/*
 * Sample hash functions for CS70.  Most of these functions hash
 * C-style strings (string), although a few work with integers.  Not
 * all of them have been extensively tested to be sure they generate
 * good hash values.
 *
 * All of the functions fall into one of two classes: integer hashers
 * and string hashers.  The integer hashers all take a signed integer
 * key; the string hashers take a C-style string (string).
 *
 * All functions return an unsigned integer suitable for use as a
 * hash-table index.  With one exception (hashStringBase256), this
 * integer can be larger than the size of the hash table, so the
 * caller must reduce the integer modulo the table size.
 *
 * The functions are:
 *
 * hashStringCRC	Uses a method sometimes called "modified CRC".
 *			This is a simple, fast algorithm that
 *			generates good hash values.  It is closely
 *			related to the hash algorithm used in ispell.
 * hashStringBase256	Treats a string as a very large base-256
 *			number and returns that number modulo the
 *			table size.  This is the only function that
 *			accepts the table size as an argument, and the
 *			only one that guarantees that its result will
 *			be in the range 0 to tableSize - 1.  It should
 *			produce good results but has not been tested
 *			extensively.
 * hashPJW		Uses a method recommended by Aho, Sethi, and
 *			Ullman's book on compilers.  Seems to generate
 *			pretty good values.
 * hashIntegerMultiply	Uses a multiplicative method.  Not extensively
 *			tested.
 * hashStringBUZ	Uses a randomization method that is intended
 *			to produce better hash values.  Seems to
 *			generate pretty good values, but doesn't do
 *			much better with the ispell dictionary than
 *			hashStringCRC.
 * hashIntegerBUZ	Uses the same randomization method by treating
 *			an integer as a 4-character string.
 * hashIntegerAbs	Returns the absolute value of the hashed
 *			integer.  Not extensively tested.  Should work
 *			well if the integer keys are well distributed
 *			and the table size is prime.
 * hashStringPreiss	Uses the method recommended in Preiss's book
 *			on data structures.  Not extensively tested.
 *			Probably produces poor hash values for long
 *			strings that differ only in the leading
 *			characters, especially if those characters are
 *			transpositions of each other.
 * hashStringWeiss1	Uses the method recommended in the first
 *			edition of Weiss's book on data structures.
 *			Not extensively tested.  Produces poor hash
 *			values for long strings that differ only in
 *			the leading characters.
 * hashStringWeiss2	Uses the method recommended in the second
 *			edition of Weiss's book on data structures.
 *			Not extensively tested.  Produces poor hash
 *			values for long strings that differ only in
 *			the leading characters.
 */

#include <string>

/*
 * Table of Contents:
 */

unsigned int	hashStringCRC(const string& key);
				// Hash a string using the fake-CRC XOR method
unsigned int	hashStringBase256(const string& key, unsigned int tableSize);
				// Hash a string by interpreting it in base 256
unsigned int	hashPJW(const string& key);
				// Hash a string with Aho/Sethi/Ullman's method
unsigned int	hashIntegerMultiply(int key);
				// Hash an integer multiplicatively
unsigned int	hashStringBUZ(const string& key);
				// Hash a string with the BUZ method
unsigned int	hashIntegerBUZ(int key);
				// Hash an integer with the BUZ method
static unsigned int hashBUZ(const unsigned char* key, int keyLength);
				// Helper function for BUZ hashing
unsigned int	hashIntegerAbs(int key);
				// Hash an integer by taking the absolute value
unsigned int	hashStringPreiss(const string& key);
				// Hash a string using Preiss's method
unsigned int	hashStringWeiss(const string& key);
				// Hash a string using Weiss's method

/*
 * Constants used by the various hash methods.  Constants marked with
 * a "32-BIT" comment are predicated on the assumption of a 32-bit
 * word, and won't work on a 16-bit or 64-bit machine.
 */
static const unsigned int BYTE_WIDTH = 8;
				// Number of bits in a byte
static const unsigned int WORD_WIDTH = sizeof (int) * BYTE_WIDTH;
				// Number of bits in a machine word (int), used
				// ..by several algorithms.

