学习 BigInteger
以下是摘抄与其他人的：
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用Java来处理高精度问题，相信对很多ACMer来说都是一件很happy的事，简单易懂。用Java刷了一些题，感觉Java还不错，在处理高精度和进制转换中，调用库函数的来处理。下面是写的一些Java中一些基本的函数的及其…… 头文件：import java.io.*; import java.util.*; import java.math.*; 读入： Scanner cin = Scanner (System.in); while(cin.hasNext())//等价于!=EOF n=cin.nextInt();//读入一个int型的数 n=cin.nextBigInteger();//读入一个大整数 输出： System.out.print(n);//打印n System.out.println();//换行 System.out.printf("%d\n",n);//也可以类似c++里的输出方式 定义： int i,j,k,a[]; a = new int[100]; BigInteger n,m; BigDecimal n; String s; 数据类型： 数据类型 类型名 位长 取值范围 默认值 布尔型 boolean 1 true,false false 字节型 byte 8 -128-127 0 字符型 char 16 ‘\u000’-\uffff ‘\u0000’ 短整型 short 16 -32768-32767 0 整型 int 32 -2147483648,2147483647 0 长整型 long 64 -9.22E18,9.22E18 0 浮点型 float 32 1.4E-45-3.4028E+38 0.0 双精度型 double 64 4.9E-324,1.7977E+308 0.0 这里特别要提出出的两种类型： BigInteger 任意大的整数，原则上是，只要你的计算机的内存足够大，可以有无限位的 BigInteger 任意大的实数，可以处理小数精度问题。 BigInteger中一些常见的函数： A=BigInteger.ONE B=BigInteger.TEN C=BigInteger.ZERO 一些常见的数的赋初值。将int型的数赋值给BigInteger，BigInteger.valueOf(k); 基本的函数： valueOf:赋初值 add:+ a.add(b); subtract:- multiply:* divide:/ remainder：this % val divideAndRemainder：a[0]=this / val; a[1]=this % val pow：a.pow(b)=a^b gcd,abs:公约数，绝对值 negate：取负数 signum：符号函数 mod：a.mod(b)=a%b; shiftLeft:左移，this << n ，this*2^n; shiftRight:右移，this >> n，this/2^n; and:等同于c++的&&,且； or：||，或; xor:异或，BigInteger xor(BigInteger val),this^val not:!,非； bitLength：返回该数的最小二进制补码表示的位的个数，即 *不包括* 符号位 (ceil(log2(this <0 ? -this : this + 1)))。对正数来说，这等价于普通二进制表示的位的个数。 bitCount：返回该数的二进制补码表示中不包扩符号位在内的位的个数。该方法在 BigIntegers 之上实现位向量风格的集合时很有用。 isProbablePrime：如果该 BigInteger 可能是素数，则返回 true ；如果它很明确是一个合数，则返回 false 。 参数 certainty 是对调用者愿意忍受的不确定性的度量：如果该数是素数的概率超过了 1 - 1/2**certainty方法，则该方法返回 true 。执行时间正比于参数确定性的值。 compareTo：根据该数值是小于、等于、或大于 val 返回 -1、0 或 1； equals：判断两数是否相等，也可以用compareTo来代替； min，max：取两个数的较小、大者； intValue，longValue，floatValue，doublue：把该数转换为该类型的数的值。
今天参考课本写了一个关于二进制与十进制转换的程序，程序算法不难，但写完后测试发现不论是二转十还是十转二，对于大于21亿即超过整数范围的数不能很好的转换。都会变成0. 1，BigInteger属于java.math.BigInteger,因此在每次使用前都要import 这个类。偶开始就忘记import了，于是总提示找不到提示符。 2，其构造方法有很多，但现在偶用到的有： BigInteger(String val) 3，BigInteger类模拟了所有的int型数学操作，如add()==“+”,divide()==“-”等，但注意其内容进行数学运算时不能直接使用数学运算符进行运算，必须使用其内部方法。而且其操作数也必须为BigInteger型。 4，当要把计算结果输出时应该使用.toString方法将其转换为10进制的字符串，详细说明如下： 5,另外说明三个个用到的函数。 BigInteger remainder(BigInteger val) compareTo 将BigInteger的数转为2进制： public class TestChange { |
其中以实现 Fibonacci数列 进行练习
Fibonacci数列的递推公式为：Fn=Fn-1+Fn-2，其中F1=F2=1。
当n比较大时，Fn也非常大，现在我们想知道，Fn除以10007的余数是多少。
说明：在本题中，答案是要求Fn除以10007的余数，因此我们只要能算出这个余数即可，而不需要先计算出Fn的准确值，再将计算的结果除以10007取余数，直接计算余数往往比先算出原数再取余简单。
import java.util.Scanner;
import java.math.BigInteger;
public class BigIntegerFibnaccui {
public static void main(String[] args) {
Scanner sc= new Scanner(System.in);
int num = sc.nextInt();
int[] resultInt = new int[num];
resultInt[0] = 1;
resultInt[1] = 1;
long[] resultLong = new long[num];
resultLong[0] = 1L;
resultLong[1] = 1L;
BigInteger[] resultBigInteger = new BigInteger[num];
resultBigInteger[0] = BigInteger.ONE;
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("--------------------output int---------------------");
for (int i = 0; i < resultInt.length; i++) {
