https://leetcode.cn/problems/prime-palindrome/description/
給你一個整數 n ，返回大於或等於 n 的最小 迴文質數。
一個整數如果恰好有兩個除數：1 和它本身，那麼它是 質數 。注意，1 不是質數。
例如，2、3、5、7、11 和 13 都是質數。
一個整數如果從左向右讀和從右向左讀是相同的，那麼它是 迴文數 。
例如，101 和 12321 都是迴文數。
測試用例保證答案總是存在，並且在 [2, 2 * 10^8] 範圍內。
示例 1：
輸入：n = 6
輸出：7
示例 2：
輸入：n = 8
輸出：11
示例 3：
輸入：n = 13
輸出：101
提示：
1 <= n <= 10^8
解答
暴力求10^8以內的質數和迴文數是超時的。
但是其實既是質數又是迴文數的數目非常少，這裏選擇了打表，大概2000多個。
時間複雜度是O(N) N是範圍內的迴文質數個數。 如果還想節省時間 可以在迴文質數表考慮二分搜索。
class Solution {
public:
//打表過 迴文質數 全部計算出來
vector<int> palPrimes = {
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,
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155292551, 155313551, 155333551, 155373551, 155424551, 155474551, 155535551, 155646551, 155666551, 155676551, 155808551, 155828551, 155868551, 156151651, 156262651, 156343651, 156424651, 156434651, 156494651, 156545651, 156595651, 156656651, 156707651, 156727651, 156757651, 156848651, 156878651, 156949651, 157090751, 157101751, 157161751, 157252751, 157393751, 157444751, 157555751, 157717751, 157878751, 157888751, 157939751, 157959751, 157989751, 158090851, 158111851, 158222851, 158252851, 158363851, 158474851, 158595851, 158676851, 158696851, 158747851, 158808851, 158858851, 158898851, 158909851, 159020951, 159040951, 159050951, 159121951, 159181951, 159191951, 159202951, 159232951, 159262951, 159292951, 159323951, 159404951, 159464951, 159565951, 159595951, 159646951, 159757951, 159808951, 159919951, 159929951, 159959951, 160020061, 160050061, 160080061, 160101061, 160131061, 160141061, 160161061, 160171061, 160393061, 160545061, 160696061, 160707061, 160717061, 160797061, 160878061, 161171161, 161282161, 161313161, 161363161, 161474161, 161484161, 161535161, 161585161, 161636161, 161787161, 161838161, 161969161, 162040261, 162232261, 162404261, 162464261, 162484261, 162565261, 162686261, 162707261, 162757261, 162898261, 162919261, 162949261, 162959261, 162979261, 162989261, 163101361, 163333361, 163434361, 163464361, 163474361, 163494361, 163515361, 163555361, 163606361, 163686361, 163696361, 163878361, 163959361, 164000461, 164070461, 164151461, 164292461, 164333461, 164454461, 164484461, 164585461, 164616461, 164696461, 164717461, 164727461, 164838461, 165101561, 165161561, 165191561, 165212561, 165343561, 165515561, 165535561, 165808561, 165878561, 165898561, 165919561, 165949561, 166000661, 166080661, 166171661, 166191661, 166404661, 166545661, 166555661, 166636661, 166686661, 166818661, 166828661, 166878661, 166888661, 166929661, 167000761, 167111761, 167262761, 167393761, 167454761, 167474761, 167484761, 167636761, 167646761, 167787761, 167888761, 167898761, 167979761, 168151861, 168191861, 168232861, 168404861, 168505861, 168515861, 168565861, 168818861, 168898861, 168929861, 168949861, 169060961, 169131961, 169141961, 169282961, 169333961, 169383961, 169464961, 169555961, 169606961, 169656961, 169666961, 169686961, 169777961, 169797961, 169858961, 169999961, 170040071, 170060071, 170232071, 170303071, 170333071, 170414071, 170424071, 170484071, 170606071, 170616071, 170646071, 170828071, 170838071, 170909071, 170979071, 171080171, 171262171, 171292171, 171343171, 171565171, 171575171, 171767171, 171919171, 171959171, 172060271, 172090271, 172161271, 172353271, 172363271, 172393271, 172474271, 172585271, 172656271, 172747271, 172767271, 172797271, 172878271, 172909271, 172959271, 173000371, 173030371, 173090371, 173252371, 173373371, 173454371, 173525371, 173585371, 173696371, 173757371, 173777371, 173828371, 173868371, 173888371, 173898371, 173919371, 174080471, 174121471, 174131471, 174181471, 174313471, 174343471, 174595471, 174646471, 174676471, 174919471, 174949471, 174979471, 174989471, 175000571, 175090571, 175101571, 175111571, 175353571, 175444571, 175555571, 175626571, 175747571, 175777571, 175848571, 175909571, 176090671, 176111671, 176141671, 176181671, 176232671, 176313671, 176333671, 176373671, 176393671, 176414671, 176585671, 176636671, 176646671, 176666671, 176696671, 176757671, 176787671, 176888671, 176898671, 176939671, 177121771, 177161771, 177202771, 177242771, 177323771, 177565771, 177616771, 177707771, 177757771, 177868771, 178101871, 178131871, 178141871, 178161871, 178353871, 178414871, 178515871, 178525871, 178656871, 178717871, 178747871, 178878871, 178969871, 178989871, 178999871, 179010971, 179060971, 179222971, 179232971, 179262971, 179414971, 179454971, 179484971, 