bzoj3798: 特殊的质数

链接

　　http://www.lydsy.com/JudgeOnline/problem.php?id=3798

题解

　　容易发现判断一个数是否合法是O(N−−√)的，而且每个数都可以单独做，因此可以分块打表。
　　每N−−√个数求一下答案，询问直接O(N)做即可。
　　适当调整打表的间隔能让计算的次数减少。

代码

//分块打表#include <cstdio>#include <algorithm>#include <cmath>#define block 150000#define maxn 300000001#define lim 100000using namespace std;int biao[2017]={0,6907,12981,18819,24523,30077,35585,41010,46430,51724,57023,62283,67489,72705,77879,82972,88055,93155,98240,103321,108284,113328,118375,123362,128270,133275,138219,143207,148121,153006,157925,162787,167675,172566,177433,182248,187048,191887,196709,201503,206333,211116,215966,220684,225463,230264,235069,239856,244581,249301,253974,258746,263482,268180,272885,277603,282271,286985,291710,296422,301101,305757,310444,315110,319813,324445,329106,333704,338394,342976,347665,352294,356909,361557,366160,370808,375439,380078,384728,389366,393993,398583,403209,407827,412333,416969,421556,426079,430660,435206,439791,444343,448901,453464,457972,462546,467135,471649,476215,480762,485275,489787,494311,498717,503251,507793,512383,516895,521398,525932,530472,534962,539450,543990,548499,552993,557493,562021,566514,570989,575503,579963,584484,588945,593357,597873,602379,606833,611346,615806,620283,624716,629187,633659,638124,642547,646968,651442,655897,660327,664771,669231,673688,678173,682576,687052,691478,695980,700326,704735,709115,713555,717989,722424,726882,731296,735740,740137,744563,748889,753318,757686,762199,766618,771012,775415,779827,784197,788611,792973,797361,801781,806180,810564,814963,819309,823752,828180,832596,836953,841364,845749,850080,854472,858875,863253,867592,872013,876358,880744,885138,889481,893857,898212,902573,906912,911332,915667,920007,924356,928780,933139,937520,941889,946295,950616,955026,959308,963624,967986,972309,976647,980962,985307,989647,993976,998272,1002562,1006935,1011215,1015619,1019959,1024321,1028638,1032962,1037265,1041665,1045928,1050175,1054476,1058798,1063072,1067388,1071730,1076029,1080355,1084692,1089019,1093331,1097657,1101903,1106214,1110568,1114845,1119226,1123489,1127772,1132097,1136475,1140769,1145026,1149293,1153592,1157925,1162244,1166586,1170911,1175158,1179444,1183812,1188093,1192378,1196660,1201001,1205285,1209591,1213868,1218111,1222393,1226677,1230996,1235257,1239605,1243837,1248112,1252388,1256652,1260962,1265205,1269497,1273689,1277958,1282286,1286557,1290771,1294997,1299249,1303447,1307765,1312014,1316314,1320577,1324799,1329102,1333417,1337630,1341880,1346124,1350402,1354624,1358925,1363167,1367411,1371680,1375934,1380190,1384448,1388664,1392850,1397133,1401374,1405619,1409899,1414173,1418381,1422676,1426913,1431165,1435430,1439692,1443939,1448219,1452383,1456637,1460920,1465120,1469369,1473621,1477838,1482078,1486323,1490584,1494787,1499018,1503239,1507485,1511686,1515936,1520184,1524402,1528622,1532811,1536997,1541268,1545503,1549669,1553884,1558140,1562352,1566525,1570716,1574950,1579176,1583352,1587542,1591780,1596005,1600182,1604386,1608561,1612824,1617053,1621217,1625407,1629636,1633816,1637991,1642288,1646485,1650670,1654854,1659060,1663265,1667470,1671700,1675962,1680125,1684320,1688539,1692725,1696863,1701029,1705278,1709505,1713725,1717894,1722095,1726276,1730436,1734628,1738807,1743049,1747205,1751415,1755537,1759726,1763839,1768063,1772246,1776452,1780671,1784845,1789019,1793234,1797448,1801691,1805871,1810034,1814143,1818274,1822528,1826619,1830793,1834965,1839214,1843403,1847581,1851727,1855856,1860038,1864207,1868375,1