4 条题解
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2
嗨害嗨，我又来了。 今天咱们聊聊P938[回文素数] 开始之前，先询问一下，有没有听说过这样一段话：
''' 打表过样例，暴力出奇迹 要是想把分数偷，贪心打表加暴搜 快读快写火车头，马上AC不用愁 (这是某位大佬用户的座右铭) '''这题就很好诠释了这一点：直接打表是效率最高的，只要122ms.（总时间，一段运行时长为13或14ms)完爆那些动辄200+ms的好吗！
思路（打表法）
#1.设定打表范围#2.打印出列表内容并设定好列表#3.判断范围并打印
打表代码：
''' DBs code: def kfs(i):#判断回文 k=str(i) p='' for i in range(6,-1,-1): p += k[i] if k == p: return True return False#return=跳出函数 for i in range(n,m,2): if kfs(i) and (i%6 == 1 or i%6 ==5): flag=1 for j in range(3,3163,2):(3163*3163>10^8) if i%j ==0: flag=0 break if flag: print(i,end=',') '''说明：设q>3且为质数，则q=6k±1 一般来说，当(a,b)=1时，存在形如ax+b的质数。
判断代码
（！！!很费手与肝！）
'''' 这里本人用了七个列表存储。也可以改一下， 就是有点费if语句。 每次一看见数比b大就break，这样节省时间也可以防止误判。 ''' if b<=100:#b<100 for i in range(5): if number_one[i] > b: break if number_one[i] >= a: print(number_one[i]) elif b<=1000: #100<b<1000 for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i] > b: break if number_two[i] >= a: print(number_two[i]) elif b<=100000:#1000<b<10000 for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i]>=a: print(number_two[i]) for i in range(len(number_three)): if number_three[i] > b: break if number_three[i]>=a: print(number_three[i]) else:#b>=10*10*10*10*10*10*10 if b<2000000: for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i]>=a: print(number_two[i]) for i in range(len(number_three)): if number_three[i]>=a: print(number_three[i]) for i in range(len(number_four_the_first)): if number_four_the_first[i]>b: break if number_four_the_first[i]>=a: print(number_four_the_first[i]) elif b<4000000: for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i]>=a: print(number_two[i]) for i in range(len(number_three)): if number_three[i]>=a: print(number_three[i]) for i in range(len(number_four_the_second)): if number_four_the_second[i] > b: break if number_four_the_second[i]>=a: print(number_four_the_second[i]) elif b<8000000: for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i]>=a: print(number_two[i]) for i in range(len(number_three)): if number_three[i]>=a: print(number_three[i]) for i in range(len(number_four_the_first)): if number_four_the_first[i]>=a: print(number_four_the_first[i]) for i in range(len(number_four_the_second)): if number_four_the_second[i]>=a: print(number_four_the_second[i]) for i in range(len(number_four_the_third)): if number_four_the_third > b: break if number_four_the_third[i]>=a: print(number_four_the_third[i]) else: for i in range(5): if number_one[i]>=a: print(number_one[i]) for i in range(len(number_two)): if number_two[i]>=a: print(number_two[i]) for i in range(len(number_three)): if number_three[i]>=a: print(number_three[i]) for i in range(len(number_four_the_first)): if number_four_the_first[i]>=a: print(number_four_the_first[i]) for i in range(len(number_four_the_second)): if number_four_the_second[i]>=a: print(number_four_the_second[i]) for i in range(len(number_four_the_third)): if number_four_the_third[i]>=a: print(number_four_the_third[i]) for i in range(len(number_four_the_fouth)): if number_four_the_fouth[i] > b: break if number_four_the_fouth[i]>=a: print(number_four_the_fouth[i])Loading:16/100……
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hetao149375
@ 2022-11-10 21:40:09
提示一下几个重点：
1.在本题中，不需要判断位数为偶数且>11的回文数！ 事实上，任何位数为偶数的回文数含有因子11,所以除了11是一个位数为偶数的回文质数以外，其他都可以排除（因为偶数位回文数的奇数位和=偶数位和，即奇数位和-偶数位和=0， 而0≡0（mod 11)，即可以被11整除）。 2.对于大于10的数，不用判断最高位为2、4、5、6、8的数，显然它们含有因子2或5。 3.这题我用的是Python 3的代码，请学习C++的同学自行研究类似的代码。
