算法导论10.3-4：紧凑的双向链表

其他 2018-07-03 15:28:41 阅读次数: 0

题目：
我们往往希望双向链表的所有元素在存储器中保持紧凑，例如，在多数组表示中，占用前m个下标位置。（在页式虚拟存储的计算环境下，即为这种情况。）假设除指向聊表本身的指针外没有其他指针指向该链表元素，试说明如何实现过程ALLOCATE-OBJECT和FREE-OBJECT，使得该表保持紧凑。（提示：使用栈的数组实现。）
解答：
在某位大牛的算法导论中的答案中，分配链表元素位置时从数组最前向最后分配空间，若删除一个元素，且该元素在存储链表的数组中并非最后一个元素，则需将数组中处于该位置右端的所有链表元素左移。该种方法一次删除操作将消耗线性时间。
本文中采用的策略有所不同。分配链表元素位置时，也是从存储链表的数组的最前断向后分配。有如下约定：
L->free的位置之后的所有数组均为空，包含L->free位置均为可分配的位置。
每次删除除了L->free - 1位置的链表元素时，需将L->free - 1位置的元素移到被删除元素的位置，并将调整该元素前后元素的prev和next指向的位置，接着将L->free减去1，此时仍然保持了L->free和其后的所有数组元素均处于待分配状态。
一些函数和结构体的声明如下：

typedef struct TIGHT_DOUBLE_ARRAY_DOUBLE_LINKED_LIST
{
    int size;
    int count;
    int head;
    int free;
    item_t * key;
    int * next;
    int * prev;
} TDADLL;
void TDADLL_traverse(TDADLL * L);
TDADLL* TDADLL_init(int size);
item_t* TDADLL_get_object(TDADLL * L, int location);
int TDADLL_get_next(TDADLL * L, int location);
void TDADLL_set_next(TDADLL * L, int location, int next);
int TDADLL_get_prev(TDADLL * L, int location);
void TDADLL_set_prev(TDADLL * L, int location, int prev);
void TDADLL_move(TDADLL * L, int src, int dest);
int TDADLL_free(TDADLL * L, int location);
int TDADLL_allocate(TDADLL * L);
int TDADLL_insert(TDADLL * L, item_t item);
int TDADLL_search(TDADLL * L, item_t item);
int TDADLL_delete(TDADLL * L, item_t item);

