为什么我的字节数组显示错误的长度？

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

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

I was working on number 8 for project euler, where the length of number is supposed to be 1000, but whenever I run this program, I receive 416. Could someone please explain to me why this isn't working?

我正在为项目euler工作8号,其中数字的长度应该是1000,但每当我运行这个程序时,我收到416.有人可以向我解释为什么这不起作用?

4 个解决方案

#1

one char doesn't mean one byte here, for example number 11 is 00001011 which can be represented by just 1 byte

一个char在这里并不意味着一个字节,例如,数字11是00001011,其可以仅由1个字节表示

Similarly in your case

同样在你的情况下

7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

is in binary

是二进制的

1011001000110011100000101111011000010111001000110011110000001000000000010100100101011100100110100100001010111010001101011100100100011110110101101111001100110111101110101000011011011101011001010111001000000101110101100000100100010011010111010111100010100110000101010101101100000110100111000111001001011111001001010110110110111011010111100010111101001011010110111000110111111011011000110110110110110001110100001011010001101110110010011100010010000000011011100101110101100011110010010010110110001111101111101100010011000110001000111111001010111110001000111010000010000011110000111101011010011010100001011110001010000001001000101111110000110000011111110000010110100010110101100111011000000001100011100111000000000100100101110101000100010001010100101111001100110011000110001110101010100001010101011000111011010110010000101010100110010110111100011100011000001001011100111000001001101111111001101111011000111011110101101010001001000110100110010011110101001101110110000000010011100101011111110110101001101000011011111110001011001110111010010001110000010100111010001011101011111000111001000011010111111001000101010001101100001000111111011001010010101100000001001100111100011001010111111010011111100100101011011010000010100100101110000010101000110010011010001001100011101101111110001000001000011101011111111011010100010010101011111011101000010111011001000000001100011111101100111011001111111100100001100110111110110110000101101000101110101111000101101111010010101000000001110100111011001000011001100010001110001000010110110011000111001000110010100110111000010110110100110010100101111111000100101011001100111100111001011100000000100110110000110001001001111011110101100101010010010000111110101011111101010101101011001001010000011000110010010111101001000110001011111001111011101010111010110111111110101011010011011101000011010010110010110101001100100010110000000110101001100101010110110011000101011000111100011000100110010011101111011111111100101110000011111110000110010001100011111101011100110001001001010100101001100011110110110000101001111010101001011101000101011011011000010010000001000110001000100101000000110010000100101000101001101111010010011101010001110011001110000001011011001111100100110010101101011000101001111110011101101010001111000111101101110111001001111101001010000011001101000111110100000000100011101000101111101001111100101111101010000100011101100000110010010001001110010100101010101101000100111000001110100010011110110000100001111001001001010111101001111001100010101000110000101111100101110001110001000011001010001000001101111100010110001000111111010101110110100100111011100100010000011111100001100011001011110010111111100011111010010100100000111100110101011000010100011100100001000101011101110000011101010110100111101101110000110010011110101110110100011001101110111101010110100000010001011111110011000010111111111101101110011110010100101011100100111101000110100001011011011010101111100001101111010110011110111000000010101101000111000100101101010110010110110010100001000000110000110011100011000111101011010110011010000100000111000101101100111111101111110100110010010011001011001010110001110111011100110101010101011000110100100001000011101111011100111010001101101011111011111001010110111011101110000001110010011001101010000010110001100101101111011111011111000100010100001000011001100010101100010100100101011101111010

Now if you check how many byte it requires to represent this number

现在,如果您检查表示此数字所需的字节数

---

More generally you can check this by

更一般地说,你可以检查一下

N length of binary string can represent up to 2^N - 1 number

N长度的二进制字符串可以表示最多2 ^ N - 1个数字

For length: 2 = (max binary string) 11 = 2^2 - 1 = 3 (in 10)

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

#2

This is because the toByteArray saves the binary representation of the number, not a decimal one. You can think of each byte representing a single digit in base-256. That's why the space required for the representation is more than twice less than the number of decimal digits.

这是因为toByteArray保存了数字的二进制表示,而不是十进制表示。你可以想到代表base-256中单个数字的每个字节。这就是为什么表示所需的空间比十进制数字少两倍以上的原因。

If you need to save each digit to a byte, convert your BigInteger to String: its length is going to equal the number of digits (plus one character for the minus character '-' if the number is negative).

如果需要将每个数字保存为一个字节,请将BigInteger转换为字符串:其长度将等于数字位数(如果数字为负数,则加上减号字符' - '的一个字符)。

#3

I don't know precisely how BigInteger stores values, but my guess would be that rather than storing them as a string, with one byte per digit, it stores them as one long number, with log_2(n) bits being used to store the number n, and therefore ceiling(log_2(n) / 8) bytes being used.

我不确切知道BigInteger如何存储值,但我的猜测是,不是将它们存储为字符串,每个数字一个字节,它将它们存储为一个长数字,log_2(n)位用于存储数字n,因此使用ceiling(log_2(n)/ 8)个字节。

#4

Because a byte array is a number in base 256 (since every digit can have range 0-255 or 0x00-0xFF) while the input number is in base 10. When you convert your number into a byte array you obtain a number which is in a different base, hence has a different amount of digits.

因为字节数组是基数256的数字(因为每个数字的范围可以是0-255或0x00-0xFF),而输入数字是基数10.当您将数字转换为字节数组时,您将获得一个数字不同的基数,因此具有不同的数字量。

To prove it you can apply the change of base of logarithms:

为了证明这一点,你可以应用对数基数的变化:

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