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1
可以直接打表，速度非常快
#include <bits/stdc++.h> using namespace std; int a, b, prime[800] = {0,2,3,5,7,11,101,131,151,181, 191,313,353,373,383,727,757,787,797, 919,929,10301,10501,10601,11311,11411,12421,12721, 12821,13331,13831,13931,14341,14741,15451,15551,16061, 16361,16561,16661,17471,17971,18181,18481,19391,19891, 19991,30103,30203,30403,30703,30803,31013,31513,32323, 32423,33533,34543,34843,35053,35153,35353,35753,36263, 36563,37273,37573,38083,38183,38783,39293,70207,70507, 70607,71317,71917,72227,72727,73037,73237,73637,74047, 74747,75557,76367,76667,77377,77477,77977,78487,78787, 78887,79397,79697,79997,90709,91019,93139,93239,93739, 94049,94349,94649,94849,94949,95959,96269,96469,96769, 97379,97579,97879,98389,98689,1003001,1008001,1022201,1028201, 1035301,1043401,1055501,1062601,1065601,1074701,1082801,1085801,1092901, 1093901,1114111,1117111,1120211,1123211,1126211,1129211,1134311,1145411, 1150511,1153511,1160611,1163611,1175711,1177711,1178711,1180811,1183811, 1186811,1190911,1193911,1196911,1201021,1208021,1212121,1215121,1218121, 1221221,1235321,1242421,1243421,1245421,1250521,1253521,1257521,1262621, 1268621,1273721,1276721,1278721,1280821,1281821,1286821,1287821,1300031, 1303031,1311131,1317131,1327231,1328231,1333331,1335331,1338331,1343431, 1360631,1362631,1363631,1371731,1374731,1390931,1407041,1409041,1411141, 1412141,1422241,1437341,1444441,1447441,1452541,1456541,1461641,1463641, 1464641,1469641,1486841,1489841,1490941,1496941,1508051,1513151,1520251, 1532351,1535351,1542451,1548451,1550551,1551551,1556551,1557551,1565651, 1572751,1579751,1580851,1583851,1589851,1594951,1597951,1598951,1600061, 1609061,1611161,1616161,1628261,1630361,1633361,1640461,1643461,1646461, 1654561,1657561,1658561,1660661,1670761,1684861,1685861,1688861,1695961, 1703071,1707071,1712171,1714171,1730371,1734371,1737371,1748471,1755571, 1761671,1764671,1777771,1793971,1802081,1805081,1820281,1823281,1824281, 1826281,1829281,1831381,1832381,1842481,1851581,1853581,1856581,1865681, 1876781,1878781,1879781,1880881,1881881,1883881,1884881,1895981,1903091, 1908091,1909091,1917191,1924291,1930391,1936391,1941491,1951591,1952591, 1957591,1958591,1963691,1968691,1969691,1970791,1976791,1981891,1982891, 1984891,1987891,1988891,1993991,1995991,1998991,3001003,3002003,3007003, 3016103,3026203,3064603,3065603,3072703,3073703,3075703,3083803,3089803, 3091903,3095903,3103013,3106013,3127213,3135313,3140413,3155513,3158513, 3160613,3166613,3181813,3187813,3193913,3196913,3198913,3211123,3212123, 3218123,3222223,3223223,3228223,3233323,3236323,3241423,3245423,3252523, 3256523,3258523,3260623,3267623,3272723,3283823,3285823,3286823,3288823, 3291923,3293923,3304033,3305033,3307033,3310133,3315133,3319133,3321233, 3329233,3331333,3337333,3343433,3353533,3362633,3364633,3365633,3368633, 3380833,3391933,3392933,3400043,3411143,3417143,3424243,3425243,3427243, 3439343,3441443,3443443,3444443,3447443,3449443,3452543,3460643,3466643, 3470743,3479743,3485843,3487843,3503053,3515153,3517153,3528253,3541453, 3553553,3558553,3563653,3569653,3586853,3589853,3590953,3591953,3594953, 3601063,3607063,3618163,3621263,3627263,3635363,3643463,3646463,3670763, 