/*-
 * Copyright (c) 2015 Nuxi, https://nuxi.nl/
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#define _SEARCH_PRIVATE
#include <search.h>
#include <stdlib.h>

#include "tsearch_path.h"

posix_tnode *
tsearch(const void *key, posix_tnode **rootp,
    int (*compar)(const void *, const void *))
{
        struct path path;
        posix_tnode **leaf, *result, *n, *x, *y, *z;
        int cmp;

        /* POSIX requires that tsearch() returns NULL if rootp is NULL. */
        if (rootp == NULL)
                return (NULL);

        /*
         * Find the leaf where the new key needs to be inserted. Return
         * if we've found an existing entry. Keep track of the path that
         * is taken to get to the node, as we will need it to adjust the
         * balances.
        */
        path_init(&path);
        leaf = rootp;
        while (*leaf != NULL) {
                if ((*leaf)->balance != 0) {
                        /*
                         * If we reach a node that has a non-zero
                         * balance on the way, we know that we won't
                         * need to perform any rotations above this
                         * point. In this case rotations are always
                         * capable of keeping the subtree in balance.
                         * Make this the root node and reset the path.
                         */
                        rootp = leaf;
                        path_init(&path);
                }
                cmp = compar(key, (*leaf)->key);
                if (cmp < 0) {
                        path_taking_left(&path);
                        leaf = &(*leaf)->llink;
                } else if (cmp > 0) {
                        path_taking_right(&path);
                        leaf = &(*leaf)->rlink;
                } else {
                        return (*leaf);
                }
        }

        /* Did not find a matching key in the tree. Insert a new node. */
        result = *leaf = malloc(sizeof(**leaf));
        if (result == NULL)
                return (NULL);
        result->key = (void *)key;
        result->llink = NULL;
        result->rlink = NULL;
        result->balance = 0;

        /*
         * Walk along the same path a second time and adjust the
         * balances. Except for the first node, all of these nodes must
         * have a balance of zero, meaning that these nodes will not get
         * out of balance.
        */
        for (n = *rootp; n != *leaf;) {
                if (path_took_left(&path)) {
                        n->balance += 1;
                        n = n->llink;
                } else {
                        n->balance -= 1;
                        n = n->rlink;
                }
        }

        /*
         * Adjusting the balances may have pushed the balance of the
         * root node out of range. Perform a rotation to bring the
         * balance back in range.
         */
        x = *rootp;
        if (x->balance > 1) {
                y = x->llink;
                if (y->balance < 0) {
                        /*
                         * Left-right case.
                         *
                         *         x
                         *        / \            z
                         *       y   D          / \
                         *      / \     -->    y   x
                         *     A   z          /|   |\
                         *        / \        A B   C D
                         *       B   C
                         */
                        z = y->rlink;
                        y->rlink = z->llink;
                        z->llink = y;
                        x->llink = z->rlink;
                        z->rlink = x;
                        *rootp = z;

                        x->balance = z->balance > 0 ? -1 : 0;
                        y->balance = z->balance < 0 ? 1 : 0;
                        z->balance = 0;
                } else {
                        /*
                         * Left-left case.
                         *
                         *        x           y
                         *       / \         / \
                         *      y   C  -->  A   x
                         *     / \             / \
                         *    A   B           B   C
                         */
                        x->llink = y->rlink;
                        y->rlink = x;
                        *rootp = y;

                        x->balance = 0;
                        y->balance = 0;
                }
        } else if (x->balance < -1) {
                y = x->rlink;
                if (y->balance > 0) {
                        /*
                         * Right-left case.
                         *
                         *       x
                         *      / \              z
                         *     A   y            / \
                         *        / \   -->    x   y
                         *       z   D        /|   |\
                         *      / \          A B   C D
                         *     B   C
                         */
                        posix_tnode *z = y->llink;
                        x->rlink = z->llink;
                        z->llink = x;
                        y->llink = z->rlink;
                        z->rlink = y;
                        *rootp = z;

                        x->balance = z->balance < 0 ? 1 : 0;
                        y->balance = z->balance > 0 ? -1 : 0;
                        z->balance = 0;
                } else {
                        /*
                         * Right-right case.
                         *
                         *       x               y
                         *      / \             / \
                         *     A   y    -->    x   C
                         *        / \         / \
                         *       B   C       A   B
                         */
                        x->rlink = y->llink;
                        y->llink = x;
                        *rootp = y;

                        x->balance = 0;
                        y->balance = 0;
                }
        }

        /* Return the new entry. */
        return (result);
}