USACO-Chapter1-Section 1.5-Prime Palindromes (pprime)

【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 <= a < b <= 100,000,000)( 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。

【样例输入】

5 500 

【样例输出】

5
7
11
101
131
151
181
191
313
353
373
383

【思路】

      看题目，Fuck~。数据10^9，O（n）都不行，但是再看看题目，发现回文是个突破口，我们既然不能通过枚举得到回文，但是可以通过构造回文实现，这样只需要我们枚举每一位最后镜像对称过去即可得到回文，然后用部分筛法求出的素数（因为整出素数一定可以整出合数）进行素数检验。输出即可。到这里，此题解决。

【补充】

      筛法求素数（就是画圈排除法，复杂度接近O（n））：

Procedure makeit;
Var
  i,j:longint;
Begin
  f[2]:=false;
  for i:=2 to 10000 do
    if f[i]=false then
    Begin
      j:=i;
      while j<=b do
      Begin
        j:=i+j;
        f[j]:=true;
      End;
    End;
End;

【代码】

• Executing...
• Test 1: TEST OK [0.011 secs, 416 KB]
• Test 2: TEST OK [0.011 secs, 416 KB]
• Test 3: TEST OK [0.011 secs, 416 KB]
• Test 4: TEST OK [0.011 secs, 416 KB]
• Test 5: TEST OK [0.011 secs, 416 KB]
• Test 6: TEST OK [0.011 secs, 416 KB]
• Test 7: TEST OK [0.011 secs, 416 KB]
• Test 8: TEST OK [0.011 secs, 416 KB]
• Test 9: TEST OK [0.011 secs, 416 KB]
• All tests OK.

