C.Interface.And.Implementations—bit vector的实现

最新推荐文章于 2023-12-29 15:06:23 发布

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#C #interface #bitset #bit vector

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本文详细介绍了位向量(Bit Vector)的概念及其实现细节，包括位向量的基本操作如设置、清除、取值等，以及高级操作如并集、交集、差集等。文章通过具体的代码示例展示了如何高效地管理和操作位向量，特别适用于需要处理大量离散整数集合的场景。

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1、The Bit interface exports functions that manipulate bit vectors, which can be used to represent sets of integers from zero to N− 1. For example, 256-bit vectors can be used to represent sets of characters efficiently.

2、Bit provides most of the set-manipulation functions provided by Set , and also a few functions that are specific to bit vectors.

3、Unlike the sets provided by Set , the sets represented by bit vectors have a well-defined universe, which is the set of integers in the range zero to N− 1. Thus, Bit can provide functions that Set cannot, such as the complement of a set.

本章bit vector类似于STL中的Bitsets，相当于一个很大的数组，数组的每一个元素是一位，每一位只存放1或者0。

由于都是0或者1，因此本章很多操作都是“&”“|”“^”等，由于之前这种代码很少写，正好趁此机会锻炼自己写运算代码的能力以及思维。

========================bit.h==================================

#ifndef BIT_INCLUDED
#define BIT_INCLUDED

#define T Bit_T
typedef struct T *T;

//exported functions
extern T    Bit_new   (int length);
extern int  Bit_length(T set);
extern int  Bit_count (T set);
extern void Bit_free  (T *set);
extern int  Bit_get   (T set, int n);
extern int  Bit_put   (T set, int n, int bit);
extern void Bit_clear (T set, int lo, int hi);
extern void Bit_set   (T set, int lo, int hi);
extern void Bit_not   (T set, int lo, int hi);
extern int  Bit_lt    (T s, T t);
extern int  Bit_eq    (T s, T t);
extern int  Bit_leq   (T s, T t);
extern void Bit_map   (T set,
    void apply(int n, int bit, void *cl), void *cl);
extern T    Bit_union (T s, T t);
extern T    Bit_inter (T s, T t);
extern T    Bit_minus (T s, T t);
extern T    Bit_diff  (T s, T t);

#undef T
#endif

===================bit.c============================

#include <stdarg.h>
#include <string.h>
#include "assert.h"
#include "bit.h"
#include "mem.h"

#define T Bit_T

struct T{
    int length;
    unsigned char *bytes;
    unsigned long *words;
};

//macros
#define BPW (8*sizeof(unsigned long))
#define nwords(len) ((((len)+BPW-1)&(~(BPW-1)))/BPW)
#define nbytes(len) ((((len)+8-1)&(~(8-1)))/8)
#define setop(sequal, snull, tnull, op)\
    if(s == t){ assert(s); return sequal; }\
    else if(s == NULL) { assert(t); return snull; }\
    else if(t == NULL) return tnull; \
    else{\
        int i; T set;\
        assert(s->length == t->length);\
        set = Bit_new(s->length);\
        for(i = nwords(s->length); --i >= 0; )\
            set->words[i] = s->words[i] op t->words[i];\
        return set;}

//static data
unsigned char msbmask[] = {
    0xFF, 0xFE, 0xFC, 0xF8,
    0xF0, 0xE0, 0xC0, 0x80
};

unsigned char lsbmask[] = {
    0x01, 0x03, 0x07, 0x0F,
    0x1F, 0x3F, 0x7F, 0xFF
};

//static functions
static T copy(T t){
    T set;

    assert(t);
    set = Bit_new(t->length);
    if(t->length > 0)
        memcpy(set->bytes, t->bytes, nbytes(t->length));
    return set;
}

