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调试合并排序

mergesort debugging c

Christoph · 技术社区 · 16 年前

移植数组的迭代版本会降低性能,因为重新扫描列表以将其划分为子列表的速度很慢;对于任何感兴趣的人,这是代码:

static void sort(struct linked_list *list,
    int (*cmp)(const void *, const void *))
{
    size_t slice_size = 1;
    for(; slice_size < list->size; slice_size *= 2)
    {
        struct node *tail = list->first;
        while(tail)
        {
            struct node *head = tail;

            size_t count = slice_size;
            while(tail && count--) // performance killer
                tail = tail->next;

            count = slice_size;
            while(head != tail && tail && count)
            {
                if(cmp(head->data, tail->data) <= 0)
                    head = head->next;
                else
                {
                    struct node *node = tail;
                    tail = tail->next;
                    remove_node(node, list);
                    insert_before(node, list, head);
                    --count;
                }
            }

            while(tail && count--) // performance killer
                tail = tail->next;
        }
    }
}

struct slice
{
    struct node *head;
    size_t size;
};

static void sort(struct linked_list *list,
    int (*cmp)(const void *, const void *))
{
    if(list->size < 2) return;

    struct slice stack[32];
    size_t top = -1;
    struct node *current = list->first;

    for(; current; current = current->next)
    {
        stack[++top] = (struct slice){ current, 1 };
        for(; top && stack[top-1].size <= stack[top].size; --top)
            merge_down(list, cmp, stack + top);
    }

    for(; top; --top)
        merge_down(list, cmp, stack + top);
}

这将把大小为1的列表推送到堆栈上,并向下合并,只要顶部列表的大小大于或等于其前一个列表。

不幸的是,对于某些输入列表,某处存在一个错误, merge_down()

static void merge_down(struct linked_list *list,
    int (*cmp)(const void *, const void *), struct slice *top)
{
    struct node *right = top->head;
    size_t count = top->size;

    --top;

    struct node *left = top->head;
    top->size += count;

{
    // sanity check: count nodes in right list
    int i = count;
    struct node *node = right;
    for(; i--; node = node->next) if(!node)
    {
        puts("too few right nodes");
        exit(0);
    }
}

    // determine merged list's head
    if(cmp(left->data, right->data) <= 0)
    {
        top->head = left;
        left = left->next;
    }
    else
    {
        top->head = right;
        struct node *node = right;
        right = right->next;
        remove_node(node, list);
        insert_before(node, list, left);
        --count;
    }

    while(left != right && count)
    {
        if(cmp(left->data, right->data) <= 0)
            left = left->next;
        else
        {
            struct node *node = right;
            right = right->next;
            remove_node(node, list);
            insert_before(node, list, left);
            --count;
        }
    }
}

struct node
{
    struct node *prev;
    struct node *next;
    long long data[]; // use `long long` for alignment
};

struct linked_list
{
    struct _list _list; // ignore
    size_t size;
    struct node *first;
    struct node *last;
};

static void insert_before(struct node *node, struct linked_list *list,
    struct node *ref_node)
{
    if(ref_node)
    {
        node->next = ref_node;
        node->prev = ref_node->prev;
        if(ref_node->prev) ref_node->prev->next = node;
        else list->first = node;
        ref_node->prev = node;
    }
    else // empty list
    {
        node->next = NULL;
        node->prev = NULL;
        list->first = node;
        list->last = node;
    }
    ++list->size;
}

static void remove_node(struct node *node, struct linked_list *list)
{
    if(node->prev) node->prev->next = node->next;
    else list->first = node->next;
    if(node->next) node->next->prev = node->prev;
    else list->last = node->prev;
    --list->size;
}

我在这里错过了什么?

5 回复 | 直到 16 年前

pmg 16 年前

您是否需要将节点复制到列表末尾?
怎么了 insert_before() 那么打电话?

insert_before(node, list, NULL);

那会搞砸的 list->first 和 node->prev .

pmg 16 年前

static void merge_down(struct linked_list *list,
    int (*cmp)(const void *, const void *), struct slice *top)
{
    struct node *right = top->head;
    size_t count = top->size;

    --top;

    struct node *left = top->head;
    top->size += count; /* possible bug? */
 /* ^^^^^^^^^^^^^^^^^^^ */

Christoph 16 年前

我自己发现了错误:

for(; current; current = current->next)
{
    stack[++top] = (struct slice){ current, 1 };
    for(; top && stack[top-1].size <= stack[top].size; --top)
        merge_down(list, cmp, stack + top);
}

current 下定决心之后 merge_down() current->next

重新排列可以解决问题:

while(current)
{
    stack[++top] = (struct slice){ current, 1 };
    current = current->next;
    for(; top && stack[top-1].size <= stack[top].size; --top)
        merge_down(list, cmp, stack + top);
}

感谢pmg的努力:我为此增加了一些选票。

pmg 16 年前

基于堆栈的方法

/* ... */
    struct slice stack[32];
    size_t top = -1;
    struct node *current = list->first;

    for(; current; current = current->next)
    {
        stack[++top] = (struct slice){ current, 1 };
        for(; top && stack[top-1].size <= stack[top].size; --top)
        /*    ^^^    */
            merge_down(list, cmp, stack + top);
    }
/* ... */

top 第一次循环时总是0,对吗?
这 merge_down() 函数永远不会被调用。我没有尝试代码,但看起来不对。

编辑
32个元素 stack 这还不够。..当列表中有32个以上的元素按顺序排列时(可能在几次遍历后),您可以在末尾之后写入 堆栈 .

Christoph 16 年前

正如kriss所要求的,这是递归版本(使用其他示例中的合并函数的标准合并排序):

static struct node *merge(struct linked_list *list,
    int (*cmp)(const void *, const void *),
    struct node *left, struct node *right, size_t right_count)
{
    struct node *head;
    if(cmp(left->data, right->data) <= 0)
    {
        head = left;
        left = left->next;
    }
    else
    {
        head = right;
        struct node *node = right;
        right = right->next;
        remove_node(node, list);
        insert_before(node, list, left);
        --right_count;
    }

    while(left != right && right_count)
    {
        if(cmp(left->data, right->data) <= 0)
            left = left->next;
        else
        {
            struct node *node = right;
            right = right->next;
            remove_node(node, list);
            insert_before(node, list, left);
            --right_count;
        }
    }

    return head;
}

static struct node *mergesort(struct linked_list *list,
    int (*cmp)(const void *, const void *), struct node *head, size_t size)
{
    if(size < 2) return head;
    size_t left_count = size / 2;
    size_t right_count = size - left_count;

    struct node *tail = head;
    size_t count = left_count;
    while(count--) tail = tail->next;

    return merge(list, cmp,
        mergesort(list, cmp, head, left_count),
        mergesort(list, cmp, tail, right_count),
        right_count);
}

static void sort(struct linked_list *list,
    int (*cmp)(const void *, const void *))
{
    mergesort(list, cmp, list->first, list->size);
}