3673763,3680863,3689863,3698963,3708073,3709073,3716173,3717173,3721273, 3722273,3728273,3732373,3743473,3746473,3762673,3763673,3765673,3768673, 3769673,3773773,3774773,3781873,3784873,3792973,3793973,3799973,3804083, 3806083,3812183,3814183,3826283,3829283,3836383,3842483,3853583,3858583, 3863683,3864683,3867683,3869683,3871783,3878783,3893983,3899983,3913193, 3916193,3918193,3924293,3927293,3931393,3938393,3942493,3946493,3948493, 3964693,3970793,3983893,3991993,3994993,3997993,3998993,7014107,7035307, 7036307,7041407,7046407,7057507,7065607,7069607,7073707,7079707,7082807, 7084807,7087807,7093907,7096907,7100017,7114117,7115117,7118117,7129217, 7134317,7136317,7141417,7145417,7155517,7156517,7158517,7159517,7177717, 7190917,7194917,7215127,7226227,7246427,7249427,7250527,7256527,7257527, 7261627,7267627,7276727,7278727,7291927,7300037,7302037,7310137,7314137, 7324237,7327237,7347437,7352537,7354537,7362637,7365637,7381837,7388837, 7392937,7401047,7403047,7409047,7415147,7434347,7436347,7439347,7452547, 7461647,7466647,7472747,7475747,7485847,7486847,7489847,7493947,7507057, 7508057,7518157,7519157,7521257,7527257,7540457,7562657,7564657,7576757, 7586857,7592957,7594957,7600067,7611167,7619167,7622267,7630367,7632367, 7644467,7654567,7662667,7665667,7666667,7668667,7669667,7674767,7681867, 7690967,7693967,7696967,7715177,7718177,7722277,7729277,7733377,7742477, 7747477,7750577,7758577,7764677,7772777,7774777,7778777,7782877,7783877, 7791977,7794977,7807087,7819187,7820287,7821287,7831387,7832387,7838387, 7843487,7850587,7856587,7865687,7867687,7868687,7873787,7884887,7891987, 7897987,7913197,7916197,7930397,7933397,7935397,7938397,7941497,7943497, 7949497,7957597,7958597,7960697,7977797,7984897,7985897,7987897,7996997, 9002009,9015109,9024209,9037309,9042409,9043409,9045409,9046409,9049409, 9067609,9073709,9076709,9078709,9091909,9095909,9103019,9109019,9110119, 9127219,9128219,9136319,9149419,9169619,9173719,9174719,9179719,9185819, 9196919,9199919,9200029,9209029,9212129,9217129,9222229,9223229,9230329, 9231329,9255529,9269629,9271729,9277729,9280829,9286829,9289829,9318139, 9320239,9324239,9329239,9332339,9338339,9351539,9357539,9375739,9384839, 9397939,9400049,9414149,9419149,9433349,9439349,9440449,9446449,9451549, 9470749,9477749,9492949,9493949,9495949,9504059,9514159,9526259,9529259, 9547459,9556559,9558559,9561659,9577759,9583859,9585859,9586859,9601069, 9602069,9604069,9610169,9620269,9624269,9626269,9632369,9634369,9645469, 9650569,9657569,9670769,9686869,9700079,9709079,9711179,9714179,9724279, 9727279,9732379,9733379,9743479,9749479,9752579,9754579,9758579,9762679, 9770779,9776779,9779779,9781879,9782879,9787879,9788879,9795979,9801089, 9807089,9809089,9817189,9818189,9820289,9822289,9836389,9837389,9845489, 9852589,9871789,9888889,9889889,9896989,9902099,9907099,9908099,9916199, 9918199,9919199,9921299,9923299,9926299,9927299,9931399,9932399,9935399, 9938399,9957599,9965699,9978799,9980899,9981899,9989899, 781}; int main() { cin >> a >> b; for (int i = 1; i <= 781; i++) if (prime[i] >= a && prime[i] <= b) cout << prime[i] << endl; return 0; } -
1
hetao2909413
LV 10
@ 2023-1-9 23:07:27
打表就是将题目中需要的答案集合提前算出来，存到代码里，根据题目所需取答案，这种方法通常只需要将程序挂着，在表打完后进行加工，最终取答案程序时间复杂度为O(1)，空间复杂度为O(n)。
基本思路：先运用暴力枚举算出所有的回文质数，然后存在一个数组中，这样子时间复杂度仅为O(1)