//functions
T Bit_new(int length){
    T set;

    assert(length >= 0);
    NEW(set);
    if(length > 0)
        set->words = CALLOC(nwords(length),
            sizeof (unsigned long));
    else
        set->words = NULL;
    set->bytes = (unsigned char *)set->words;
    set->length = length;

    return set;
}

void Bit_free(T *set){
    assert(set && *set);
    FREE((*set)->words);
    FREE(*set);
}

int Bit_length(T set){
    assert(set);
    return set->length;
}

int Bit_count(T set){
    int length = 0, n;
    static char count[] = {
        0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4 };

    assert(set);
    for(n = nbytes(set->length); --n >= 0; ){
        unsigned char c = set->bytes[n];
        length += count[c&0xF] + count[c>>4];
    }

    return length;
}

int Bit_get(T set, int n){
    assert(set);
    assert(0 <= n && n < set->length);
    return ((set->bytes[n/8]>>(n%8))&1);
}

int Bit_put(T set, int n, int bit){
    int prev;

    assert(set);
    assert(bit == 0 || bit == 1);
    assert(0 <= n && n < set->length);
    prev = ((set->bytes[n/8]>>(n%8))&1);
    if(bit == 1)
        set->bytes[n/8] |= 1<<(n%8);
    else
        set->bytes[n/8] &= ~(1 <<(n%8));
    return prev;
}

void Bit_set(T set, int lo, int hi){
    //check set, lo, adn hi
    assert(set);
    assert(0 <= lo && hi < set->length);
    assert(lo <= hi);
    if(lo/8 < hi/8){
        //set the most significant bits in byte lo/8
        set->bytes[lo/8] |= msbmask[lo%8];
        //set all the bits in bytes lo/8+1..hi/8-1
        {
            int i;
            for(i = lo/8+1; i < hi/8; ++i)
                set->bytes[i] = 0xFF;
        }
        //set the least significant bits in byte in hi/8
        set->bytes[hi/8] |= lsbmask[hi%8];
    }else{
        //set bits lo%8..hi%8 in byte lo/8
        set->bytes[lo/8] |= (msbmask[lo%8]&lsbmask[hi%8]);
    }
}

void Bit_clear(T set, int lo, int hi){
    //check set, lo, and hi
    assert(set);
    assert(0 < lo && hi < set->length);
    assert(lo <= hi);
    if(lo/8 < hi/8){
        int i;
        set->bytes[lo/8] &= ~msbmask[lo%8];
        for(i = lo/8 + 1; i < hi/8; ++i)
            set->bytes[i] = 0;
        set->bytes[hi/8] &= ~lsbmask[hi%8];
    }else{
        set->bytes[lo/8] &= ~(msbmask[lo%8]&lsbmask[hi%8]);
    }
}

void Bit_not(T set, int lo, int hi){
    //check set, lo, and hi
    assert(set);
    assert(0 < lo && hi < set->length);
    assert(lo <= hi);
    if(lo/8 < hi/8){
        int i;
        set->bytes[lo/8] ^= msbmask[lo%8];
        for(i = lio/8 + 1; i < hi/8; ++i)
            set->bytes[i] ^= 0xFF;
        set->bytes[hi/8] ^= lsbmask[hi%8];
    }else{
        set->bytes[lo/8] ^= (msbmask[lo%8]&lsbmask[hi%8]);
    }
}

void Bit_map(T set,
    void apply(int n, int bit, void *cl), void *cl){
    int n;

    assert(set);
    for(n = 0; n < set->length; ++n)
        apply(n, ((set->bytes[n/8]>>(n%8))&1), cl);
}

int Bit_eq(T s, T t){
    int i;

    assert(s && t);
    assert(s->length == t->length);
    for(i = nwords(s->length); --i >= 0; )
        if(s->words[i] != t->words[i])
            return 0;
    return 1;
}

int Bit_leq(T s, T t){
    int i;
    
    assert(s && t);
    assert(s->length == t->length);
    for(i = nwords(s->length); --i >= 0; )
        if((s->words[i] & ~t->words[i]) != 0)
            return 0;
    return 1;
}

int Bit_lt(T s, T t){
    int i, lt = 0;

    assert(s && t);
    assert(s->length == t->length);
    for(i = nwords(s->length); --i >= 0; ){
        if((s->words[i]&~t->words[i]) != 0)
            return 0;
        else if(s->words[i] != t->words[i])
            lt |= 1;
    }

    return lt;
}

T Bit_union(T s, T t){
    setop(copy(t), copy(t), copy(s), |);
}

T Bit_inter(T s, T t){
    setop(copy(t),
        Bit_new(t->length), Bit_new(s->length), &);
}

T Bit_minus(T s, T t){
    setop(Bit_new(s->length),
        Bit_new(t->length), copy(s), &~);
}

T Bit_diff(T s, T t){
    setop(Bit_new(s->length), copy(t), copy(s), ^);
}