為什么我的字節數組顯示錯誤的長度？

Question

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

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

我正在為項目euler工作8號，其中數字的長度應該是1000，但每當我運行這個程序時，我收到416.有人可以向我解釋為什么這不起作用？

Answer 1

一個char 在這里並不意味着一個byte ， 例如，數字11是00001011 ，它可以僅由1 byte表示

同樣在你的情況下

7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

是二進制的

1011001000110011100000101111011000010111001000110011110000001000000000010100100101011100100110100100001010111010001101011100100100011110110101101111001100110111101110101000011011011101011001010111001000000101110101100000100100010011010111010111100010100110000101010101101100000110100111000111001001011111001001010110110110111011010111100010111101001011010110111000110111111011011000110110110110110001110100001011010001101110110010011100010010000000011011100101110101100011110010010010110110001111101111101100010011000110001000111111001010111110001000111010000010000011110000111101011010011010100001011110001010000001001000101111110000110000011111110000010110100010110101100111011000000001100011100111000000000100100101110101000100010001010100101111001100110011000110001110101010100001010101011000111011010110010000101010100110010110111100011100011000001001011100111000001001101111111001101111011000111011110101101010001001000110100110010011110101001101110110000000010011100101011111110110101001101000011011111110001011001110111010010001110000010100111010001011101011111000111001000011010111111001000101010001101100001000111111011001010010101100000001001100111100011001010111111010011111100100101011011010000010100100101110000010101000110010011010001001100011101101111110001000001000011101011111111011010100010010101011111011101000010111011001000000001100011111101100111011001111111100100001100110111110110110000101101000101110101111000101101111010010101000000001110100111011001000011001100010001110001000010110110011000111001000110010100110111000010110110100110010100101111111000100101011001100111100111001011100000000100110110000110001001001111011110101100101010010010000111110101011111101010101101011001001010000011000110010010111101001000110001011111001111011101010111010110111111110101011010011011101000011010010110010110101001100100010110000000110101001100101010110110011000101011000111100011000100110010011101111011111111100101110000011111110000110010001100011111101011100110001001001010100101001100011110110110000101001111010101001011101000101011011011000010010000001000110001000100101000000110010000100101000101001101111010010011101010001110011001110000001011011001111100100110010101101011000101001111110011101101010001111000111101101110111001001111101001010000011001101000111110100000000100011101000101111101001111100101111101010000100011101100000110010010001001110010100101010101101000100111000001110100010011110110000100001111001001001010111101001111001100010101000110000101111100101110001110001000011001010001000001101111100010110001000111111010101110110100100111011100100010000011111100001100011001011110010111111100011111010010100100000111100110101011000010100011100100001000101011101110000011101010110100111101101110000110010011110101110110100011001101110111101010110100000010001011111110011000010111111111101101110011110010100101011100100111101000110100001011011011010101111100001101111010110011110111000000010101101000111000100101101010110010110110010100001000000110000110011100011000111101011010110011010000100000111000101101100111111101111110100110010010011001011001010110001110111011100110101010101011000110100100001000011101111011100111010001101101011111011111001010110111011101110000001110010011001101010000010110001100101101111011111011111000100010100001000011001100010101100010100100101011101111010

現在，如果您檢查表示此數字所需的字節數

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更一般地說，你可以檢查一下

N長度的二進制字符串可以表示最多2^N - 1數字

長度 ：2 =（最大二進制字符串） 11 = 2 ^ 2 - 1 = 3（10）

Answer 2

這是因為toByteArray保存了數字的二進制表示，而不是十進制表示。 你可以想到代表base-256中單個數字的每個字節。 這就是為什么表示所需的空間比十進制數字少兩倍以上的原因。

如果需要將每個數字保存為一個字節，請將BigInteger轉換為String ：其長度將等於數字位數（如果數字為負數，則加上減號字符'-'一個字符）。

Answer 3

我不確切知道BigInteger如何存儲值，但我的猜測是，不是將它們存儲為字符串，每個數字一個字節，它將它們存儲為一個長數字，其中log_2（n）位用於存儲數字n，因此使用的是ceiling（log_2（n）/ 8）個字節。

Answer 4

因為字節數組是基數為256的數字（因為每個數字的范圍可以是0-255或0x00-0xFF），而輸入數字是基數10.當您將數字轉換為字節數組時，您將獲得一個數字不同的基數，因此具有不同的數字量。

為了證明這一點，你可以應用對數基數的變化：

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