{
 ID  : c_CaM.19
 LANG: PASCAL
 TASK: pprime
}
Program CaM(input,output);
Const
  filename='pprime';
Var
  f:array[0..100000] of boolean;
  a,b,i,j,t,k,l:longint;
  g:byte;
  s:string;
  d:array[0..10000] of longint;
  q:array[1..1229] of longint=(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
53,59,61,67,71,73,79,83,89,97,101,
103,107,109,113,127,131,137,139,149,151,
157,163,167,173,179,181,191,193,197,199,
211,223,227,229,233,239,241,251,
257,263,269,271,277,281,283,293,
307,311,313,317,331,337,347,349,
353,359,367,373,379,383,389,397,401,
409,419,421,431,433,439,443,449,
457,461,463,467,479,487,491,499,
503,509,521,523,541,547,
557,563,569,571,577,587,593,599,601,
607,613,617,619,631,641,643,647,
653,659,661,673,677,683,691,701,
709,719,727,733,739,743,751,
757,761,769,773,787,797,
809,811,821,823,827,829,839,
853,857,859,863,877,881,883,887,
907,911,919,929,937,941,947,
953,967,971,977,983,991,997,
1009,1013,1019,1021,1031,1033,1039,1049,1051,
1061,1063,1069,1087,1091,1093,1097,
1103,1109,1117,1123,1129,1151,
1153,1163,1171,1181,1187,1193,1201,
1213,1217,1223,1229,1231,1237,1249,
1259,1277,1279,1283,1289,1291,1297,1301,
1303,1307,1319,1321,1327,
1361,1367,1373,1381,1399,
1409,1423,1427,1429,1433,1439,1447,1451,
1453,1459,1471,1481,1483,1487,1489,1493,1499,
1511,1523,1531,1543,1549,
1553,1559,1567,1571,1579,1583,1597,1601,
1607,1609,1613,1619,1621,1627,1637,
1657,1663,1667,1669,1693,1697,1699,
1709,1721,1723,1733,1741,1747,
1753,1759,1777,1783,1787,1789,1801,
1811,1823,1831,1847,
1861,1867,1871,1873,1877,1879,1889,1901,
1907,1913,1931,1933,1949,1951,
1973,1979,1987,1993,1997,1999,
2003,2011,2017,2027,2029,2039,
2053,2063,2069,2081,2083,2087,2089,2099,
2111,2113,2129,2131,2137,2141,2143,
2153,2161,2179,
2203,2207,2213,2221,2237,2239,2243,2251,
2267,2269,2273,2281,2287,2293,2297,
2309,2311,2333,2339,2341,2347,2351,
2357,2371,2377,2381,2383,2389,2393,2399,
2411,2417,2423,2437,2441,2447,
2459,2467,2473,2477,
2503,2521,2531,2539,2543,2549,2551,
2557,2579,2591,2593,
2609,2617,2621,2633,2647,
2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,
2707,2711,2713,2719,2729,2731,2741,2749,
2753,2767,2777,2789,2791,2797,2801,
2803,2819,2833,2837,2843,2851,
2857,2861,2879,2887,2897,
2903,2909,2917,2927,2939,
2953,2957,2963,2969,2971,2999,3001,
3011,3019,3023,3037,3041,3049,
3061,3067,3079,3083,3089,
3109,3119,3121,3137,
3163,3167,3169,3181,3187,3191,
3203,3209,3217,3221,3229,3251,
3253,3257,3259,3271,3299,3301,
3307,3313,3319,3323,3329,3331,3343,3347,
3359,3361,3371,3373,3389,3391,
3407,3413,3433,3449,
3457,3461,3463,3467,3469,3491,3499,
3511,3517,3527,3529,3533,3539,3541,3547,
3557,3559,3571,3581,3583,3593,
3607,3613,3617,3623,3631,3637,3643,
3659,3671,3673,3677,3691,3697,3701,
3709,3719,3727,3733,3739,
3761,3767,3769,3779,3793,3797,
3803,3821,3823,3833,3847,3851,
3853,3863,3877,3881,3889,
3907,3911,3917,3919,3923,3929,3931,3943,3947,
3967,3989,4001,
4003,4007,4013,4019,4021,4027,4049,4051,
4057,4073,4079,4091,4093,4099,
4111,4127,4129,4133,4139,
4153,4157,4159,4177,4201,
4211,4217,4219,4229,4231,4241,4243,
4253,4259,4261,4271,4273,4283,4289,4297,
4327,4337,4339,4349,
4357,4363,4373,4391,4397,
4409,4421,4423,4441,4447,4451,
4457,4463,4481,4483,4493,
4507,4513,4517,4519,4523,4547,4549,
4561,4567,4583,4591,4597,
4603,4621,4637,4639,4643,4649,4651,
4657,4663,4673,4679,4691,
4703,4721,4723,4729,4733,4751,
4759,4783,4787,4789,4793,4799,4801,
4813,4817,4831,
4861,4871,4877,4889,
4903,4909,4919,4931,4933,4937,4943,4951,
4957,4967,4969,4973,4987,4993,4999,
5003,5009,5011,5021,5023,5039,5051,
5059,5077,5081,5087,5099,5101,
5107,5113,5119,5147,
5153,5167,5171,5179,5189,5197,
5209,5227,5231,5233,5237,
5261,5273,5279,5281,5297,
5303,5309,5323,5333,5347,5351,
5381,5387,5393,5399,
5407,5413,5417,5419,5431,5437,5441,5443,5449,
5471,5477,5479,5483,5501,
5503,5507,5519,5521,5527,5531,
5557,5563,5569,5573,5581,5591,
5623,5639,5641,5647,5651,
5653,5657,5659,5669,5683,5689,5693,5701,
5711,5717,5737,5741,5743,5749,
5779,5783,5791,5801,
5807,5813,5821,5827,5839,5843,5849,5851,
5857,5861,5867,5869,5879,5881,5897,
5903,5923,5927,5939,
5953,5981,5987,
6007,6011,6029,6037,6043,6047,
6053,6067,6073,6079,6089,6091,6101,
6113,6121,6131,6133,6143,6151,
6163,6173,6197,6199,
6203,6211,6217,6221,6229,6247,
6257,6263,6269,6271,6277,6287,6299,6301,
6311,6317,6323,6329,6337,6343,
6353,6359,6361,6367,6373,6379,6389,6397,
6421,6427,6449,6451,
6469,6473,6481,6491,
6521,6529,6547,6551,
6553,6563,6569,6571,6577,6581,6599,
6607,6619,6637,
6653,6659,6661,6673,6679,6689,6691,6701,
6703,6709,6719,6733,6737,
6761,6763,6779,6781,6791,6793,
6803,6823,6827,6829,6833,6841,
6857,6863,6869,6871,6883,6899,
6907,6911,6917,6947,6949,
6959,6961,6967,6971,6977,6983,6991,6997,7001,
7013,7019,7027,7039,7043,
7057,7069,7079,
7103,7109,7121,7127,7129,7151,
7159,7177,7187,7193,
7207,7211,7213,7219,7229,7237,7243,7247,
7253,7283,7297,
7307,7309,7321,7331,7333,7349,7351,
7369,7393,
7411,7417,7433,7451,
7457,7459,7477,7481,7487,7489,7499,
7507,7517,7523,7529,7537,7541,7547,7549,
7559,7561,7573,7577,7583,7589,7591,
7603,7607,7621,7639,7643,7649,
7669,7673,7681,7687,7691,7699,
7703,7717,7723,7727,7741,
7753,7757,7759,7789,7793,
7817,7823,7829,7841,
7853,7867,7873,7877,7879,7883,7901,
7907,7919,7927,7933,7937,7949,7951,
7963,7993,
8009,8011,8017,8039,
8053,8059,8069,8081,8087,8089,8093,8101,
8111,8117,8123,8147,
8161,8167,8171,8179,8191,
8209,8219,8221,8231,8233,8237,8243,
8263,8269,8273,8287,8291,8293,8297,
8311,8317,8329,
8353,8363,8369,8377,8387,8389,
8419,8423,8429,8431,8443,8447,
8461,8467,8501,
8513,8521,8527,8537,8539,8543,
8563,8573,8581,8597,8599,
8609,8623,8627,8629,8641,8647,
8663,8669,8677,8681,8689,8693,8699,
8707,8713,8719,8731,8737,8741,8747,
8753,8761,8779,8783,
8803,8807,8819,8821,8831,8837,8839,8849,
8861,8863,8867,8887,8893,
8923,8929,8933,8941,8951,
8963,8969,8971,8999,9001,
9007,9011,9013,9029,9041,9043,9049,
9059,9067,9091,
9103,9109,9127,9133,9137,9151,
9157,9161,9173,9181,9187,9199,
9203,9209,9221,9227,9239,9241,
9257,9277,9281,9283,9293,
9311,9319,9323,9337,9341,9343,9349,
9371,9377,9391,9397,
9403,9413,9419,9421,9431,9433,9437,9439,
9461,9463,9467,9473,9479,9491,9497,
9511,9521,9533,9539,9547,9551,
9587,9601,
9613,9619,9623,9629,9631,9643,9649,
9661,9677,9679,9689,9697,
9719,9721,9733,9739,9743,9749,
9767,9769,9781,9787,9791,
9803,9811,9817,9829,9833,9839,9851,
9857,9859,9871,9883,9887,9901,
9907,9923,9929,9931,9941,9949,9967,9973);