static const unsigned int CRC_HASH_SHIFT = 5;
				// How much to shift hash by, per char hashed

static const unsigned int PJW_HASH_SHIFT = 4;
				// How much to shift hash by, per char hashed
static const unsigned int PJW_HASH_RIGHT_SHIFT = 24;
				// Right-shift amount, if top 4 bits NZ
				// 32-BIT
static const unsigned int PJW_HASH_MASK = 0xf0000000;
				// Mask for extracting top 4 bits
				// 32-BIT

static const unsigned int PREISS_HASH_SHIFT = 6;
				// How much to shift hash by, per char hashed
static const unsigned int PREISS_HASH_MASK =
			    ~0U << (WORD_WIDTH - PREISS_HASH_SHIFT);
				// Mask for extracting top bits

static const unsigned int WEISS_HASH_SHIFT = 5;
				// How much to shift hash by, per char hashed
static const unsigned int WEISS_HASH_MULTIPLIER = 37;
				// How much to multiply by, per char hashed

/*
 * Constants for the BUZ algorithm.  BUZ_INIT is the initial value of
 * the hash function.  The lookup table is used to widen and randomize
 * the bytes of the key.  All values were gotten from /dev/random on a
 * Linux box.
 */
const unsigned int BUZINIT = 0x7b4402a2;
static unsigned int BUZ_Table[256] =
    {
    0xc70bb269, 0x13299943, 0xe9cee5e1, 0x32119a79,
    0xc2365851, 0x169ee8e3, 0x094c1ed8, 0x58e1d4e0,
    0x96eb1762, 0xfe296797, 0x89082f47, 0x27d5078d,
    0x8ebb9de0, 0x14df49e0, 0x38d21c63, 0x1f5b2770,
    0xaa6b0150, 0x7b0b656e, 0x98d37bc2, 0x4d7e85ec,
    0x987910e2, 0xb8cbac89, 0xa3f664a3, 0xeca3003c,
    0x7b364137, 0xb2a6edae, 0x5ef72906, 0x64a9e7b7,
    0x28cd6520, 0xca3c72df, 0x57398ce2, 0x8db893d4,
    0x0a5995cd, 0x2d109fb4, 0x0491162f, 0xb3488737,
    0x6fc4eb03, 0x9903cb21, 0xe82ff831, 0xb03ff8e5,
    0x054836ca, 0x5335e6f8, 0x01396c2a, 0xf9000899,
    0x03ed9d63, 0x2bf6946b, 0x9097fa8b, 0xacd8dfc7,
    0x8488b8a6, 0x0e39cd2e, 0xac1a4517, 0xcd49e035,
    0xe98b7e7b, 0xd3571502, 0xd602805e, 0xe7143cfe,
    0x46db0a6b, 0x0a4c9ebe, 0x4e2e1ca7, 0x3040fc62,
    0xe8818c02, 0x37155e7b, 0xe44ba138, 0x43cacdd4,
    0x53d986ba, 0xdd4dca35, 0x0f680f71, 0x6c1a551e,
    0x74263e95, 0xcfc4f5d5, 0x37b8ef45, 0xc00ac71d,
    0x3b059e0d, 0x208bc754, 0x41335fbe, 0x785a0ffc,
    0x189f024f, 0xd669c2d8, 0xe1b20f87, 0xba2550da,
    0x10167369, 0x85fad38f, 0x97d20e4e, 0x5bc0da5e,
    0x80799570, 0x93eb4058, 0x139042a6, 0x40b34bf6,
    0x15c21dfa, 0x8f852660, 0xa3d20fb3, 0x3d175cf9,
    0x792441a8, 0xdc5e71b5, 0x925f6350, 0x66e8d08b,
    0xc4606b59, 0x85d8b88c, 0x1ea4f459, 0x664f62bc,
    0x77407de3, 0x73d158ca, 0xb76ab172, 0xe9ed1aeb,
    0x93dc2009, 0xeb9da6ac, 0x3d26cf05, 0x675132bc,
    0xc29196fe, 0x2a62486f, 0x914e75e1, 0xa1c31883,
    0x1c28291c, 0xc73c668c, 0xf4ac07e6, 0x87c9a9ac,
    0xb7196ea7, 0x67cb7fa2, 0x55987797, 0x29ce38ea,
    0x427361b3, 0x5b5667a6, 0x68a72fb0, 0xcef8235a,
    0xd06e8f5b, 0x4d3633f5, 0x214d3a19, 0xbd09ec15,
    0x5c61c24b, 0x3928573c, 0x26083ab8, 0x857a5dee,
    0x3203e50c, 0x52a1a713, 0xa8270ee2, 0xdfb643a9,
    0x7797c1f3, 0x0f8ddc9f, 0x9368de21, 0x638ebd4e,
    0xd91808d7, 0x28ce69b8, 0xe424b0ce, 0xfe52fdef,
    0x89126c74, 0xdb5f3d91, 0xba488f47, 0x2b15cdb8,
    0xa517b0f9, 0x53950632, 0x1159546a, 0xe50f65a3,
    0x5f26b5d1, 0x68a3a955, 0xc2b78ea1, 0x49c33701,
    0x45457aee, 0xd49b550a, 0x244379b8, 0xec826af5,
    0x4fa6e0c9, 0xd4633425, 0x82f0bd85, 0xc23ccc2e,
    0xac73e11a, 0xdc94b283, 0x13e59bb2, 0x23b4880e,
    0x1d295c45, 0xef67488c, 0x6b74149e, 0xdf90d4ac,
    0xfc6e65a9, 0x406a3734, 0x86999303, 0xc73e7180,
    0x3c8a0b31, 0x75fa9249, 0xaca5e0e2, 0x4d0cc60d,
    0x4b174606, 0x836fb602, 0x4f9fc83a, 0xe16477a7,
    0xda1506a9, 0x905b28b7, 0x4229f5c2, 0xdf4c9144,
    0x731888e9, 0x2e37421f, 0x0c67c385, 0x44a2e520,
    0xfe3ee655, 0x92547582, 0x9525f4d4, 0xdaa8caf8,
    0xa25bd583, 0x0e315733, 0xd35fea29, 0xc9cfaa0f,
    0xc6bdf7e9, 0xa48b4e01, 0xfd30ffe0, 0xd0f63421,
    0x2b84803d, 0xe1b368a4, 0xbae5daa5, 0x4dd6336a,
    0xb60c4030, 0x7bb552f1, 0xf1b91481, 0xc8929b82,
    0xa1c22bf8, 0xd585aae4, 0x17fb4f6a, 0xa9c0d32e,
    0x2036f9b5, 0x3a95d611, 0xd554f25d, 0x3441153f,
    0x7fa89ff4, 0x8f91241c, 0x4b2cc5a9, 0xd3035a00,
    0x5c80707f, 0xe610fd47, 0xf60958c2, 0xb55a6fe7,
    0x3e1ba335, 0x2dead082, 0x1a8877e8, 0xd0791aad,
    0x9706ee52, 0xfb1dc525, 0x7fa1ba54, 0x6a3e9f81,
    0xa85a906a, 0x86ce1b46, 0x3b05833e, 0xc8d8fdcb,
    0x44e606c5, 0x8807beb2, 0xe46047d3, 0x85b9f5f8,
    0x56ed0cba, 0x3cf4e646, 0x970fd9dd, 0xd0600895,
    0x2d0a5f92, 0x891c4220, 0x017fbfe0, 0x4dde2016,
    0x3a6e421d, 0x7e3f2285, 0xdf7956e3, 0x52fdcf83
    };

