用这样一组数字，0，1，1，2，3，5，8……..，求第100个数是多少！

初看这道题很简单，我们只需要设定一个数组，然后往里面放入对应的值，除了前两个数字位，后面每个数字位都是前两个数字位的和。刚开始我用了int数组来存放这组数，发现根本放不下去，到了第47位数的时候就存在数值溢出了，然后我换为long型数组，同样放不下去，到了第93位数的时候也存在数值溢出了。这样，只能用BigInteger类了，这是java提供的可以存储任意精度的整数的类，用它我们不需要考虑数值溢出的错误。即使我们求第1000个数值也没有什么问题。不过，它的数值运算必须以方法调用方式取代运算符方式来实现，由于这么做复杂了许多，运算速度会比较慢，所以在确定数值不会溢出的情况下，是不推荐用这种型式来进行数值存储和运算的。以下是具体代码。

package test; import java.math.BigInteger; public class BigIntegertest { public static void main(String[] args) { int num = 100; //整型数组 int[] resultInt = new int[100]; resultInt[0] = 0; resultInt[1] = 1; //长整型数组 long[] resultLong = new long[100]; resultLong[0] = 0L; resultLong[1] = 1L; //BigInteger数组 BigInteger[] resultBigInteger = new BigInteger[100]; resultBigInteger[0] = BigInteger.ZERO; resultBigInteger[1] = BigInteger.ONE; for (int i = 2; i < num; i++) { resultInt[i] = resultInt[i – 1] + resultInt[i – 2]; resultLong[i] = resultLong[i – 1] + resultLong[i – 2]; resultBigInteger[i] = resultBigInteger[i – 1].add(resultBigInteger[i – 2]); } System.out.println(“——————–用整型来存储数值的结果！———————“); for (int i = 0; i < resultInt.length; i++) { System.out.println(“resultInt[” + i + “] = “+ resultInt[i]); } System.out.println(“——————–用长整型来存储数值的结果！———————“); for (int i = 0; i < resultLong.length; i++) { System.out.println(“resultLong[” + i + “] = “+ resultLong[i]); } System.out.println(“——————–用BigInteger来存储数值的结果！———————“); for (int i = 0; i < resultBigInteger.length; i++) { System.out.println(“resultBigInteger[” + i + “] = “+ resultBigInteger[i]); } } }

结果：

——————–用整型来存储数值的结果！——————— resultInt[0] = 0 resultInt[1] = 1 resultInt[2] = 1 resultInt[3] = 2 resultInt[4] = 3 resultInt[5] = 5 resultInt[6] = 8 resultInt[7] = 13 resultInt[8] = 21 resultInt[9] = 34 resultInt[10] = 55 resultInt[11] = 89 resultInt[12] = 144 resultInt[13] = 233 resultInt[14] = 377 resultInt[15] = 610 resultInt[16] = 987 resultInt[17] = 1597 resultInt[18] = 2584 resultInt[19] = 4181 resultInt[20] = 6765 resultInt[21] = 10946 resultInt[22] = 17711 resultInt[23] = 28657 resultInt[24] = 46368 resultInt[25] = 75025 resultInt[26] = 121393 resultInt[27] = 196418 resultInt[28] = 317811 resultInt[29] = 514229 resultInt[30] = 832040 resultInt[31] = 1346269 resultInt[32] = 2178309 resultInt[33] = 3524578 resultInt[34] = 5702887 resultInt[35] = 9227465 resultInt[36] = 14930352 resultInt[37] = 24157817 resultInt[38] = 39088169 resultInt[39] = 63245986 resultInt[40] = 102334155 resultInt[41] = 165580141 resultInt[42] = 267914296 resultInt[43] = 433494437 resultInt[44] = 701408733 resultInt[45] = 1134903170 resultInt[46] = 1836311903 resultInt[47] = -1323752223 resultInt[48] = 512559680 resultInt[49] = -811192543 resultInt[50] = -298632863 resultInt[51] = -1109825406 resultInt[52] = -1408458269 resultInt[53] = 1776683621 resultInt[54] = 368225352 resultInt[55] = 2144908973 resultInt[56] = -1781832971 resultInt[57] = 363076002 resultInt[58] = -1418756969 resultInt[59] = -1055680967 resultInt[60] = 1820529360 resultInt[61] = 764848393 resultInt[62] = -1709589543 resultInt[63] = -944741150 resultInt[64] = 1640636603 resultInt[65] = 695895453 resultInt[66] = -1958435240 resultInt[67] = -1262539787 resultInt[68] = 1073992269 resultInt[69] = -188547518 resultInt[70] = 885444751 resultInt[71] = 696897233 resultInt[72] = 1582341984 resultInt[73] = -2015728079 resultInt[74] = -433386095 resultInt[75] = 1845853122 resultInt[76] = 1412467027 resultInt[77] = -1036647147 resultInt[78] = 375819880 