杭电OJ--2098 分拆素数和
Problem Description
把一个偶数拆成两个不同素数的和，有几种拆法呢？
Input
输入包含一些正的偶数，其值不会超过10000，个数不会超过500，若遇0，则结束。
Output
对应每个偶数，输出其拆成不同素数的个数，每个结果占一行。
Sample Input
30 26 0
Sample Output
3 2
也是很水的一道题。
先打表，然后判断即可。
#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
using namespace std;
/**思路：
* 用空间换时间，将10000以内的素数全部存储起来，然后直接测试即可。
*
*
*/
/*先打表，计算出10000以内的素数*/
int prime[] = {
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 };
int bsearch(int n, int v)
{
int left, right, middle;
left = -1, right = n;
while (left + 1 != right)
{
middle = left + (right - left) / 2;
if (prime[middle] < v)
{
left = middle;
}
else
{
right = middle;
}
}
if (right >= n || prime[right] != v)
{
right = -1;
}
return right;
}
int main()
{
int array_len = sizeof(prime) / sizeof(int);
int num;
while (scanf("%d", &num) && num != 0)
{
//现在开始拆分素数
int count = 0; //用来记录个数
for (int i = 0; i < array_len; ++i)
{
int one_part = prime[i];
int other_part = num - one_part;
if (one_part == other_part)
continue;
/*最好利用二分查找来查找数字other_part
*/
int ret = bsearch(array_len, other_part);
if (ret != -1) //找到了，说明有一组拆分
{
++count;
//printf("%d %d\n", one_part, other_part);
}
}
printf("%d\n", count / 2);
}
return 0;
}