/* This software is licensed by the MIT License, see LICENSE file */
/*                                Copyright © 2022 Gregory Lirent */

#include "__internal/rbtree.h"

typedef enum libcdsb_rbtree_node_direction {
    RBD_LEFT  = 1,
    RBD_RIGHT = 2
} rbdir_t;

#define rbdir_dir(cur, d) (&((cur)->left))[(d)>>1]
#define rbdir_inv(cur, d) (&((cur)->left))[(d)&1]

/*#####################################################################################################################*/

rbnode_t LIBCDSB_RBTREE_NODE_EMPTY[1] = {{
   .colored = 0,
   .value   = 0,
   .parent  = rbnode_empty,
   .left    = rbnode_empty,
   .right   = rbnode_empty
}};

/*#####################################################################################################################*/

static inline void rotate(rbnode_t **x, rbnode_t *c, rbdir_t d) {
    rbnode_t* n = rbdir_inv(c, d);

    rbdir_inv(c, d) = rbdir_dir(n, d);
    n->parent = c->parent;

    if (!rbnode_is_empty(rbdir_dir(n, d)))
        rbdir_dir(n, d)->parent = c;

    if (!rbnode_is_root(c)) {
        if (c->parent->left == c) c->parent->left  = n;
        else                      c->parent->right = n;
    } else *x = n;

    rbdir_dir(n, d) = c;
    c->parent = n;
}

static inline void replace(rbnode_t** x, rbnode_t* c, rbnode_t* n) {
    if (!rbnode_is_root(c)) {
        if (c->parent->left == c) {
            c->parent->left = n;
        } else c->parent->right = n;
    } else *x = n;
    n->parent = c->parent;
}


/*#####################################################################################################################*/


static void delete_fixup(rbnode_t** x, rbnode_t* n) {
    rbdir_t d;
    rbnode_t *s, *p;

    while (!rbnode_is_root(n) && !n->colored) {
        p = n->parent;
        d = (p->left == n) ? RBD_LEFT : RBD_RIGHT;
        s = rbdir_inv(p, d);

        if (s->colored) {
            s->colored = 0;
            p->colored = 1;
            rotate(x, p, d);
            p = n->parent;
            s = rbdir_inv(p, d);
        }

        if (!rbdir_dir(s, d)->colored && !rbdir_inv(s, d)->colored) {
            s->colored = 1;
            n = p;
        } else {
            if (!rbdir_inv(s, d)->colored) {
                rbdir_dir(s, d)->colored = 0;
                s->colored = 1;
                rotate(x, s, (d == RBD_LEFT) ? RBD_RIGHT : RBD_LEFT);
                p = n->parent;
                s = rbdir_inv(p, d);
            }

            s->colored = p->colored;
            p->colored = 0;
            rbdir_inv(s, d)->colored = 0;

            rotate(x, p, d);

            n = *x;
        }
    }

    n->colored = 0;
}

/*#####################################################################################################################*/


rbnode_t* libcdsb_rbtree_node_delete(rbnode_t** x, rbnode_t* c) {
    rbnode_t *n, *t;
    int s;

    s = c->colored;

    if (rbnode_is_empty(c->left)) {
        n = c->right;
        replace(x, c, c->right);
    } else if (rbnode_is_empty(c->right)) {
        n = c->left;
        replace(x, c, c->left);
    } else {
        t = c->right;

        while (!rbnode_is_empty(t->left)) {
            t = t->left;
        }

        s = t->colored;
        n = t->right;

        if (t->parent == c) {
            n->parent = t;
        } else {
            replace(x, t, t->right);
            c->right->parent = t;
            t->right = c->right;
        }

        replace(x, c, t);
        c->left->parent = t;
        t->colored = c->colored;
        t->left = c->left;
    }

    if (!s) delete_fixup(x, n);

    return c;
}



void libcdsb_rbtree_node_fixup(rbnode_t** x, rbnode_t* n) {
    rbdir_t d[2];
    rbnode_t *u, *p, *gp;

    while (n->parent->colored) {
        p    = n->parent;
        gp   = p->parent;
        d[0] = (gp->right == p) ? RBD_LEFT : RBD_RIGHT;
        u    = rbdir_dir(gp, d[0]);

        if (rbdir_dir(p, d[0]) == n) {
            d[1] = (d[0] == RBD_LEFT) ? RBD_RIGHT : RBD_LEFT;
        } else d[1] = 0;

        if (u->colored) {
             u->colored = 0;
             p->colored = 0;
            gp->colored = 1;

            n = gp;
        } else {
            if (d[1]) {
                rotate(x, n = p, d[1]);
                 p = n->parent;
                gp = p->parent;
            }
             p->colored = 0;
            gp->colored = 1;

            rotate(x, gp, d[0]);
        }

        if (rbnode_is_root(n)) break;
    }

    (*x)->colored = 0;
}


void* libcdsb_rbtree_node_create(void* v, rbnode_t* p, int c, int n) {
    rbnode_t* x;

    x = malloc(n);

    x->left    = rbnode_empty;
    x->right   = rbnode_empty;
    x->value   = v;
    x->colored = c;
    x->parent  = p;

    return x;
}