872540,1876750,1880878,1885060,1889297,1893453,1897679,1901914,1906069,1910178,1914346,1918528,1922737,1926888,1931029,1935238,1939421,1943602,1947727,1951862,1956076,1960267,1964430,1968635,1972724,1976891,1981017,1985214,1989438,1993573,1997721,2001898,2006033,2010199,2014373,2018537,2022702,2026883,2031020,2035213,2039323,2043518,2047682,2051851,2055971,2060105,2064275,2068399,2072561,2076720,2080845,2084942,2089097,2093257,2097407,2101582,2105738,2109871,2113990,2118142,2122304,2126472,2130618,2134829,2138962,2143126,2147172,2151307,2155442,2159590,2163758,2167857,2171965,2176089,2180269,2184426,2188547,2192704,2196835,2200944,2205083,2209267,2213444,2217573,2221739,2225896,2230006,2234079,2238231,2242347,2246480,2250627,2254788,2258956,2263079,2267183,2271245,2275351,2279483,2283602,2287747,2291870,2295997,2300125,2304177,2308305,2312443,2316527,2320691,2324784,2328942,2333021,2337139,2341233,2345411,2349535,2353608,2357731,2361872,2366049,2370149,2374259,2378388,2382543,2386653,2390846,2394902,2399011,2403099,2407218,2411351,2415525,2419627,2423655,2427745,2431863,2436001,2440153,2444352,2448408,2452482,2456605,2460744,2464800,2468912,2473016,2477113,2481259,2485399,2489485,2493631,2497687,2501804,2505870,2509986,2514115,2518175,2522247,2526330,2530464,2534604,2538640,2542791,2546914,2551055,2555158,2559256,2563388,2567510,2571581,2575664,2579784,2583836,2587996,2592090,2596186,2600254,2604332,2608394,2612446,2616565,2620672,2624787,2628831,2632916,2636967,2641068,2645217,2649274,2653318,2657389,2661469,2665564,2669664,2673788,2677901,2682014,2686173,2690185,2694253,2698331,2702412,2706497,2710548,2714585,2718791,2722854,2726903,2730937,2735080,2739146,2743293,2747379,2751458,2755521,2759665,2763725,2767807,2771910,2775981,2780032,2784117,2788181,2792309,2796375,2800480,2804531,2808593,2812655,2816741,2820817,28249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97,7756540,7760403,7764213,7768083,7771905,7775729,7779545,7783381,7787226,7791111,7795028,7798890,7802758,7806612,7810459,7814302,7818155,7822033,7825842,7829704,7833550,7837438,7841312,7845183,7848885,7852736,7856583,7860490,7864364,7868183,7872018,7875854,7879768,7883588,7887428,7891312,7895233,7899144,7902975,7906819,7910582,7914416,7918312,7922224,7926037,7929911,7933766,7937545,7941378,7945188,7949032,7952909,7956760,7960587,7964451,7968282,7972124,7975961,7979866,7983734,7987569,7991425,7995266,7999125,8002935,8006751,8010615,8014495,8018323,8022105,8025983,8029775,8033583,8037448,8041400,8045223,8049029,8052854,8056748,8060613,8064377,8068236,8072033,8075950,8079782,8083627,8087510,8091339,8095135,8098912,8102726,8106543,8110337,8114188,8118011,8121898,8125719};int prime[30000000], a, b;bool mark[lim];inline bool fang(int x){    int t=sqrt(x);    return t*t==x;}void init(){    int i, j;    for(i=2;i*i<=b;i++)    {        if(!mark[i])prime[++prime[0]]=i;        for(j=1;(long long)i*prime[j]<=b and (long long)i*prime[j]<lim;j++)        {            mark[i*prime[j]]=1;            if(i%prime[j]==0)break;        }    }}inline bool judge(int x){    int i;    for(i=1;prime[i]*prime[i]<=x and i<=prime[0];i++)if(x%prime[i]==0)return false;    for(i=1;i*i<x;i++)if(fang(x-i*i))return true;    return false;}int solve(int x){    int i, j, ans;    for(i=0;i<=x;i+=block);i-=block;ans=biao[i/block];    for(j=i+1;j<=x;j++)if(judge(j))ans++;    return ans;}int main(){    scanf("%d%d",&a,&b);    init();    printf("%d",solve(b)-solve(a-1));    return 0;}