/*
 * Hash a string using the modified CRC method.  The basic idea of
 * this function is that the hash value is rotated left by 5 bits and
 * then the next character is exclusive-or'ed in to the hash value.
 * The implementation is complicated by the lact of a rotate operation
 * in C++.
 *
 * This hash function does not work well with table sizes that are a
 * power of two.
 */
unsigned int hashStringCRC(		// Hash a string
    const string&	key)		// Key to be hashed
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	{
	/*
	 * The following expression could be done in one line, but it
	 * would be really nasty, and a modern compiler ought to
	 * generate the same code whether it's one line or several.
	 * So we'll break it up to make it easier to read.
	 *
	 * First, we shift the value left to make room for bits from
	 * the new key character.
	 */
	unsigned int leftShiftedValue = hashValue << CRC_HASH_SHIFT;
	/*
	 * Shifting left lost the top bits, so we have to extract and
	 * position them separately with a right shift.  If we were
	 * writing in assembly, we could do all of this in a single
	 * rotate instruction, but C++ doesn't give us access to that
	 * machine operation so we have to do it the hard way.
	 */
	unsigned int rightShiftedValue =
	  hashValue >> (WORD_WIDTH - CRC_HASH_SHIFT);
	/*
	 * Put the shifted values together, and then XOR them with the
	 * next key character (stepping past it in the process).
	 */
	hashValue = (leftShiftedValue | rightShiftedValue) ^ (unsigned)*i;
	}
    return hashValue;
    }

