题解：P1217 [USACO1.5]回文质数 Prime Palindromes
题目链接：P1217 [USACO1.5]回文质数 Prime Palindromes
关键步骤: 线性筛，生成回文数，判断质数，二分查找
线性筛：求 maxn
生成回文数：根据题目最后的提示，首位一定是奇数。偶数位回文数都整除
判断质数：bool isNotPrime[maxn] 布尔数组判断，以上则在质数数组中判断是否可以整除，判断到质数大于回文数的平方根时中断,使用乘法判断边界。
二分查找：b 对应的下标不需要二分因为我在生成结果数组（下面代码里是vector<int>result）时处理过了，不过如果打表，也要二分一下。a需要二分一下，不过也可以在生成结果数组时处理a，有点懒得处理了，所以使用二分
时间33ms，内存696KB,不打表的C++14 (GCC 9)代码:
/*
zqm
*/
#include<bits/stdc++.h>
using namespace std;
#define maxn 10005
class Solution{
bool isNotPrime[maxn]={true,true,false};
int primes[1229];
int cntP = 0;
vector<int>result;
int cnt = 0;
bool isPrime(int r){
if(r<maxn){
return !isNotPrime[r];
}else{
for(int i=0;primes[i]*primes[i]<=r&&i<cntP;i++){
if((r%primes[i])==0){
return false;
}
}
return true;// not necessarily a prime number, true for r < 1e8
}
}
int firstNotSmaller(int a){
// 二分查找？需要吗？a需要，现在b不需要
int ai=-1,left=0,right=cnt-1,mid;
while(left<=right){
mid = (left+right)/2;
if(result[mid]>=a){
ai = mid;
right = mid-1;
}else{
left = mid+1;
}
}
return ai;
}
public:
Solution(int a, int b){
// 抄了一个线性筛（欧拉筛）
int jmax = min(maxn,b+1);
for(int j = 2;j<jmax;j++){
if(!isNotPrime[j]){
primes[cntP++]=j;
}
for(int i=0;i<cntP;i++){
if(primes[i]*j>maxn){
break;
}
isNotPrime[primes[i]*j] = true;
if(j % primes[i] == 0) break;
}
}
// 生成[5, b]之间结果，不过感觉生成[a,b]的更好？
int r;
int r_max = min(b+1,10); // 1
for(int r=5;r<r_max;r+=2){
if(isPrime(r)){
result.push_back(r);++cnt;
}
}
r = 11;// 2 // 偶数位回文数，都整除11，除了11都不是质数
r_max = min(b+1,r+1);
if(r<r_max&&isPrime(r)){
result.push_back(r);++cnt;
}
r_max = min(b+1,1000); // 3
bool breaknow=false;
for(int d1=1;d1<=9;d1+=2){
for(int d2=0;d2<=9;d2++){
r = d1*101+10*d2;
if(r>=r_max){
breaknow=true;
break;
}
if(isPrime(r)){
result.push_back(r);++cnt;
}
}
if(breaknow){
break;
}
}
r_max = min(b+1,int(1e5));// 5
breaknow=false;
for(int d1=1;d1<=9;d1+=2){
for(int d2=0;d2<=9;d2++){
for(int d3=0;d3<=9;d3++){
r=10001*d1 + 1010*d2 +100*d3;
if(r>=r_max){breaknow=true;break;}
if(isPrime(r)){
result.push_back(r);++cnt;
}
}
if(breaknow)break;
}
if(breaknow)break;
}
r_max = min(b+1,int(1e7)); // 7
breaknow=false;
for(int d1=1;d1<=9;d1+=2){
for(int d2=0;d2<=9;d2++){
for(int d3=0;d3<=9;d3++){
for(int d4=0;d4<=9;d4++){
r=1000001*d1 + 100010*d2 +10100*d3+1000*d4;
if(r>=r_max){breaknow=true;break;}
if(isPrime(r)){
result.push_back(r);++cnt;
}
}
if(breaknow)break;
}
if(breaknow)break;
}
if(breaknow)break;
}
}
void solve(int a, int b){
int ai=firstNotSmaller(a),bi=cnt-1;
for(int i=ai;i<=bi;i++){
printf("%d\n", result[i]);
}
}
};
int main(){
ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
int a=5,b=500;
scanf("%d%d",&a,&b);
Solution s(a,b);
s.solve(a,b);
}时间27ms，内存808KB的打表的C++14 (GCC 9)代码，使用了两个二分查找。（PS：cin，cout换成scanf和printf快了3ms，可能因为数据量太少，二分几乎没有改变时间，汗）：
/*
zqm
*/
#include<bits/stdc++.h>
using namespace std;
class Solution{
int cnt = 779;
int result[779]={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};
int firstNotSmaller(int a){
int ai=-1,left=0,right=cnt-1,mid;
while(left<=right){
mid = (left+right)/2;
if(result[mid]>=a){
ai = mid;
right = mid-1;
}else{
left = mid+1;
}
}
return ai;
}
int lastNotBigger(int b){
int bi=-1,left=0,right=cnt-1,mid;
while(left<=right){
mid = (left+right)/2;
if(result[mid]<=b){
bi = mid;
left = mid+1;
}else{
right = mid-1;
}
}
return bi;
}
public:
void solve(int a, int b){
int ai=firstNotSmaller(a),bi=lastNotBigger(b);
for(int i=ai;i<=bi;i++){
printf("%d\n", result[i]);
}
}
};
int main(){
ios_base::sync_with_stdio(false);
Solution s;
int a,b;
scanf("%d%d", &a, &b);
s.solve(a,b);
}