Java 最大幂：求给定数字n的x和y，其中x^y=n

我想找到给定数字的基数和指数，使指数最大。例如：16可以表示为2^4，4^2。解是2^4，因为4是可能的最高指数

到目前为止，我有以下解决方案；我想知道它是否有明显的缺陷或性能问题：

public void getHighestPower(double a)
{
  double answer = 0;

  if(a%1 == 0) {

    for (int i = 2; i <= Math.sqrt(a); i++) {

      double res = Math.log(a) / Math.log(i);

      if (res > 0) {

        if (res % 1 == 0) {

          System.out.println(res);
          break;
        }
      }
    }
  }
}

public void获取最高权限（双a）
{
双答案=0；
如果（a%1==0）{
对于（int i=2；i 0）{
如果（res%1==0）{
系统输出打印项次（res）；
打破
}
}
}
}
}

我觉得这是针对整数的。在这种情况下，FPU函数可能会出现问题，例如，

res

是

double

，您正在测试分数部分是否为零，这将由于

log，/，%

操作的舍入错误而输出错误答案。有了你，我会觉得安全多了

if (fabs(res-floor(res)-0.5)>=0.5-1e-40)

而不是

if (res % 1 == 0)

但是，您的

pow

中的

log

和除法操作仍然会在结果的小数部分产生噪声。因此，对于更大的数字，您可能会遇到麻烦

从性能的角度来看，你可以考虑将数字分解成它的素数因子，然后使用分解中使用的最小指数作为<代码> y>代码>如果数字是可分解的。

x

将是每个

y

指数倍数使用的所有素数的乘积。如果指数不是y的倍数，或者素数分解失败（

a！=1

，最后），结果是原始的

a

so

a^1

。所有这些都是可以单独在整数上计算的。下面是C++中执行此操作的简单示例：

void分解（int&x，int&y，inta）
{
常量整型素数[]=
{
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
{ 2,3,5,7,9,11,13... }

    4 =     2^2
    8 =     2^3
    9 =     3^2
   16 =     2^4
   25 =     5^2
   27 =     3^3
   32 =     2^5
   36 =     6^2
   49 =     7^2
   64 =     2^6
   81 =     3^4
  100 =    10^2
  121 =    11^2
  125 =     5^3
  128 =     2^7
  144 =    12^2
  169 =    13^2
  196 =    14^2
  216 =     6^3
  225 =    15^2
  243 =     3^5
  256 =     2^8
  289 =    17^2
  324 =    18^2
  343 =     7^3
  361 =    19^2
  400 =    20^2
  441 =    21^2
  484 =    22^2
  512 =     2^9
  529 =    23^2
  576 =    24^2
  625 =     5^4
  676 =    26^2
  729 =     3^6
  784 =    28^2
  841 =    29^2
  900 =    30^2
  961 =    31^2
 1000 =    10^3
 1024 =    2^10