804,10805,10809,10816,10817,10818,10820,10825,10826,10829,10832,10834,10837,10841,10845,10852,10853,10858,10861,10865,10874,10877,10880,10882,10888,10889,10890,10897,10898,10900,10909,10916,10917,10930,10933,10937,10946,10949,10952,10953,10954,10957,10960,10961,10964,10970,10973,10980,10984,10985,10993,10996,11002,11009,11012,11016,11024,11025,11026,11029,11034,11041,11042,11045,11048,11050,11057,11061,11065,11069,11072,11074,11080,11089,11090,11093,11097,11101,11105,11106,11108,11113,11114,11117,11125,11133,11138,11140,11141,11146,11149,11152,11156,11161,11162,11168,11169,11170,11173,11177,11185,11188,11194,11197,11204,11213,11216,11221,11225,11234,11236,11237,11240,11241,11245,11250,11252,11257,11258,11261,11268,11272,11273,11281,11282,11285,11290,11296,11300,11304,11306,11314,11317,11321,11322,11329,11332,11336,11338,11344,11345,11348,11349,11353,11357,11365,11368,11369,11378,11380,11386,11392,11393,11401,11402,11405,11412,11413,11417,11425,11426,11428,11432,11434,11437,11441,11444,11449,11450,11453,11458,11461,11464,11465,11466,11474,11482,11485,11489,11492,11493,11497,11498,11509,11513,11520,11521,11525,11530,11538,11540,11545,11549,11552,11554,11560,11565,11570,11581,11584,11588,11593,11597,11600,11601,11602,11617,11618,11621,11624,11626,11629,11633,11636,11642,11645,11650,11657,11664,11665,11668,11673,11674,11677,11680,11681,11689,11698,11700,11701,11705,11709,11713,11714,11716,11717,11720,11722,11728,11729,11737,11738,11745,11752,11754,11762,11764,11765,11773,11777,11785,11789,11794,11801,11808,11809,11810,11812,11813,11817,11821,11826,11828,11833,11834,11840,11848,11849,11858,11860,11861,11866,11876,11881,11882,11885,11889,11890,11897,11898,11905,11906,11908,11909,11912,11917,11920,11925,11930,11933,11936,11941,11944,11945,11953,11956,11962,11965,11969,11972,11978,11981,11986,11988,12002,12004,12005,12010,12013,12017,12020,12025,12037,12041,12049,12050,12053,12058,12064,12069,12073,12074,12077,12085,12097,12100,12101,12104,12105,12106,12109,12112,12113,12114,12116,12125,12130,12132,12136,12137,12146,12148,12149,12157,12161,12164,12168,12170,12176,12178,12181,12185,12186,12193,12196,12197,12200,12202,12205,12209,12218,12221,12226,12233,12240,12241,12242,12244,12249,12250,12253,12260,12266,12269,12274,12277,12281,12289,12290,12296,12301,12304,12308,12317,12321,12322,12325,12329,12330,12337,12340,12346,12349,12352,12356,12357,12365,12368,12370,12373,12377,12385,12389,12392,12393,12394,12401,12402,12409,12410,12413,12416,12421,12424,12429,12433,12434,12436,12437,12442,12448,12456,12457,12458,12461,12465,12469,12473,12482,12484,12490,12493,12497,12500,12505,12506,12514,12517,12520,12532,12538,12541,12544,12545,12546,12548,12553,12554,12557,12560,12564,12569,12577,12580,12584,12589,12593,12601,12602,12605,12608,12610,12613,12618,12625,12629,12634,12637,12641,12644,12645,12653,12658,12665,12674,12676,12680,12681,12682,12688,12689,12697,12701,12704,12706,12708,12713,12717,12721,12722,12724,12725,12740,12745,12746,12752,12753,12757,12762,12769,12770,12773,12776,12778,12781,12785,12789,12794,12800,12802,12805,12808,12809,12816,12818,12820,12821,12826,12829,12832,12833,12836,12841,12842,12850,12853,12861,12868,12869,12872,12874,12884,12889,12890,12893,12897,12898,12904,12905,12913,12916,12917,12928,12932,12937,12938,12941,12944,12946,12953,12960,12961,12962,12965,12968,12970,12973,12985,12994,12996,12997,13000,13001,13005,13009,13010,13012,13021,13025,13028,13032,13033,13037,13042,13045,13049,13050,13058,13060,13061,13073,13077,13085,13088,13093,13096,13105,13106,13108,13109,13117,13120,13121,13122,13124,13130,13136,13138,13140,13141,13154,13162,13165,13169,13172,13177,13181,13185,13189,13192,13194,13204,13210,13213,13217,13220,13221,13225,13226,13229,13234,13241,13249,13250,13252,13253,13256,13261,13264,13273,13274,13282,13284,13285,13289,13297,13298,13306,13309,13312,13313,13316,13320,13322,13325,13328,13329,13337,13345,13346,13352,13357,13364,13369,13378,13381,13385,13394,13396,13397,13401,13402,13410,13417,13418,13421,13426,13428,13429,13437,13441,13444,13445,13448,13450,13456,13457,13460,13465,13466,13469,13472,13474,13477,13480,13481,13492,13498,13505,13513,13514,13520,13522,13525,13537,13540,13544,13546,13549,13553,13556,13562,13565,13568,13572,13573,13576,13577,13586,13597,13600,13610,13613,13617,13621,13625,13626,13633,13634,13637,13645,13648,13649,13652,13653,13658,13666,13669,13672,13673,13681,13682,13689,13690,13693,13697,13698,13700,13705,13709,13712,13714,13721,13725,13729,13730,13732,13736,13738,13745,13753,13754,13757,13765,13768,13769,13770,13778,13780,13781,13786,13789,13793,13796,13801,13810,13817,13828,13829,13833,13834,13837,13840,13841,13842,13844,13850,13856,13858,13864,13873,13876,13877,13885,13896,13897,13898,13901,13906,13913,13914,13921,13922,13924,13925,13928,13933,13940,13941,13945,13949,13952,13954,13957,13960,13968,13969,13973,13977,13978,13985,13988,13994,13997,14002,14004,14005,14009,14013,14020,14024,14026,14029,14032,14033,14036,14045,14050,14057,14065,14066,14068,14081,14085,14089,14090,14093,14096,14112,14114,14116,14120,14125,14130,14132,14138};
long long  size_squ=4000;
bool judge=false;

int main()
{
    long long  sq;
    long long  size_z2=sqrt(N*N*2)/2;
    while(~scanf("%lld%lld",&a,&b))
    {
        if((a*a+b*b==0)||(a*a+b*b==1))
        {
            printf("NO\n");
            continue;
        }
        judge=false;
        sq=a*a+b*b;
        long long z2;
        for(long long  i=0;i<size_squ&&sq>=squ[i];i++)
        {
            b2=0;
            double temp=double(sq)/double(squ[i]);
            if(temp!=int (temp))
                continue;
            else
                z2=int(temp);
            for(long long  j=0;j<size_z2&&b2>=0&&z2!=1;j++)
            {
                b2=z2-j*j;
                int aa=sqrt(b2);
                if(b2==aa*aa)
                {
                    judge=true;
                    break;
                }
            }
            if(judge) break;
        }
        if(judge)
            printf("NO\n");
        else
            printf("YES\n");
    }
    return 0;
}

丁神的数论法也是好牛，本人数论太菜看不懂。。。