resultInt[79] = -660827267 resultInt[80] = -285007387 resultInt[81] = -945834654 resultInt[82] = -1230842041 resultInt[83] = 2118290601 resultInt[84] = 887448560 resultInt[85] = -1289228135 resultInt[86] = -401779575 resultInt[87] = -1691007710 resultInt[88] = -2092787285 resultInt[89] = 511172301 resultInt[90] = -1581614984 resultInt[91] = -1070442683 resultInt[92] = 1642909629 resultInt[93] = 572466946 resultInt[94] = -2079590721 resultInt[95] = -1507123775 resultInt[96] = 708252800 resultInt[97] = -798870975 resultInt[98] = -90618175 resultInt[99] = -889489150 ——————–用长整型来存储数值的结果！——————— resultLong[0] = 0 resultLong[1] = 1 resultLong[2] = 1 resultLong[3] = 2 resultLong[4] = 3 resultLong[5] = 5 resultLong[6] = 8 resultLong[7] = 13 resultLong[8] = 21 resultLong[9] = 34 resultLong[10] = 55 resultLong[11] = 89 resultLong[12] = 144 resultLong[13] = 233 resultLong[14] = 377 resultLong[15] = 610 resultLong[16] = 987 resultLong[17] = 1597 resultLong[18] = 2584 resultLong[19] = 4181 resultLong[20] = 6765 resultLong[21] = 10946 resultLong[22] = 17711 resultLong[23] = 28657 resultLong[24] = 46368 resultLong[25] = 75025 resultLong[26] = 121393 resultLong[27] = 196418 resultLong[28] = 317811 resultLong[29] = 514229 resultLong[30] = 832040 resultLong[31] = 1346269 resultLong[32] = 2178309 resultLong[33] = 3524578 resultLong[34] = 5702887 resultLong[35] = 9227465 resultLong[36] = 14930352 resultLong[37] = 24157817 resultLong[38] = 39088169 resultLong[39] = 63245986 resultLong[40] = 102334155 resultLong[41] = 165580141 resultLong[42] = 267914296 resultLong[43] = 433494437 resultLong[44] = 701408733 resultLong[45] = 1134903170 resultLong[46] = 1836311903 resultLong[47] = 2971215073 resultLong[48] = 4807526976 resultLong[49] = 7778742049 resultLong[50] = 12586269025 resultLong[51] = 20365011074 resultLong[52] = 32951280099 resultLong[53] = 53316291173 resultLong[54] = 86267571272 resultLong[55] = 139583862445 resultLong[56] = 225851433717 resultLong[57] = 365435296162 resultLong[58] = 591286729879 resultLong[59] = 956722026041 resultLong[60] = 1548008755920 resultLong[61] = 2504730781961 resultLong[62] = 4052739537881 resultLong[63] = 6557470319842 resultLong[64] = 10610209857723 resultLong[65] = 17167680177565 resultLong[66] = 27777890035288 resultLong[67] = 44945570212853 resultLong[68] = 72723460248141 resultLong[69] = 117669030460994 resultLong[70] = 190392490709135 resultLong[71] = 308061521170129 resultLong[72] = 498454011879264 resultLong[73] = 806515533049393 resultLong[74] = 1304969544928657 resultLong[75] = 2111485077978050 resultLong[76] = 3416454622906707 resultLong[77] = 5527939700884757 resultLong[78] = 8944394323791464 resultLong[79] = 14472334024676221 resultLong[80] = 23416728348467685 resultLong[81] = 37889062373143906 resultLong[82] = 61305790721611591 resultLong[83] = 99194853094755497 resultLong[84] = 160500643816367088 resultLong[85] = 259695496911122585 resultLong[86] = 420196140727489673 resultLong[87] = 679891637638612258 resultLong[88] = 1100087778366101931 resultLong[89] = 1779979416004714189 resultLong[90] = 2880067194370816120 resultLong[91] = 4660046610375530309 resultLong[92] = 7540113804746346429 resultLong[93] = -6246583658587674878 resultLong[94] = 1293530146158671551 resultLong[95] = -4953053512429003327 resultLong[96] = -3659523366270331776 resultLong[97] = -8612576878699335103 resultLong[98] = 6174643828739884737 resultLong[99] = -2437933049959450366 ——————–用BigInteger来存储数值的结果！