System.out.println("resultInt[" + i + "] = "+ resultInt[i]);
}
System.out.println("--------------------output long---------------------");
for (int i = 0; i < resultLong.length; i++) {
System.out.println("resultLong[" + i + "] = "+ resultLong[i]);
}
System.out.println("--------------------output bigInteger---------------------");
for (int i = 0; i < resultBigInteger.length; i++) {
System.out.println("resultBigInteger[" + i + "] = "+ resultBigInteger[i]);
}
}
}
心得：
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。
结果：
100
--------------------output int---------------------
resultInt[0] = 1
resultInt[1] = 1
resultInt[2] = 2
resultInt[3] = 3
resultInt[4] = 5
resultInt[5] = 8
resultInt[6] = 13
resultInt[7] = 21
resultInt[8] = 34
resultInt[9] = 55
resultInt[10] = 89
resultInt[11] = 144
resultInt[12] = 233
resultInt[13] = 377
resultInt[14] = 610
resultInt[15] = 987
resultInt[16] = 1597
resultInt[17] = 2584
resultInt[18] = 4181
resultInt[19] = 6765
resultInt[20] = 10946
resultInt[21] = 17711
resultInt[22] = 28657
resultInt[23] = 46368
resultInt[24] = 75025
resultInt[25] = 121393
resultInt[26] = 196418
resultInt[27] = 317811
resultInt[28] = 514229
resultInt[29] = 832040
resultInt[30] = 1346269
resultInt[31] = 2178309
resultInt[32] = 3524578
resultInt[33] = 5702887
resultInt[34] = 9227465
resultInt[35] = 14930352
resultInt[36] = 24157817
resultInt[37] = 39088169
resultInt[38] = 63245986
resultInt[39] = 102334155
resultInt[40] = 165580141
resultInt[41] = 267914296
resultInt[42] = 433494437
resultInt[43] = 701408733
resultInt[44] = 1134903170
resultInt[45] = 1836311903
resultInt[46] = -1323752223
resultInt[47] = 512559680
resultInt[48] = -811192543
resultInt[49] = -298632863
resultInt[50] = -1109825406
resultInt[51] = -1408458269
resultInt[52] = 1776683621
resultInt[53] = 368225352
resultInt[54] = 2144908973
resultInt[55] = -1781832971
resultInt[56] = 363076002
resultInt[57] = -1418756969
resultInt[58] = -1055680967
resultInt[59] = 1820529360
resultInt[60] = 764848393
resultInt[61] = -1709589543
resultInt[62] = -944741150
resultInt[63] = 1640636603
resultInt[64] = 695895453
resultInt[65] = -1958435240
resultInt[66] = -1262539787
resultInt[67] = 1073992269
resultInt[68] = -188547518
resultInt[69] = 885444751
resultInt[70] = 696897233
resultInt[71] = 1582341984
resultInt[72] = -2015728079
resultInt[73] = -433386095
resultInt[74] = 1845853122
resultInt[75] = 1412467027
resultInt[76] = -1036647147
resultInt[77] = 375819880
resultInt[78] = -660827267
resultInt[79] = -285007387
resultInt[80] = -945834654
resultInt[81] = -1230842041
resultInt[82] = 2118290601
resultInt[83] = 887448560
resultInt[84] = -1289228135
resultInt[85] = -401779575
resultInt[86] = -1691007710
resultInt[87] = -2092787285
resultInt[88] = 511172301
resultInt[89] = -1581614984
resultInt[90] = -1070442683
resultInt[91] = 1642909629
resultInt[92] = 572466946
resultInt[93] = -2079590721
resultInt[94] = -1507123775
resultInt[95] = 708252800
resultInt[96] = -798870975
resultInt[97] = -90618175
resultInt[98] = -889489150
resultInt[99] = -980107325
--------------------output long---------------------
resultLong[0] = 1
resultLong[1] = 1
resultLong[2] = 2
