skiplist_with_rank.h

/*
 * Copyright (C) 2015, Leo Ma <begeekmyfriend@gmail.com>
 */

#ifndef _SKIPLIST_H
#define _SKIPLIST_H

struct sk_link {
        struct sk_link *next, *prev;
        int span;
};

static inline void list_init(struct sk_link *link)
{
        link->prev = link;
        link->next = link;
}

static inline void
__list_add(struct sk_link *link, struct sk_link *prev, struct sk_link *next)
{
        link->next = next;
        link->prev = prev;
        next->prev = link;
        prev->next = link;
}

static inline void __list_del(struct sk_link *prev, struct sk_link *next)
{
        prev->next = next;
        next->prev = prev;
}

static inline void list_add(struct sk_link *link, struct sk_link *next)
{
        __list_add(link, next->prev, next);
}

static inline void list_del(struct sk_link *link)
{
        __list_del(link->prev, link->next);
        list_init(link);
}

static inline int list_empty(struct sk_link *link)
{
        return link->next == link;
}

#define list_entry(ptr, type, member) \
        ((type *)((char *)(ptr) - (size_t)(&((type *)0)->member)))

#define skiplist_foreach_forward(pos, end) \
        for (; pos != end; pos = (pos)->next)

#define skiplist_foreach_forward_safe(pos, n, end) \
        for (n = (pos)->next; pos != end; pos = n, n = (pos)->next)

#define skiplist_foreach_backward(pos, end) \
        for (; pos != end; pos = (pos)->prev)

#define skiplist_foreach_backward_safe(pos, n, end) \
        for (n = (pos)->prev; pos != end; pos = n, n = (pos)->prev)

#define MAX_LEVEL 32  /* Should be enough for 2^32 elements */

struct range_spec {
        int min, max;
        int minex, maxex;
};

struct skiplist {
        int level;
        int count;
        struct sk_link head[MAX_LEVEL];
};

struct skipnode {
        int key;
        int value;
        struct sk_link link[0];
};

static struct skipnode *skipnode_new(int level, int key, int value)
{
        struct skipnode *node;
        node = malloc(sizeof(*node) + level * sizeof(struct sk_link));
        if (node != NULL) {
                node->key = key;
                node->value = value;
        }
        return node;
}

static void skipnode_delete(struct skipnode *node)
{
        free(node);
}

static struct skiplist *skiplist_new(void)
{
        int i;
        struct skiplist *list = malloc(sizeof(*list));
        if (list != NULL) {
                list->level = 1;
                list->count = 0;
                for (i = 0; i < sizeof(list->head) / sizeof(list->head[0]); i++) {
                        list_init(&list->head[i]);
                        list->head[i].span = 0;
                }
        }
        return list;
}

static void skiplist_delete(struct skiplist *list)
{
        struct sk_link *n;
        struct skipnode *node;
        struct sk_link *pos = list->head[0].next;
        skiplist_foreach_forward_safe(pos, n, &list->head[0]) {
                node = list_entry(pos, struct skipnode, link[0]);
                skipnode_delete(node);
        }
        free(list);
}

static int random_level(void)
{
        int level = 1;
        const double p = 0.25;
        while ((random() & 0xffff) < 0xffff * p) {
                level++;
        }
        return level > MAX_LEVEL ? MAX_LEVEL : level;
}

static struct skipnode *
skiplist_insert(struct skiplist *list, int key, int value)
{
        struct skipnode *nd;
        int rank[MAX_LEVEL];
        struct sk_link *update[MAX_LEVEL];
        int level = random_level();
        if (level > list->level) {
                list->level = level;
        }

        struct skipnode *node = skipnode_new(level, key, value);
        if (node != NULL) {
                int i = list->level - 1;
                struct sk_link *pos = &list->head[i];
                struct sk_link *end = &list->head[i];

                for (; i >= 0; i--) {
                        rank[i] = i == list->level - 1 ? 0 : rank[i + 1];
                        pos = pos->next;
                        skiplist_foreach_forward(pos, end) {
                                nd = list_entry(pos, struct skipnode, link[i]);
                                if (nd->key >= key) {
                                        end = &nd->link[i];
                                        break;
                                }
                                rank[i] += nd->link[i].span;
                        }

                        update[i] = end;
                        pos = end->prev;
                        pos--;
                        end--;
                }

                for (i = 0; i < list->level; i++) {
                        if (i < level) {
                                list_add(&node->link[i], update[i]);
                                node->link[i].span = rank[0] - rank[i] + 1;
                                update[i]->span -= node->link[i].span - 1;
                        } else {
                                update[i]->span++;
                        }
                }

                list->count++;
        }

        return node;
}

static void
__remove(struct skiplist *list, struct skipnode *node, int level, struct sk_link **update)
{
        int i;
        int remain_level = list->level;
        for (i = 0; i < list->level; i++) {
                if (i < level) {
                        list_del(&node->link[i]);
                        update[i] = node->link[i].next;
                        update[i]->span += node->link[i].span - 1;
                } else {
                        update[i]->span--;
                }

                if (list_empty(&list->head[i])) {
                        if (remain_level == list->level) {
                                remain_level = i + 1;
                        }
                }
        }

        skipnode_delete(node);
        list->count--;
        list->level = remain_level;
}

static void skiplist_remove(struct skiplist *list, int key)
{
        struct skipnode *node;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct sk_link *n, *update[MAX_LEVEL];

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward_safe(pos, n, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (node->key > key) {
                                end = &node->link[i];
                                break;
                        } else if (node->key == key) {
                                __remove(list, node, i + 1, update);
                                return;
                        }
                }
                update[i] = end;
                pos = end->prev;
                pos--;
                end--;
        }
}

static int key_gte_min(int key, struct range_spec *range)
{
        return range->maxex ? (key > range->max) : (key >= range->max);
}

static int key_lte_max(int key, struct range_spec *range)
{
        return range->minex ? (key < range->min) : (key <= range->min);
}