/*
 * Hash a string by interpreting it as a base-256 number.  Unlike the
 * other hash functions in this file, this function must be passed the
 * table size as an argument and performs the modulo function itself
 * (otherwise it wouldn't be able to generate a correct result).
 *
 * Note that instead of multiplying by 256, we shift left by 8 bits
 * (BYTE_WIDTH).  This is faster on almost all machines, and happens to be
 * a bit easier to write in C++ due to the definition of BYTE_WIDTH.
 */
unsigned int hashStringBase256(
    const string&	key,		// Key to be hashed
    unsigned int	tableSize)	// Size of hash table (hash modulus)
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	{
	hashValue = (hashValue << BYTE_WIDTH) + (unsigned)*i;
	hashValue %= tableSize;
	}
    return hashValue;
    }

/*
 * Hash a string using an algorithm taken from Aho, Sethi, and Ullman,
 * "Compilers: Principles, Techniques, and Tools," Addison-Wesley,
 * 1985, p. 436.  PJW stands for Peter J. Weinberger, who apparently
 * originally suggested the function.
 *
 * The basic idea of this algorithm is similar to that of the modified
 * CRC algorithm, except that instead of shifting the top bits right
 * so that they line up with the newly emptied bottom bits (a rotate),
 * the top bits are shifted only far enough to line up with the top
 * half of the character just XOR-ed into the hash value.
 */
unsigned int hashPJW(			// Hash a string, Aho/Sethi/Ullman
    const string&	key)		// Key to be hashed
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	{
	hashValue = (hashValue << PJW_HASH_SHIFT) + (unsigned)*i;
	unsigned int rotate_bits = hashValue & PJW_HASH_MASK;
	hashValue ^= rotate_bits | (rotate_bits >> PJW_HASH_RIGHT_SHIFT);
	}
    return hashValue;
    }

/*
 * Hash an integer by multiplication.  This algorithm was suggested by
 * Knuth.
 */
unsigned int hashIntegerMultiply(	// Hash an integer by multiplication
    int			key)		// Key to be hashed
    {
    return (unsigned int)key * (unsigned int)(key + 3);
    }

/*
 * Hash a string using the BUZ algorithm.  See the helper function for
 * more information on the origins and operation of the underlying
 * algorithm.
 *
 * After the string has been hashed according to the BUZ algorithm,
 * the resulting integer is re-hashed twice.  Bob Uzgalis claimed in
 * his lecture that this produced better hash values.
 *
 * The BUZ algorithm is the only string-hashing method in this file
 * that generates non-sequential hash values when the keys differ by
 * one in the last character (e.g., "foo1' and "foo2").  For this
 * reason, BUZ is a good choice if you are using linear probing and
 * you expect that many of your keys will differ only in the last
 * character (such as variable names).
 */
unsigned int hashStringBUZ (
    const string&	key)		// Key to be hashed
    {
    /*
     * Hash the string using the BUZ method (see hashBUZ).
     */
    unsigned int hashValue = BUZINIT;	// Result
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	{
	unsigned int ch = *i;
	if (hashValue & (1 << (WORD_WIDTH - 1)))
	    hashValue = ((hashValue << 1) | 1) ^ BUZ_Table[ch];
	else
	    hashValue = (hashValue << 1) ^ BUZ_Table[ch];
	}

    /*
     * Re-hash the hash value twice in hopes of getting more
     * randomness.  By casting &hashValue into a pointer to unsigned
     * character, we effectively treat it as a 4-character string
     * inside hashBUZ, and re-hash that string to get a new hash value.
     */
    hashValue = hashBUZ((unsigned char*)&hashValue, sizeof hashValue);
    return hashBUZ((unsigned char*)&hashValue, sizeof hashValue);
    }

/*
 * Hash an integer using the BUZ algorithm.  There's nothing fancy
 * here; see the comments at the end of hashStringBUZ and the comments
 * for hashBuz for more information.  We hash three times in hopes of
 * getting more randomness.
 */
unsigned int hashIntegerBUZ (
    int			key)		/* Key to be hashed */
    {
    unsigned int hashValue = hashBUZ((unsigned char*)&key, sizeof key);
    hashValue = hashBUZ((unsigned char*)&hashValue, sizeof hashValue);
    return hashBUZ((unsigned char*)&hashValue, sizeof hashValue);
    }

