rbtree.c

/* The authors of this work have released all rights to it and placed it
in the public domain under the Creative Commons CC0 1.0 waiver
(http://creativecommons.org/publicdomain/zero/1.0/).

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Retrieved from: http://en.literateprograms.org/Red-black_tree_(C)?oldid=19567
*/

#ifndef RBTREE
#define RBTREE

#include "rbtree.h"
#include <assert.h>
#include <stdlib.h>

typedef rbtree_node node;
typedef enum rbtree_node_color color;

static node grandparent(node n);
static node sibling(node n);
static node uncle(node n);
static void verify_properties(rbtree t);
static void verify_property_1(node root);
static void verify_property_2(node root);
static color node_color(node n);
static void verify_property_4(node root);
static void verify_property_5(node root);
static void verify_property_5_helper(node n, int black_count, int* black_count_path);

static node new_node(void* key, void* value, color node_color, node left, node right);
static node lookup_node(rbtree t, void* key, compare_func compare);
static void rotate_left(rbtree t, node n);
static void rotate_right(rbtree t, node n);

static void replace_node(rbtree t, node oldn, node newn);
static void insert_case1(rbtree t, node n);
static void insert_case2(rbtree t, node n);
static void insert_case3(rbtree t, node n);
static void insert_case4(rbtree t, node n);
static void insert_case5(rbtree t, node n);
static node maximum_node(node root);
static void delete_case1(rbtree t, node n);
static void delete_case2(rbtree t, node n);
static void delete_case3(rbtree t, node n);
static void delete_case4(rbtree t, node n);
static void delete_case5(rbtree t, node n);
static void delete_case6(rbtree t, node n);

node grandparent(node n) {
    assert (n != NULL);
    assert (n->parent != NULL); /* Not the root node */
    assert (n->parent->parent != NULL); /* Not child of root */
    return n->parent->parent;
}
node sibling(node n) {
    assert (n != NULL);
    assert (n->parent != NULL); /* Root node has no sibling */
    if (n == n->parent->left)
        return n->parent->right;
    else
        return n->parent->left;
}
node uncle(node n) {
    assert (n != NULL);
    assert (n->parent != NULL); /* Root node has no uncle */
    assert (n->parent->parent != NULL); /* Children of root have no uncle */
    return sibling(n->parent);
}
void verify_properties(rbtree t) {
#ifdef VERIFY_RBTREE
    verify_property_1(t->root);
    verify_property_2(t->root);
    /* Property 3 is implicit */
    verify_property_4(t->root);
    verify_property_5(t->root);
#endif
}
void verify_property_1(node n) {
    assert(node_color(n) == RED || node_color(n) == BLACK);
    if (n == NULL) return;
    verify_property_1(n->left);
    verify_property_1(n->right);
}
void verify_property_2(node root) {
    assert(node_color(root) == BLACK);
}
color node_color(node n) {
    return n == NULL ? BLACK : n->color;
}
void verify_property_4(node n) {
    if (node_color(n) == RED) {
        assert (node_color(n->left)   == BLACK);
        assert (node_color(n->right)  == BLACK);
        assert (node_color(n->parent) == BLACK);
    }
    if (n == NULL) return;
    verify_property_4(n->left);
    verify_property_4(n->right);
}
void verify_property_5(node root) {
    int black_count_path = -1;
    verify_property_5_helper(root, 0, &black_count_path);
}