179717971, 179777971, 179808971, 179858971, 179868971, 179909971, 179969971, 179999971, 180070081, 180101081, 180161081, 180292081, 180515081, 180535081, 180545081, 180565081, 180616081, 180757081, 180959081, 181111181, 181515181, 181545181, 181666181, 181737181, 181797181, 181888181, 182010281, 182202281, 182373281, 182585281, 182616281, 182636281, 182777281, 182858281, 182949281, 183232381, 183626381, 183656381, 183737381, 183898381, 183979381, 183989381, 184030481, 184212481, 184222481, 184303481, 184393481, 184414481, 184545481, 184585481, 184606481, 184636481, 184747481, 184818481, 184878481, 185232581, 185373581, 185393581, 185525581, 185555581, 185595581, 185676581, 185757581, 185838581, 185858581, 185868581, 185999581,
186010681, 186040681, 186050681, 186070681, 186101681, 186131681, 186151681, 186161681, 186424681, 186484681, 186505681, 186565681, 186656681, 186676681, 186787681, 186898681, 187090781, 187101781, 187111781, 187161781, 187272781, 187404781, 187434781, 187444781, 187525781, 187767781, 187909781, 187939781, 187999781, 188010881, 188060881, 188141881, 188151881, 188303881, 188373881, 188414881, 188454881, 188505881, 188525881, 188535881, 188616881, 188636881, 188646881, 188727881, 188777881, 188868881, 188888881, 188898881, 188979881, 189080981, 189131981, 189262981, 189292981, 189464981, 189535981, 189595981, 189727981, 189787981, 189838981, 189898981, 189929981, 190000091, 190020091, 190080091, 190101091, 190252091, 190404091, 190434091, 190464091, 190494091, 190656091, 190696091, 190717091, 190747091, 190777091, 190858091, 190909091, 191090191, 191171191, 191232191, 191292191, 191313191, 191565191, 191595191, 191727191, 191757191, 191838191, 191868191, 191939191, 191969191, 192101291, 192191291, 192202291, 192242291, 192313291, 192404291, 192454291, 192484291, 192767291, 192797291, 192898291, 193000391, 193030391, 193191391, 193212391, 193282391, 193303391, 193383391, 193414391, 193464391, 193555391, 193686391, 193858391, 193888391, 194000491, 194070491, 194121491, 194222491, 194232491, 194292491, 194303491, 194393491, 194505491, 194595491, 194606491, 194787491, 194939491, 194999491, 195010591, 195040591, 195070591, 195151591, 195202591, 195242591, 195353591, 195505591, 195545591, 195707591, 195767591, 195868591, 195878591, 195949591, 195979591, 196000691, 196090691, 196323691, 196333691, 196363691, 196696691, 196797691, 196828691, 196878691, 197030791, 197060791, 197070791, 197090791, 197111791, 197121791, 197202791, 197292791, 197343791, 197454791, 197525791, 197606791, 197616791, 197868791, 197898791, 197919791, 198040891, 198070891, 198080891, 198131891, 198292891, 198343891, 198353891, 198383891, 198454891, 198565891, 198656891, 198707891, 198787891, 198878891, 198919891, 199030991, 199080991, 199141991, 199171991, 199212991, 199242991, 199323991, 199353991, 199363991, 199393991, 199494991, 199515991, 199545991, 199656991, 199767991, 199909991, 199999991
};
int primePalindrome(int n) {
for (int i = 0; i < palPrimes.size(); i++) {
if (palPrimes[i] >= n) {
return palPrimes[i];
}
}
return -1;
}
};
解法2
現場計算 迴文質數，不是篩質數，而是製作迴文數判斷是否是質數。
由於數據範圍是1e8 我們迴文數只需要計算1~99999999範圍內的迴文質數即可， 1e8的迴文質數就一個 100030001；
粗略估計時間，八位迴文數因爲是對稱關係，只需要確定前四位即可,前四位可填充0~9個數字，也就是10^4的計算量， 判斷他是不是質數時間複雜度是O(sqrt(N))
時間 不超過1e8 應該不超過時間限制
class Solution {
public:
vector<int> vv;
void CheckAndPush(string str) {
//檢查是不是素數
int num = atoi(str.c_str());
for (int i = 2; i <= num / i; i++) {
if (num % i == 0) return;
}
vv.push_back(num);
}
void dfs(string& str,int idx) {
int len = str.size();
if (len % 2 == 0 && idx >= len / 2) { CheckAndPush(str); return; }
else if (len % 2 != 0 && idx > len / 2) { CheckAndPush(str); return;}
for (int i = 0; i <= 9; i++) {
char c = '0' + i;
if (len % 2 != 0 && idx == len / 2) {
str[idx] = c;
dfs(str, idx + 1);
}
else {
str[idx] = c; str[len - idx - 1] = c;
dfs(str, idx + 1);
}
}
}
void makenum(int len) {
string str;
{
for (int i = 1; i <= 9; i+=2) {
str = "00";
str[0] = ('0' + i); str[1]=('0' + i);
for (int j = len - 2; j > 0; j--) {
str.insert(str.begin()+1,'0');
}
dfs(str,1);
}
}
}
void init() {
vv = { 2, 3, 5, 7,11 ,100030001};
//製作 3 4 5 6 7 8位的
for (int i = 3; i <= 8; i++) {
makenum(i);
//cout << "makenum " << i << ",fuinish" << endl;
}
sort(vv.begin(), vv.end());
}
int primePalindrome(int n) {
init();
for (int i = 0; i < vv.size(); i++) {
if (vv[i] >= n) {
return vv[i];
}
}
return 0;
}
};