#include <iostream> using namespace std; int k1, k2; int a, b;//区间 int main() { cin >> a >> b; int i = 0, c[1000] = { 5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919,929,10301,10501,10601,11311,11411,12421,12721,12821,13331,13831,13931,14341,14741, 15451,15551,16061,16361,16561,16661,17471,17971,18181,18481,19391,19891,19991,30103,30203,30403,30703,30803,31013,31513,32323,32423,33533,34543,34843,35053,35153,35353,35753,36263,36563,37273,37573,38083,38183,38783, 39293,70207,70507,70607,71317,71917,72227,72727,73037,73237,73637,74047,74747,75557,76367,76667,77377,77477,77977,78487,78787,78887,79397,79697,79997,90709,91019,93139,93239,93739,94049,94349,94649,94849,94949,95959, 96269,96469,96769,97379,97579,97879,98389,98689,1003001,1008001,1022201,1028201,1035301,1043401,1055501,1062601,1065601,1074701,1082801,1085801,1092901,1093901,1114111,1117111,1120211,1123211,1126211,1129211,1134311, 1145411,1150511,1153511,1160611,1163611,1175711,1177711,1178711,1180811,1183811,1186811,1190911,1193911,1196911,1201021,1208021,1212121,1215121,1218121,1221221,1235321,1242421,1243421,1245421,1250521,1253521,1257521, 1262621,1268621,1273721,1276721,1278721,1280821,1281821,1286821,1287821,1300031,1303031,1311131,1317131,1327231,1328231,1333331,1335331,1338331,1343431,1360631,1362631,1363631,1371731,1374731,1390931,1407041,1409041, 1411141,1412141,1422241,1437341,1444441,1447441,1452541,1456541,1461641,1463641,1464641,1469641,1486841,1489841,1490941,1496941,1508051,1513151,1520251,1532351,1535351,1542451,1548451,1550551,1551551,1556551,1557551, 1565651,1572751,1579751,1580851,1583851,1589851,1594951,1597951,1598951,1600061,1609061,1611161,1616161,1628261,1630361,1633361,1640461,1643461,1646461,1654561,1657561,1658561,1660661,1670761,1684861,1685861,1688861, 1695961,1703071,1707071,1712171,1714171,1730371,1734371,1737371,1748471,1755571,1761671,1764671,1777771,1793971,1802081,1805081,1820281,1823281,1824281,1826281,1829281,1831381,1832381,1842481,1851581,1853581,1856581,1865681,1876781,1878781,1879781,1880881,1881881, 1883881,1884881,1895981,1903091,1908091,1909091,1917191,1924291,1930391,1936391,1941491,1951591,1952591,1957591,1958591,1963691,1968691,1969691,1970791,1976791,1981891,1982891,1984891,1987891,1988891,1993991,1995991,1998991,3001003,3002003,3007003,3016103,3026203,3064603,3065603,3072703,3073703,3075703,3083803,3089803,3091903,3095903,3103013,3106013,3127213,3135313,3140413,3155513,3158513,3160613,3166613,3181813,3187813,3193913,3196913,3198913,3211123,3212123,3218123,3222223,3223223,3228223,3233323,3236323,3241423,3245423,3252523,3256523,3258523,3260623,3267623,3272723,3283823,3285823,3286823,3288823,3291923,3293923,3304033,3305033,3307033,3310133,3315133,3319133,3321233,3329233,3331333,3337333,3343433,3353533,3362633,3364633,3365633,3368633,3380833,3391933,3392933,3400043,3411143,3417143,3424243,3425243,3427243,3439343,3441443,3443443,3444443,3447443,3449443,3452543,3460643,3466643,3470743,3479743,3485843,3487843,3503053,3515153,3517153,3528253,3541453,3553553,3558553,3563653,3569653,3586853,3589853,3590953,3591953,3594953,3601063,3607063,3618163,3621263,3627263,3635363,3643463,3646463,3670763,3673763,3680863,3689863,3698963,3708073,3709073,3716173,3717173,3721273,3722273,3728273,3732373,3743473,3746473,3762673,3763673,3765673,3768673,3769673,3773773,3774773,3781873,3784873,3792973,3793973,3799973,3804083,3806083,3812183,3814183,3826283,3829283,3836383,3842483,3853583,3858