void verify_property_5_helper(node n, int black_count, int* path_black_count) {
    if (node_color(n) == BLACK) {
        black_count++;
    }
    if (n == NULL) {
        if (*path_black_count == -1) {
            *path_black_count = black_count;
        } else {
            assert (black_count == *path_black_count);
        }
        return;
    }
    verify_property_5_helper(n->left,  black_count, path_black_count);
    verify_property_5_helper(n->right, black_count, path_black_count);
}
rbtree rbtree_create() {
    rbtree t = malloc(sizeof(struct rbtree_t));
    t->root = NULL;
    t->size = 0;
    verify_properties(t);
    return t;
}
node new_node(void* key, void* value, color node_color, node left, node right) {
    node result = malloc(sizeof(struct rbtree_node_t));
    result->key = key;
    result->value = value;
    result->color = node_color;
    result->left = left;
    result->right = right;
    if (left  != NULL)  left->parent = result;
    if (right != NULL) right->parent = result;
    result->parent = NULL;
    return result;
}
node lookup_node(rbtree t, void* key, compare_func compare) {
    node n = t->root;
    while (n != NULL) {
        int comp_result = compare(key, n->key);
        if (comp_result == 0) {
            return n;
        } else if (comp_result < 0) {
            n = n->left;
        } else {
            assert(comp_result > 0);
            n = n->right;
        }
    }
    return n;
}
void* rbtree_lookup(rbtree t, void* key, void* def, compare_func compare) {
    node n = lookup_node(t, key, compare);
    return n == NULL ? def : n->value;
}
void rotate_left(rbtree t, node n) {
    node r = n->right;
    replace_node(t, n, r);
    n->right = r->left;
    if (r->left != NULL) {
        r->left->parent = n;
    }
    r->left = n;
    n->parent = r;
}

void rotate_right(rbtree t, node n) {
    node L = n->left;
    replace_node(t, n, L);
    n->left = L->right;
    if (L->right != NULL) {
        L->right->parent = n;
    }
    L->right = n;
    n->parent = L;
}
void replace_node(rbtree t, node oldn, node newn) {
    if (oldn->parent == NULL) {
        t->root = newn;
    } else {
        if (oldn == oldn->parent->left)
            oldn->parent->left = newn;
        else
            oldn->parent->right = newn;
    }
    if (newn != NULL) {
        newn->parent = oldn->parent;
    }
}
void rbtree_insert(rbtree t, void* key, void* value, compare_func compare) {
    t->size++;
    node inserted_node = new_node(key, value, RED, NULL, NULL);
    if (t->root == NULL) {
        t->root = inserted_node;
    } else {
        node n = t->root;
        while (1) {
            int comp_result = compare(key, n->key);
            if (comp_result == 0) {
                n->value = value;
                return;
            } else if (comp_result < 0) {
                if (n->left == NULL) {
                    n->left = inserted_node;
                    break;
                } else {
                    n = n->left;
                }
            } else {
                assert (comp_result > 0);
                if (n->right == NULL) {
                    n->right = inserted_node;
                    break;
                } else {
                    n = n->right;
                }
            }
        }
        inserted_node->parent = n;
    }
    insert_case1(t, inserted_node);
    verify_properties(t);
}
void insert_case1(rbtree t, node n) {
    if (n->parent == NULL)
        n->color = BLACK;
    else
        insert_case2(t, n);
}
void insert_case2(rbtree t, node n) {
    if (node_color(n->parent) == BLACK)
        return; /* Tree is still valid */
    else
        insert_case3(t, n);
}
void insert_case3(rbtree t, node n) {
    if (node_color(uncle(n)) == RED) {
        n->parent->color = BLACK;
        uncle(n)->color = BLACK;
        grandparent(n)->color = RED;
        insert_case1(t, grandparent(n));
    } else {
        insert_case4(t, n);
    }
}
void insert_case4(rbtree t, node n) {
    if (n == n->parent->right && n->parent == grandparent(n)->left) {
        rotate_left(t, n->parent);
        n = n->left;
    } else if (n == n->parent->left && n->parent == grandparent(n)->right) {
        rotate_right(t, n->parent);
        n = n->right;
    }
    insert_case5(t, n);
}
void insert_case5(rbtree t, node n) {
    n->parent->color = BLACK;
    grandparent(n)->color = RED;
    if (n == n->parent->left && n->parent == grandparent(n)->left) {
        rotate_right(t, grandparent(n));
    } else {
        assert (n == n->parent->right && n->parent == grandparent(n)->right);
        rotate_left(t, grandparent(n));
    }
}
void rbtree_delete(rbtree t, void* key, compare_func compare) {
    t->size--;
    node child;
    node n = lookup_node(t, key, compare);
    if (n == NULL) return;  /* Key not found, do nothing */
    if (n->left != NULL && n->right != NULL) {
        /* Copy key/value from predecessor and then delete it instead */
        node pred = maximum_node(n->left);
        n->key   = pred->key;
        n->value = pred->value;
        n = pred;
    }