resultLong[3] = 3
resultLong[4] = 5
resultLong[5] = 8
resultLong[6] = 13
resultLong[7] = 21
resultLong[8] = 34
resultLong[9] = 55
resultLong[10] = 89
resultLong[11] = 144
resultLong[12] = 233
resultLong[13] = 377
resultLong[14] = 610
resultLong[15] = 987
resultLong[16] = 1597
resultLong[17] = 2584
resultLong[18] = 4181
resultLong[19] = 6765
resultLong[20] = 10946
resultLong[21] = 17711
resultLong[22] = 28657
resultLong[23] = 46368
resultLong[24] = 75025
resultLong[25] = 121393
resultLong[26] = 196418
resultLong[27] = 317811
resultLong[28] = 514229
resultLong[29] = 832040
resultLong[30] = 1346269
resultLong[31] = 2178309
resultLong[32] = 3524578
resultLong[33] = 5702887
resultLong[34] = 9227465
resultLong[35] = 14930352
resultLong[36] = 24157817
resultLong[37] = 39088169
resultLong[38] = 63245986
resultLong[39] = 102334155
resultLong[40] = 165580141
resultLong[41] = 267914296
resultLong[42] = 433494437
resultLong[43] = 701408733
resultLong[44] = 1134903170
resultLong[45] = 1836311903
resultLong[46] = 2971215073
resultLong[47] = 4807526976
resultLong[48] = 7778742049
resultLong[49] = 12586269025
resultLong[50] = 20365011074
resultLong[51] = 32951280099
resultLong[52] = 53316291173
resultLong[53] = 86267571272
resultLong[54] = 139583862445
resultLong[55] = 225851433717
resultLong[56] = 365435296162
resultLong[57] = 591286729879
resultLong[58] = 956722026041
resultLong[59] = 1548008755920
resultLong[60] = 2504730781961
resultLong[61] = 4052739537881
resultLong[62] = 6557470319842
resultLong[63] = 10610209857723
resultLong[64] = 17167680177565
resultLong[65] = 27777890035288
resultLong[66] = 44945570212853
resultLong[67] = 72723460248141
resultLong[68] = 117669030460994
resultLong[69] = 190392490709135
resultLong[70] = 308061521170129
resultLong[71] = 498454011879264
resultLong[72] = 806515533049393
resultLong[73] = 1304969544928657
resultLong[74] = 2111485077978050
resultLong[75] = 3416454622906707
resultLong[76] = 5527939700884757
resultLong[77] = 8944394323791464
resultLong[78] = 14472334024676221
resultLong[79] = 23416728348467685
resultLong[80] = 37889062373143906
resultLong[81] = 61305790721611591
resultLong[82] = 99194853094755497
resultLong[83] = 160500643816367088
resultLong[84] = 259695496911122585
resultLong[85] = 420196140727489673
resultLong[86] = 679891637638612258
resultLong[87] = 1100087778366101931
resultLong[88] = 1779979416004714189
resultLong[89] = 2880067194370816120
resultLong[90] = 4660046610375530309
resultLong[91] = 7540113804746346429
resultLong[92] = -6246583658587674878
resultLong[93] = 1293530146158671551
resultLong[94] = -4953053512429003327
resultLong[95] = -3659523366270331776
resultLong[96] = -8612576878699335103
resultLong[97] = 6174643828739884737
resultLong[98] = -2437933049959450366
resultLong[99] = 3736710778780434371
--------------------output bigInteger---------------------
resultBigInteger[0] = 1
resultBigInteger[1] = 1
resultBigInteger[2] = 2
resultBigInteger[3] = 3
resultBigInteger[4] = 5
resultBigInteger[5] = 8
resultBigInteger[6] = 13
resultBigInteger[7] = 21
resultBigInteger[8] = 34
resultBigInteger[9] = 55
resultBigInteger[10] = 89
resultBigInteger[11] = 144
resultBigInteger[12] = 233