/*
 * Do one pass of the BUZ algorithm on a fixed key.
 *
 * The BUZ algorithm was invented by Robert (Bob) Uzgalis.  I don't
 * have a reference for it yet, because I learned it from a lecture,
 * not a paper.  The basic idea is to use a (constant) lookup table of
 * random numbers to generate wider random bits for each input
 * character.
 *
 * The innards of the function are very similar to the modified CRC
 * method, with one minor and one major change.  The minor change is
 * that the hash value is rotated only one bit at a time, rather than
 * 5.  The major change is that instead of XOR-ing the key character
 * in directly, the character is used as an index to look up a 32-bit
 * random number in a table.  The idea is that you get 32 bits of
 * information into the hash value at each step, rather than 8.  For
 * that reason, hashBUZ should work better with very short string keys
 * and very small integer keys.
 */
static unsigned int hashBUZ (
    const unsigned char* key,		/* Key to be hashed */
    int			keylen)		/* Length of the key */
    {
    unsigned int hashValue = BUZINIT;
    while (--keylen >= 0)
	{
	unsigned int ch = *key++;
	if (hashValue & (1 << (WORD_WIDTH - 1)))
	    hashValue = ((hashValue << 1) | 1) ^ BUZ_Table[ch];
	else
	    hashValue = (hashValue << 1) ^ BUZ_Table[ch];
	}
    return hashValue;
    }

/*
 * Hash an integer by taking the absolute value.  This is recommended
 * in Bruno Preiss, "Data Structures and Algorithms with
 * Object-Oriented Design Patterns in C++", Wiley, 1999, p. 210.
 *
 * I (Prof. Kuenning) do not have any particular reason to believe
 * that this is a good hash function.
 */
unsigned int hashIntegerAbs(
    int			key)		/* Key to be hashed */
    {
    if (key >= 0)
	return (unsigned int)key;
    else
	return (unsigned int)(-key);
    }

/*
 * Hash a string using the method given in Bruno Preiss, "Data
 * Structures and Algorithms with Object-Oriented Design Patterns in
 * C++", Wiley, 1999, p. 213.
 *
 * This is NOT a very good hash function, especially with non-prime
 * table sizes.
 *
 * This function is somewhat related to the modified CRC function.
 * However, instead of right-shifting the top bits back down so that
 * they have a further effect on the low bits, they are simply folded
 * back into the same (top) bits of the new hash value.  The net
 * result is that the first few characters of the key will only have
 * an effect on the top bits of the hash value.  If the table size is
 * a power of 2, this important early-character information will be
 * completely lost when the hash value is taken modulo the table size.
 */
unsigned int hashStringPreiss(
    const string&	key)		// Key to be hashed
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	hashValue = (hashValue & PREISS_HASH_MASK)
	  ^ (hashValue << PREISS_HASH_SHIFT)
	  ^ (unsigned)*i;
    return hashValue;
    }

/*
 * Hash a string using the method given in Mark Allen Weiss,
 * "Algorithms, Data Structures, and Problem Solving with C++" (first
 * edition), Addison-Wesley, 1996, p. 611.
 *
 * I (Prof. Kuenning) am suspicious of this hash function, but some
 * very quick tests suggest that it may work better than expected.
 *
 * Again, this function is related to the modified CRC function.
 * However, there is no attempt to preserve the top bits of the hash
 * value.  Instead, the bottom few bits of the function are just the
 * XOR of all the input characters.  This means that early information in the
 * key will be almost completely lost.
 */
unsigned int hashStringWeiss1(
    const string&	key)		// Key to be hashed
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	hashValue = hashValue ^ (hashValue << WEISS_HASH_SHIFT) ^ (unsigned)*i;
    return hashValue;
    }

/*
 * Hash a string using the method given in Mark Allen Weiss,
 * "Algorithms, Data Structures, and Problem Solving with C++" (second
 * edition), Addison-Wesley, 1999, p. 728.
 *
 * I (Prof. Kuenning) am very suspicious of this hash function.
 *
 * Again, this function is related to the modified CRC function.
 * However, as with hashStringWeiss1, there is no attempt to preserve
 * the top bits of the hash value.  Since the multiplier is not a
 * power of two, the bottom few bits (about 5) are a bit more
 * complicated than the XOR of all the input keys.  But again, the
 * early information in a long key will be lost.
 */
unsigned int hashStringWeiss2(
    const string&	key)		// Key to be hashed
    {
    unsigned int hashValue = 0;
    for (string::const_iterator i = key.begin();  i != key.end();  i++)
	hashValue = hashValue * WEISS_HASH_MULTIPLIER + (unsigned)*i;
    return hashValue;
    }