Procedure innt;
Begin
  assign(input,filename+'.in'); reset(input);
  assign(output,filename+'.out'); rewrite(output);
End;

Procedure outt;
Begin
  close(input);
  close(output);
End;

Begin
  innt;
  readln(a,b);
  d[1]:=5;d[2]:=7;d[3]:=11;
  t:=3;
  {3}
  for i:=1 to 9 do
    for j:=0 to 9 do
    Begin
      inc(t);
      d[t]:=i*101+j*10;
    End;
  {4,5}
  for i:=1 to 9 do
    for j:=0 to 9 do
      for k:=0 to 9 do
      Begin
        inc(t);
        d[t]:=i*10001+j*1010+k*100;
      End;
  {6,7}
  for i:=1 to 9 do
    for j:=0 to 9 do
      for k:=0 to 9 do
        for l:=0 to 9 do
        Begin
          inc(t);
          d[t]:=i*1000001+j*100010+k*10100+l*1000
        End;

  for i:=1 to t do
  Begin
    g:=0;
    for j:=1 to 1229 do
      if (d[i] mod q[j]=0)and(q[j]<d[i]) then
      Begin
        g:=1;
        break;
      End;
    if (g=0)and(a<=d[i])and(b>=d[i]) then writeln(d[i]);
  End;
  outt;
End.