5 
BigInteger number = new BigInteger("7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450");
byte[] array = number.toByteArray();

System.out.println((int)array.length);

我正在为项目 euler 处理数字 8，其中数字的长度应该是 1000，但是每当我运行这个程序时，我都会收到 416。有人可以向我解释为什么这不起作用吗？

4

4 回答 4

6

这里一char不代表一，例如number只能用 1 表示byte 1100001011byte

同样在你的情况下

7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

是二进制的

1011001000110011100000101111011000010111001000110011110000001000000000010100100101011100100110100100001010111010001101011100100100011110110101101111001100110111101110101000011011011101011001010111001000000101110101100000100100010011010111010111100010100110000101010101101100000110100111000111001001011111001001010110110110111011010111100010111101001011010110111000110111111011011000110110110110110001110100001011010001101110110010011100010010000000011011100101110101100011110010010010110110001111101111101100010011000110001000111111001010111110001000111010000010000011110000111101011010011010100001011110001010000001001000101111110000110000011111110000010110100010110101100111011000000001100011100111000000000100100101110101000100010001010100101111001100110011000110001110101010100001010101011000111011010110010000101010100110010110111100011100011000001001011100111000001001101111111001101111011000111011110101101010001001000110100110010011110101001101110110000000010011100101011111110110101001101000011011111110001011001110111010010001110000010100111010001011101011111000111001000011010111111001000101010001101100001000111111011001010010101100000001001100111100011001010111111010011111100100101011011010000010100100101110000010101000110010011010001001100011101101111110001000001000011101011111111011010100010010101011111011101000010111011001000000001100011111101100111011001111111100100001100110111110110110000101101000101110101111000101101111010010101000000001110100111011001000011001100010001110001000010110110011000111001000110010100110111000010110110100110010100101111111000100101011001100111100111001011100000000100110110000110001001001111011110101100101010010010000111110101011111101010101101011001001010000011000110010010111101001000110001011111001111011101010111010110111111110101011010011011101000011010010110010110101001100100010110000000110101001100101010110110011000101011000111100011000100110010011101111011111111100101110000011111110000110010001100011111101011100110001001001010100101001100011110110110000101001111010101001011101000101011011011000010010000001000110001000100101000000110010000100101000101001101111010010011101010001110011001110000001011011001111100100110010101101011000101001111110011101101010001111000111101101110111001001111101001010000011001101000111110100000000100011101000101111101001111100101111101010000100011101100000110010010001001110010100101010101101000100111000001110100010011110110000100001111001001001010111101001111001100010101000110000101111100101110001110001000011001010001000001101111100010110001000111111010101110110100100111011100100010000011111100001100011001011110010111111100011111010010100100000111100110101011000010100011100100001000101011101110000011101010110100111101101110000110010011110101110110100011001101110111101010110100000010001011111110011000010111111111101101110011110010100101011100100111101000110100001011011011010101111100001101111010110011110111000000010101101000111000100101101010110010110110010100001000000110000110011100011000111101011010110011010000100000111000101101100111111101111110100110010010011001011001010110001110111011100110101010101011000110100100001000011101111011100111010001101101011111011111001010110111011101110000001110010011001101010000010110001100101101111011111011111000100010100001000011001100010101100010100100101011101111010

现在，如果您检查表示这个数字需要多少字节

更一般地，您可以通过以下方式检查

N二进制字符串的长度最多可以表示2^N - 1数字

对于长度：2 =（最大二进制字符串）11= 2^2 - 1 = 3（在 10 中）

于 2013-08-11T23:16:04.850 回答
3

这是因为toByteArray保存数字的二进制表示，而不是十进制表示。您可以认为每个字节代表 base-256 中的单个数字。这就是为什么表示所需的空间比小数位数少两倍多的原因。

如果您需要将每个数字保存为一个字节，请将您的转换BigInteger为String：它的长度将等于位数（如果数字为负数，则加一个字符作为减号'-'）。

于 2013-08-11T23:16:41.220 回答
1

我不知道 BigInteger 是如何存储值的，但我的猜测是，它不是将它们存储为字符串，每个数字一个字节，而是将它们存储为一个长数字，使用 log_2(n) 位来存储数字 n，因此使用了上限 (log_2(n) / 8) 个字节。

于 2013-08-11T23:16:27.790 回答
1

因为字节数组是以 256 为基数的数字（因为每个数字的范围可以是 0-255 或 0x00-0xFF），而输入数字是以 10 为基数的。当您将数字转换为字节数组时，您会获得一个位于不同的基数，因此具有不同数量的数字。

为了证明这一点，您可以应用对数底的变化：

logA(C) = logB(C) / logB(A)
log10(C) = log256(C) / log256(10)
1000 ~= 416 / log256(10)
1000 ~= 416 / (log2(10)/log2(256))
1000 ~= 416 / (3.3219/8)
1000 ~= 416 / 0.4152
1000 * 0.4152 ~= 416
415.2 ~= 416
于 2013-08-11T23:29:44.940 回答