resultBigInteger[13] = 377
resultBigInteger[14] = 610
resultBigInteger[15] = 987
resultBigInteger[16] = 1597
resultBigInteger[17] = 2584
resultBigInteger[18] = 4181
resultBigInteger[19] = 6765
resultBigInteger[20] = 10946
resultBigInteger[21] = 17711
resultBigInteger[22] = 28657
resultBigInteger[23] = 46368
resultBigInteger[24] = 75025
resultBigInteger[25] = 121393
resultBigInteger[26] = 196418
resultBigInteger[27] = 317811
resultBigInteger[28] = 514229
resultBigInteger[29] = 832040
resultBigInteger[30] = 1346269
resultBigInteger[31] = 2178309
resultBigInteger[32] = 3524578
resultBigInteger[33] = 5702887
resultBigInteger[34] = 9227465
resultBigInteger[35] = 14930352
resultBigInteger[36] = 24157817
resultBigInteger[37] = 39088169
resultBigInteger[38] = 63245986
resultBigInteger[39] = 102334155
resultBigInteger[40] = 165580141
resultBigInteger[41] = 267914296
resultBigInteger[42] = 433494437
resultBigInteger[43] = 701408733
resultBigInteger[44] = 1134903170
resultBigInteger[45] = 1836311903
resultBigInteger[46] = 2971215073
resultBigInteger[47] = 4807526976
resultBigInteger[48] = 7778742049
resultBigInteger[49] = 12586269025
resultBigInteger[50] = 20365011074
resultBigInteger[51] = 32951280099
resultBigInteger[52] = 53316291173
resultBigInteger[53] = 86267571272
resultBigInteger[54] = 139583862445
resultBigInteger[55] = 225851433717
resultBigInteger[56] = 365435296162
resultBigInteger[57] = 591286729879
resultBigInteger[58] = 956722026041
resultBigInteger[59] = 1548008755920
resultBigInteger[60] = 2504730781961
resultBigInteger[61] = 4052739537881
resultBigInteger[62] = 6557470319842
resultBigInteger[63] = 10610209857723
resultBigInteger[64] = 17167680177565
resultBigInteger[65] = 27777890035288
resultBigInteger[66] = 44945570212853
resultBigInteger[67] = 72723460248141
resultBigInteger[68] = 117669030460994
resultBigInteger[69] = 190392490709135
resultBigInteger[70] = 308061521170129
resultBigInteger[71] = 498454011879264
resultBigInteger[72] = 806515533049393
resultBigInteger[73] = 1304969544928657
resultBigInteger[74] = 2111485077978050
resultBigInteger[75] = 3416454622906707
resultBigInteger[76] = 5527939700884757
resultBigInteger[77] = 8944394323791464
resultBigInteger[78] = 14472334024676221
resultBigInteger[79] = 23416728348467685
resultBigInteger[80] = 37889062373143906
resultBigInteger[81] = 61305790721611591
resultBigInteger[82] = 99194853094755497
resultBigInteger[83] = 160500643816367088
resultBigInteger[84] = 259695496911122585
resultBigInteger[85] = 420196140727489673
resultBigInteger[86] = 679891637638612258
resultBigInteger[87] = 1100087778366101931
resultBigInteger[88] = 1779979416004714189
resultBigInteger[89] = 2880067194370816120
resultBigInteger[90] = 4660046610375530309
resultBigInteger[91] = 7540113804746346429
resultBigInteger[92] = 12200160415121876738
resultBigInteger[93] = 19740274219868223167
resultBigInteger[94] = 31940434634990099905
resultBigInteger[95] = 51680708854858323072
resultBigInteger[96] = 83621143489848422977
resultBigInteger[97] = 135301852344706746049
resultBigInteger[98] = 218922995834555169026
resultBigInteger[99] = 354224848179261915075
请按任意键继续. . .
如上可以见:用BigInteger不会出现负数形式！