    assert(n->left == NULL || n->right == NULL);
    child = n->right == NULL ? n->left  : n->right;
    if (node_color(n) == BLACK) {
        n->color = node_color(child);
        delete_case1(t, n);
    }
    replace_node(t, n, child);
    if (n->parent == NULL && child != NULL) // root should be black
        child->color = BLACK;
    free(n);

    verify_properties(t);
}
static node maximum_node(node n) {
    assert (n != NULL);
    while (n->right != NULL) {
        n = n->right;
    }
    return n;
}
void delete_case1(rbtree t, node n) {
    if (n->parent == NULL)
        return;
    else
        delete_case2(t, n);
}
void delete_case2(rbtree t, node n) {
    if (node_color(sibling(n)) == RED) {
        n->parent->color = RED;
        sibling(n)->color = BLACK;
        if (n == n->parent->left)
            rotate_left(t, n->parent);
        else
            rotate_right(t, n->parent);
    }
    delete_case3(t, n);
}
void delete_case3(rbtree t, node n) {
    if (node_color(n->parent) == BLACK &&
        node_color(sibling(n)) == BLACK &&
        node_color(sibling(n)->left) == BLACK &&
        node_color(sibling(n)->right) == BLACK)
    {
        sibling(n)->color = RED;
        delete_case1(t, n->parent);
    }
    else
        delete_case4(t, n);
}
void delete_case4(rbtree t, node n) {
    if (node_color(n->parent) == RED &&
        node_color(sibling(n)) == BLACK &&
        node_color(sibling(n)->left) == BLACK &&
        node_color(sibling(n)->right) == BLACK)
    {
        sibling(n)->color = RED;
        n->parent->color = BLACK;
    }
    else
        delete_case5(t, n);
}
void delete_case5(rbtree t, node n) {
    if (n == n->parent->left &&
        node_color(sibling(n)) == BLACK &&
        node_color(sibling(n)->left) == RED &&
        node_color(sibling(n)->right) == BLACK)
    {
        sibling(n)->color = RED;
        sibling(n)->left->color = BLACK;
        rotate_right(t, sibling(n));
    }
    else if (n == n->parent->right &&
             node_color(sibling(n)) == BLACK &&
             node_color(sibling(n)->right) == RED &&
             node_color(sibling(n)->left) == BLACK)
    {
        sibling(n)->color = RED;
        sibling(n)->right->color = BLACK;
        rotate_left(t, sibling(n));
    }
    delete_case6(t, n);
}
void delete_case6(rbtree t, node n) {
    sibling(n)->color = node_color(n->parent);
    n->parent->color = BLACK;
    if (n == n->parent->left) {
        assert (node_color(sibling(n)->right) == RED);
        sibling(n)->right->color = BLACK;
        rotate_left(t, n->parent);
    }
    else
    {
        assert (node_color(sibling(n)->left) == RED);
        sibling(n)->left->color = BLACK;
        rotate_right(t, n->parent);
    }
}

void destroy_nodes(rbtree_node n) {
    if (n->left != NULL) destroy_nodes(n->left);
    if (n->right != NULL) destroy_nodes(n->right);
    free(n);
}

void rbtree_destroy(rbtree t) {
    if (t->root != NULL) destroy_nodes(t->root);
    free(t);
}

int rbtree_size(rbtree t) {
    return sizeof(struct rbtree_t) + sizeof(struct rbtree_t) + sizeof(struct rbtree_node_t) * t->size;
}

#endif