/* Returns if there is node key in range */
static int key_in_range(struct skiplist *list, struct range_spec *range)
{
        if (range->min > range->max ||
                (range->min == range->max && (range->minex || range->maxex))) {
                return 0;
        }

        if (list_empty(&list->head[0])) {
                return 0;
        }

        struct sk_link *link = list->head[0].next;
        struct skipnode *node = list_entry(link, struct skipnode, link[0]);
        if (!key_lte_max(node->key, range)) {
                return 0;
        }

        link = list->head[0].prev;
        node = list_entry(link, struct skipnode, link[0]);
        if (!key_gte_min(node->key, range)) {
                return 0;
        }

        return 1;
}


/* search the first node key that is contained in the specified range
 * where min and max are inclusive. */
static struct skipnode *
first_in_range(struct skiplist *list, struct range_spec *range)
{
        struct skipnode *node;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];

        if (!key_in_range(list, range)) {
                return NULL;
        }

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (key_gte_min(node->key, range)) {
                                pos = node->link[i].prev;
                                end = node->link[i].next;
                                goto CONTINUE;
                        }
                }
                pos = end->prev;
CONTINUE:
                pos--;
                end--;
        }

        return node;
}

/* search the last node key that is contained in the specified range
 * where min and max are inclusive. */
static struct skipnode *
last_in_range(struct skiplist *list, struct range_spec *range)
{
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct skipnode *node = NULL;

        if (!key_in_range(list, range)) {
                return NULL;
        }

        for (; i >= 0; i--) {
                pos = pos->prev;
                skiplist_foreach_backward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (key_lte_max(node->key, range)) {
                                pos = node->link[i].next;
                                end = node->link[i].prev;
                                goto CONTINUE;
                        }
                }
                pos = end->next;
CONTINUE:
                pos--;
                end--;
        }

        return node;
}

/* remove all the nodes with key in range
 * where min and max are inclusive. */
static int remove_in_range(struct skiplist *list, struct range_spec *range)
{
        int removed = 0;
        struct skipnode *node;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct sk_link *n, *update[MAX_LEVEL];

        if (key_in_range(list, range)) {
                return 0;
        }

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward_safe(pos, n, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (!key_lte_max(node->key, range)) {
                                end = &node->link[i];
                                break;
                        } else if (key_gte_min(node->key, range)) {
                                /* we allow nodes with same key. */
                                __remove(list, node, i + 1, update);
                                removed++;
                        }
                }
                update[i] = end;
                pos = end->prev;
                pos--;
                end--;
        }

        return removed;
}

/* remove all the nodes with key rank in range
 * where start and stop are inclusive. */
static int remove_in_rank(struct skiplist *list, int start, int stop)
{
        struct skipnode *node;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        int removed = 0, traversed = 0;
        struct sk_link *n, *update[MAX_LEVEL] = {0};

        if (start <= 0 || stop <= 0 || start > list->count) {
                return 0;
        }

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward_safe(pos, n, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (traversed + node->link[i].span > stop) {
                                end = &node->link[i];
                                break;
                        } else if (traversed + node->link[i].span >= start) {
                                /* we allow nodes with same key. */
                                __remove(list, node, i + 1, update);
                                removed++;
                        }
                        traversed += node->link[i].span;
                }
                update[i] = end;
                pos = end->prev;
                pos--;
                end--;
        }

        return removed;
}

/* Get the node key rank */
static int skiplist_key_rank(struct skiplist *list, int key)
{
        int rank = 0;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct skipnode *node;

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (node->key >= key) {
                                end = &node->link[i];
                                break;
                        }
                        rank += node->link[i].span;
                }
                if (node->key == key) {
                        return rank + node->link[i].span;
                }
                pos = end->prev;
                pos--;
                end--;
        }

        return 0;
}

/* search the node with specified key. */
static struct skipnode *skiplist_search_by_key(struct skiplist *list, int key)
{
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct skipnode *node;

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (node->key >= key) {
                                end = &node->link[i];
                                break;
                        }
                }
                if (node->key == key) {
                        return node;
                }
                pos = end->prev;
                pos--;
                end--;
        }

        return NULL;
}

/* search the node with specified key rank. */
static struct skipnode *skiplist_search_by_rank(struct skiplist *list, int rank)
{
        if (rank == 0 || rank > list->count) {
                return NULL;
        }

        int i = list->level - 1;
        int traversed = 0;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];
        struct skipnode *node;

        for (; i >= 0; i--) {
                pos = pos->next;
                skiplist_foreach_forward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        if (traversed + node->link[i].span > rank) {
                                end = &node->link[i];
                                break;
                        }
                        traversed += node->link[i].span;
                        if (rank == traversed) {
                                return node;
                        }
                }
                pos = end->prev;
                pos--;
                end--;
        }

        return NULL;
}

static void skiplist_dump(struct skiplist *list)
{
        int traversed = 0;
        struct skipnode *node;
        int i = list->level - 1;
        struct sk_link *pos = &list->head[i];
        struct sk_link *end = &list->head[i];

        printf("\nTotal %d nodes: \n", list->count);
        for (; i >= 0; i--) {
                traversed = 0;
                pos = pos->next;
                printf("level %d:\n", i + 1);
                skiplist_foreach_forward(pos, end) {
                        node = list_entry(pos, struct skipnode, link[i]);
                        traversed += node->link[i].span;
                        printf("key:0x%08x value:0x%08x rank:%u\n",
                                node->key, node->value, traversed);
                }
                pos = &list->head[i];
                pos--;
                end--;
        }
}

#endif  /* _SKIPLIST_H */