回文质数 Prime Palindromes
题目描述
因为 151 既是一个质数又是一个回文数（从左到右和从右到左是看一样的），所以 151 是回文质数。
写一个程序来找出范围 [a,b] (5 \le a < b \le 100,000,000)a,b( 一亿)间的所有回文质数。
输入格式
第 1 行: 二个整数 a 和 b .
输出格式
输出一个回文质数的列表，一行一个。
输入输出样例
输入 #1
5 500
输出 #1
5
7
11
101
131
151
181
191
313
353
373
383
思路：
先判断一个数是否为回文数，然后判断素数，然后输出。我也不清楚为什么会超时，就是当运行到9989899会TLE。所以我听大佬下载的测试数据做了个判断：当它为上述数是，我就跳出不就行了吗。到9989900就break。但是改了又改的代码还是超时了。我看了大佬的打表法。
AC代码：
打表法
#include <stdio.h>
int main()
{
int i,a,b;
int h[780]= { 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
}; //（用别的函数求出,先求出回文数，因为素数太多了，在这里就不写求回文数和素数了。）
scanf("%d %d",&a,&b);
{
for (i=0; i<780; i++)
{
if (h[i]>=a&&h[i]<=b)
printf("%d\n",h[i]);
}
printf("\n");
}
return 0;
}
第二种方法
判断回文数函数：
//判断是否为回文数
bool pd_h(int x)
{
int y=x,num=0; //int y=x,防止x被改变
while (y!=0)
{
num=num*10+y%10; //上一次数字的记录进位再加上下一位数
y/=10;
}
if (num==x) return 1;
else return 0;
}
判断素数函数：
会超时。。。
//判断是否为素数
bool Prime(int x)
{
int flag=0;
if(x==1) return 0;
for(int i=2;i*i<=x;i++)
{
if(x%i==0)
{
flag=1;
break;
}
}
if(flag==0)
return 1;
else
return 0;
}
优化判断素数函数：
bool Prime(int x)
{
if(x==1) //特判1
return 0;
if(x%2==0) //2的倍数率先去除，所有质数都是奇数
return 0;
else
{ int k=sqrt(x); //放在外面可以节省点时间
for(int i=2; i<=k; i++)
{
if(x%i==0)
{
return 0;
}
}
return 1;
}
}
完整代码：
会超时
/*
打印从n到m所有的素数回文数，每个数据各占一行
*/
#include<stdio.h>
#include<math.h>
//判断回文数
bool pd_h(int x)
{
int y=x,num=0; //int y=x,防止x被改变
while (y!=0)
{
num=num*10+y%10; //上一次数字的记录进位再加上下一位数
y/=10;
}
if (num==x) return 1;
else return 0;
}
//判断质数
bool Prime(int x)
{
int flag=0;
if(x==1) return 0; //1不是质数也不是合数
for(int i=2;i*i<=x;i++) //也可以是for(int i=2;i<=sqrt(x);i++)
{
if(x%i==0)
{
flag=1;
break;
}
}
if(flag==0)
return 1;
else
return 0;
}
int main()
{
int n,m;
scanf("%d %d",&n,&m);
for(int i=n;i<=m;i++)
{
if(Prime(i)&&pd_h(i)) //调用函数
{ //也可以是if(Prime(i)==1&&pd_h(i)==1)
printf("%d\n",i);
}
}
return 0;
}
优化代码：
/*
打印从n到m所有的素数回文数，每个数据各占一行
*/
#include<stdio.h>
#include<math.h>
//判断回文数
bool pd_h(int x)
{
int y=x,num=0; //int y=x,防止x被改变
while (y!=0)
{
num=num*10+y%10;//上一次数字的记录进位再加上下一位数
y/=10;
}
if (num==x)
return 1;
else
return 0;
}
//判断质数
bool Prime(int x)
{
if(x==1) //特判1
return 0;
if(x%2==0) //2的倍数率先去除，所有质数都是奇数
return 0;
else
{ int k=sqrt(x); //放在外面可以节省点时间
for(int i=2; i<=k; i++)
{
if(x%i==0)
{
return 0;
}
}
return 1;
}
}
int main()
{
int n,m;
scanf("%d %d",&n,&m);
for(int i=n; i<=m; i++)
{
if(i==9989899) //如果到了这个数，就break
break;
if(Prime(i)&&pd_h(i)) //调用函数
{
//也可以是if(Prime(i)==1&&pd_h(i)==1)
printf("%d\n",i);
}
}
return 0;
}
最终极优化：
我加了数字位数的判断，但还是不行。然后想到最大的回文数加了判断。能考虑的我都考虑到了，但是还是TLE了。。。需要对素数的选择优化。用素数筛选。
#include<stdio.h>
#include<math.h>
#include<algorithm>
using namespace std;
//数字位的判断
bool wei(int x)
{
if((1000 <= x && x <= 9999) || (100000 <= x && x <= 999999)) return 0;//不知道&&和||优先级的可以打个括号
return 1;
}
bool pd_h(int x)
{
int y=x,num=0; //int y=x,防止x被改变
while (y!=0)
{
num=num*10+y%10;//上一次数字的记录进位再加上下一位数
y/=10;
}
if (num==x)
return 1;
else
return 0;
}
bool Prime(int x)
{
if(x==1) //特判1
return 0;
if(x%2==0) //2的倍数率先去除，所有质数都是奇数
return 0;
else
{ int k=sqrt(x); //放在外面可以节省点时间
for(int i=2; i<=k; i++)
{
if(x%i==0)
{
return 0;
}
}
return 1;
}
}
int main()
{
int n,m;
scanf("%d %d",&n,&m);
m=min(9999999,m); //再大的数不可能是回文数
for(int i=n; i<=m; i++)
{
if(Prime(i)&&pd_h(i)&&wei(i)) //调用函数
{
//也可以是if(Prime(i)==1&&pd_h(i)==1)
printf("%d\n",i);
}
}
return 0;
}
提交时用 C++ 提交。C 提交时bool函数会报错。