583,3863683,3864683,3867683,3869683,3871783,3878783,3893983,3899983,3913193,3916193,3918193,3924293,3927293,3931393,3938393,3942493,3946493,3948493,3964693,3970793,3983893,3991993,3994993,3997993,3998993,7014107,7035307,7036307,7041407,7046407,7057507,7065607,7069607,7073707,7079707,7082807,7084807,7087807,7093907,7096907,7100017,7114117,7115117,7118117,7129217,7134317,7136317,7141417,7145417,7155517,7156517,7158517,7159517,7177717,7190917,7194917,7215127,7226227,7246427,7249427,7250527,7256527,7257527,7261627,7267627,7276727,7278727,7291927,7300037,7302037,7310137,7314137,7324237,7327237,7347437,7352537,7354537,7362637,7365637,7381837,7388837,7392937,7401047,7403047,7409047,7415147,7434347,7436347,7439347,7452547,7461647,7466647,7472747,7475747,7485847,7486847,7489847,7493947,7507057,7508057,7518157,7519157,7521257,7527257,7540457,7562657,7564657,7576757,7586857,7592957,7594957,7600067,7611167,7619167,7622267,7630367,7632367,7644467,7654567,7662667,7665667,7666667,7668667,7669667,7674767,7681867,7690967,7693967,7696967,7715177,7718177,7722277,7729277,7733377,7742477,7747477,7750577,7758577,7764677,7772777,7774777,7778777,7782877,7783877,7791977,7794977,7807087,7819187,7820287,7821287,7831387,7832387,7838387,7843487,7850587,7856587,7865687,7867687,7868687,7873787,7884887,7891987,7897987,7913197,7916197,7930397,7933397,7935397,7938397,7941497,7943497,7949497,7957597,7958597,7960697,7977797,7984897,7985897,7987897,7996997,9002009,9015109,9024209,9037309,9042409,9043409,9045409,9046409,9049409,9067609,9073709,9076709,9078709,9091909,9095909,9103019,9109019,9110119,9127219,9128219,9136319,9149419,9169619,9173719,9174719,9179719,9185819,9196919,9199919,9200029,9209029,9212129,9217129,9222229,9223229,9230329,9231329,9255529,9269629,9271729,9277729,9280829,9286829,9289829,9318139,9320239,9324239,9329239,9332339,9338339,9351539,9357539,9375739,9384839,9397939,9400049,9414149,9419149,9433349,9439349,9440449,9446449,9451549,9470749,9477749,9492949,9493949,9495949,9504059,9514159,9526259,9529259,9547459,9556559,9558559,9561659,9577759,9583859,9585859,9586859,9601069,9602069,9604069,9610169,9620269,9624269,9626269,9632369,9634369,9645469,9650569,9657569,9670769,9686869,9700079,9709079,9711179,9714179,9724279,9727279,9732379,9733379,9743479,9749479,9752579,9754579,9758579,9762679,9770779,9776779,9779779,9781879,9782879,9787879,9788879,9795979,9801089,9807089,9809089,9817189,9818189,9820289,9822289,9836389,9837389, 9845489,9852589,9871789,9888889,9889889,9896989,9902099,9907099,9908099,9916199,9918199,9919199,9921299,9923299,9926299,9927299,9931399,9932399,9935399,9938399,9957599,9965699,9978799,9980899,9981899,9989899 }; while (c[i] != 0) i++; for (int j = 0;j < i;j++) if (a <= c[j] && c[j] <= b) printf("%d\n", c[j]); return 0; } -
0
hetao6640877
LV 10
@ 2024-3-19 23:06:39
#include <bits/stdc++.h> using namespace std; const int N=1e7+10; int l,r,k; int primes[N]; bool huiwen(int x){ int t=0,wx; wx=x; while (x!=0){ t=t*10+x%10; x/=10; } if (wx==t)return true; return false; } int main(){ scanf("%d%d",&l,&r); bool f[r+10]; memset(f,false,sizeof(f)); for (int i=2;i<=r;i++){ if (!f[i])primes[++k]=i; for (int j=1;primes[j]*i<=r;j++){ f[i*primes[j]]=true; if (i%primes[j]==0)break; } } for (int i=l;i<=r;i++){ if (!f[i]&&huiwen(i))printf("%d\n",i); } return 0; }
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