实现如下：

//functions for tight static double array double linked list
void TDADLL_traverse(TDADLL * L) {
    if (L == NULL) {
        fprintf(stderr, "Not initialized.\n");
        return;
    }
    if (L->head == 0) {
        fprintf(stderr, "Empty linked list.\n");
    }
    int location = L->head;
    printf("Total elements number is %3d. Linked list size is %3d. Linked list head is %d\n", \
        L->count, L->size, L->head);
    while (location != 0) {
        printf("%3d item prev is %3d, location is %3d, next is %3d.\n", \
            TDADLL_get_object(L, location)->key, TDADLL_get_prev(L, location), location, \
            TDADLL_get_next(L, location));
        location = TDADLL_get_next(L, location);
    }
    printf("Free space start postion is %3d\n", L->free);
}
TDADLL* TDADLL_init(int size) {
    TDADLL * L = (TDADLL*)malloc(sizeof(TDADLL));
    if (!L) {
        fprintf(stderr, "Tight static double array double linked list init fail.\n");
        return NULL;
    }
    L->size = size;
    L->count = 0;
    L->head = 0;
    L->free = 1;
    L->key = (item_t*)calloc(size, sizeof(item_t));
    L->prev = (int*)calloc(size, sizeof(int));
    L->next = (int*)calloc(size, sizeof(int));
    if (!L->key || !L->next || !L->prev) {
        fprintf(stderr, "Tighe static double array double linked list content init fail.\n");
        return NULL;
    }
    return L;
}
item_t* TDADLL_get_object(TDADLL * L, int location) {
    return L->key + location - 1;
}
int TDADLL_get_next(TDADLL * L, int location) {
    return L->next[location - 1];
}
void TDADLL_set_next(TDADLL * L, int location, int next) {
    L->next[location - 1] = next;
}
int TDADLL_get_prev(TDADLL * L, int location) {
    return L->prev[location - 1];
}
void TDADLL_set_prev(TDADLL * L, int location, int prev) {
    L->prev[location - 1] = prev;
}
void TDADLL_move(TDADLL * L, int src, int dest) {
    if (src <= 0 || src > L->size || dest <= 0 || dest > L->size) {
        fprintf(stderr, "Move Out of range.\n");
        return;
    }
    L->next[dest - 1] = L->next[src - 1];
    L->prev[dest - 1] = L->prev[src - 1];
    L->key[dest - 1] = L->key[src - 1];
}
int TDADLL_free(TDADLL * L, int location) {
    if (location <= 0 || location > L->size) {
        fprintf(stderr, "Free %d Out of range.\n", location);
        return 0;
    }
    if (location >= L->free && L->free != 0) {
        fprintf(stderr, "Free %d Out of range.\n", location);
        return 0;
    }
    if (L->free == 0) {
        TDADLL_move(L, L->size, location);
        L->free = L->size;
        if (L->size == L->head)
            L->head = location;
    } else if (L->free != location + 1) {
        TDADLL_move(L, L->free - 1, location);
        L->free = L->free -1;
        if (L->free == L->head)
            L->head = location;
    } else {
        L->free--;
        return 1;
    }
    //printf("location: %d free:%d\n", location, L->free);
    int next = TDADLL_get_next(L, location);
    int prev = TDADLL_get_prev(L, location);
    if (next != 0) {
        TDADLL_set_prev(L, next, location);
    }
    if (prev != 0) {
        TDADLL_set_next(L, prev, location);
    }
    return 1;
}
int TDADLL_allocate(TDADLL * L) {
    if (L->free == 0) {
        fprintf(stderr, "Allocatet Out of range.\n");
        return 0;
    }
    int location = L->free;
    if (L->free == L->size) {
        L->free = 0;
    } else {
        L->free++;
    }
    return location;
}
int TDADLL_insert(TDADLL * L, item_t item) {
    if (L == NULL) {
        fprintf(stderr, "Not initialized.\n");
        return 0;
    }
    int location = TDADLL_allocate(L);
    if (location == 0) {
        fprintf(stderr, "Allocate location fail.\n");
        return location;
    }
    TDADLL_set_next(L, location, L->head);
    TDADLL_set_prev(L, location, 0);
    *TDADLL_get_object(L, location) = item;
    if (L->head != 0) {
        TDADLL_set_prev(L, L->head, location);
    }
    L->count++;
    L->head = location;
    return location;
}
int TDADLL_search(TDADLL * L, item_t item) {
    if (L == NULL) {
        fprintf(stderr, "Not initialized.\n");
        return 0;
    }
    if (L->head == 0) {
        fprintf(stderr, "Empty linked list.\n");
        return 0;
    }
    int location = L->head;
    while (location != 0) {
        if (TDADLL_get_object(L, location)->key == item.key) {
            return location;
        }
        location = TDADLL_get_next(L, location);
    }
    fprintf(stderr, "Item %d cannot be found.\n", item.key);
    return 0;
}
int TDADLL_delete(TDADLL * L, item_t item) {
    int location = TDADLL_search(L, item);
    if (location == 0) {
        fprintf(stderr, "Delete %d fail.\n", item.key);
        return 0;
    }
    int next = TDADLL_get_next(L, location);
    int prev = TDADLL_get_prev(L, location);
    //printf("location:%d next:%d prev:%d\n", location, next, prev);
    if (next != 0) {
        TDADLL_set_prev(L, next, prev);
    }
    if (prev != 0) {
        TDADLL_set_next(L, prev, next);
    }
    if (location == L->head) {
        L->head = next;
    }
    L->count--;
    //TDADLL_traverse(L);
    return TDADLL_free(L, location);
}
//--------------------------------------------------------------------------

可用如下代码进行测试：

void test_for_TDADLL() {
    TDADLL * L = TDADLL_init(SIZE);
    item_t item = {0, NULL};
    for (int i = 0; i < SIZE; ++i)
    {
        item.key = i;
        TDADLL_insert(L, item);
    }
    TDADLL_traverse(L);
    for (int i = 0; i < 10; ++i)
    {
        item.key = i + 10;
        TDADLL_delete(L, item);
    }
    TDADLL_traverse(L);
    for (int i = 0; i < SIZE; ++i)
    {
        item.key = i;
        TDADLL_delete(L, item);
    }
    TDADLL_traverse(L);
    printf("-------------------------------------------------------------------\n");
    for (int i = 0; i < SIZE; ++i)
    {
        item.key = i;
        TDADLL_insert(L, item);
    }
    TDADLL_traverse(L);
    for (int i = 0; i < 10; ++i)
    {
        item.key = i + 10;
        TDADLL_delete(L, item);
    }
    TDADLL_traverse(L);
    for (int i = SIZE; i >= -1; --i)
    {
        item.key = i;
        TDADLL_delete(L, item);
    }
    TDADLL_traverse(L);
}

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