——————— resultBigInteger[0] = 0 resultBigInteger[1] = 1 resultBigInteger[2] = 1 resultBigInteger[3] = 2 resultBigInteger[4] = 3 resultBigInteger[5] = 5 resultBigInteger[6] = 8 resultBigInteger[7] = 13 resultBigInteger[8] = 21 resultBigInteger[9] = 34 resultBigInteger[10] = 55 resultBigInteger[11] = 89 resultBigInteger[12] = 144 resultBigInteger[13] = 233 resultBigInteger[14] = 377 resultBigInteger[15] = 610 resultBigInteger[16] = 987 resultBigInteger[17] = 1597 resultBigInteger[18] = 2584 resultBigInteger[19] = 4181 resultBigInteger[20] = 6765 resultBigInteger[21] = 10946 resultBigInteger[22] = 17711 resultBigInteger[23] = 28657 resultBigInteger[24] = 46368 resultBigInteger[25] = 75025 resultBigInteger[26] = 121393 resultBigInteger[27] = 196418 resultBigInteger[28] = 317811 resultBigInteger[29] = 514229 resultBigInteger[30] = 832040 resultBigInteger[31] = 1346269 resultBigInteger[32] = 2178309 resultBigInteger[33] = 3524578 resultBigInteger[34] = 5702887 resultBigInteger[35] = 9227465 resultBigInteger[36] = 14930352 resultBigInteger[37] = 24157817 resultBigInteger[38] = 39088169 resultBigInteger[39] = 63245986 resultBigInteger[40] = 102334155 resultBigInteger[41] = 165580141 resultBigInteger[42] = 267914296 resultBigInteger[43] = 433494437 resultBigInteger[44] = 701408733 resultBigInteger[45] = 1134903170 resultBigInteger[46] = 1836311903 resultBigInteger[47] = 2971215073 resultBigInteger[48] = 4807526976 resultBigInteger[49] = 7778742049 resultBigInteger[50] = 12586269025 resultBigInteger[51] = 20365011074 resultBigInteger[52] = 32951280099 resultBigInteger[53] = 53316291173 resultBigInteger[54] = 86267571272 resultBigInteger[55] = 139583862445 resultBigInteger[56] = 225851433717 resultBigInteger[57] = 365435296162 resultBigInteger[58] = 591286729879 resultBigInteger[59] = 956722026041 resultBigInteger[60] = 1548008755920 resultBigInteger[61] = 2504730781961 resultBigInteger[62] = 4052739537881 resultBigInteger[63] = 6557470319842 resultBigInteger[64] = 10610209857723 resultBigInteger[65] = 17167680177565 resultBigInteger[66] = 27777890035288 resultBigInteger[67] = 44945570212853 resultBigInteger[68] = 72723460248141 resultBigInteger[69] = 117669030460994 resultBigInteger[70] = 190392490709135 resultBigInteger[71] = 308061521170129 resultBigInteger[72] = 498454011879264 resultBigInteger[73] = 806515533049393 resultBigInteger[74] = 1304969544928657 resultBigInteger[75] = 2111485077978050 resultBigInteger[76] = 3416454622906707 resultBigInteger[77] = 5527939700884757 resultBigInteger[78] = 8944394323791464 resultBigInteger[79] = 14472334024676221 resultBigInteger[80] = 23416728348467685 resultBigInteger[81] = 37889062373143906 resultBigInteger[82] = 61305790721611591 resultBigInteger[83] = 99194853094755497 resultBigInteger[84] = 160500643816367088 resultBigInteger[85] = 259695496911122585 resultBigInteger[86] = 420196140727489673 resultBigInteger[87] = 679891637638612258 resultBigInteger[88] = 1100087778366101931 resultBigInteger[89] = 1779979416004714189 resultBigInteger[90] = 2880067194370816120 resultBigInteger[91] = 4660046610375530309 resultBigInteger[92] = 7540113804746346429 resultBigInteger[93] = 12200160415121876738 resultBigInteger[94] = 19740274219868223167 resultBigInteger[95] = 31940434634990099905 resultBigInteger[96] = 51680708854858323072 resultBigInteger[97] = 83621143489848422977 resultBigInteger[98] = 135301852344706746049 resultBigInteger[99] = 218922995834555169026