/*
  Copyright 2011 David Robillard <http://drobilla.net>

  Permission to use, copy, modify, and/or distribute this software for any
  purpose with or without fee is hereby granted, provided that the above
  copyright notice and this permission notice appear in all copies.

  THIS SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/

#include <assert.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "zix/common.h"
#include "zix/tree.h"

typedef struct ZixTreeNodeImpl ZixTreeNode;

struct ZixTreeImpl {
	ZixTreeNode*   root;
	ZixDestroyFunc destroy;
	ZixComparator  cmp;
	void*          cmp_data;
	size_t         size;
	bool           allow_duplicates;
};

struct ZixTreeNodeImpl {
	void*                   data;
	struct ZixTreeNodeImpl* left;
	struct ZixTreeNodeImpl* right;
	struct ZixTreeNodeImpl* parent;
	int_fast8_t             balance;
};

#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define MAX(a, b) (((a) > (b)) ? (a) : (b))

// Uncomment these for debugging features
// #define ZIX_TREE_DUMP         1
// #define ZIX_TREE_VERIFY       1
// #define ZIX_TREE_HYPER_VERIFY 1

#if defined(ZIX_TREE_VERIFY) || defined(ZIX_TREE_HYPER_VERIFY)
#    include "tree_debug.h"
#    define ASSERT_BALANCE(n) assert(verify_balance(n))
#else
#    define ASSERT_BALANCE(n)
#endif

#ifdef ZIX_TREE_DUMP
#    include "tree_debug.h"
#    define DUMP(t) zix_tree_print(t->root, 0)
#    define DEBUG_PRINTF(fmt, ...) printf(fmt, __VA_ARGS__)
#else
#    define DUMP(t)
#    define DEBUG_PRINTF(fmt, ...)
#endif

ZIX_API
ZixTree*
zix_tree_new(bool           allow_duplicates,
             ZixComparator  cmp,
             void*          cmp_data,
             ZixDestroyFunc destroy)
{
	ZixTree* t = (ZixTree*)malloc(sizeof(ZixTree));
	t->root             = NULL;
	t->destroy          = destroy;
	t->cmp              = cmp;
	t->cmp_data         = cmp_data;
	t->size             = 0;
	t->allow_duplicates = allow_duplicates;
	return t;
}

static void
zix_tree_free_rec(ZixTree* t, ZixTreeNode* n)
{
	if (n) {
		zix_tree_free_rec(t, n->left);
		zix_tree_free_rec(t, n->right);
		if (t->destroy) {
			t->destroy(n->data);
		}
		free(n);
	}
}

ZIX_API
void
zix_tree_free(ZixTree* t)
{
	if (t) {
		zix_tree_free_rec(t, t->root);
		free(t);
	}
}

size_t
zix_tree_size(ZixTree* t)
{
	return t->size;
}

static void
rotate(ZixTreeNode* p, ZixTreeNode* q)
{
	assert(q->parent == p);
	assert(p->left == q || p->right == q);

	q->parent = p->parent;
	if (q->parent) {
		if (q->parent->left == p) {
			q->parent->left = q;
		} else {
			q->parent->right = q;
		}
	}

	if (p->right == q) {
		// Rotate left
		p->right = q->left;
		q->left  = p;
		if (p->right) {
			p->right->parent = p;
		}
	} else {
		// Rotate right
		assert(p->left == q);
		p->left  = q->right;
		q->right = p;
		if (p->left) {
			p->left->parent = p;
		}
	}

	p->parent = q;
}

/**
 * Rotate left about @a p.
 *
 *    p              q
 *   / \            / \
 *  A   q    =>    p   C
 *     / \        / \
 *    B   C      A   B
 */
static ZixTreeNode*
rotate_left(ZixTreeNode* p, int* height_change)
{
	ZixTreeNode* const q = p->right;
	*height_change = (q->balance == 0) ? 0 : -1;

	DEBUG_PRINTF("LL %ld\n", (intptr_t)p->data);

	assert(p->balance == 2);
	assert(q->balance == 0 || q->balance == 1);

	rotate(p, q);

	// p->balance -= 1 + MAX(0, q->balance);
	// q->balance -= 1 - MIN(0, p->balance);
	--q->balance;
	p->balance = -(q->balance);

	ASSERT_BALANCE(p);
	ASSERT_BALANCE(q);
	return q;
}

/**
 * Rotate right about @a p.
 *
 *      p          q
 *     / \        / \
 *    q   C  =>  A   p
 *   / \            / \
 *  A   B          B   C
 *
 */
static ZixTreeNode*
rotate_right(ZixTreeNode* p, int* height_change)
{
	ZixTreeNode* const q = p->left;
	*height_change = (q->balance == 0) ? 0 : -1;

	DEBUG_PRINTF("RR %ld\n", (intptr_t)p->data);

	assert(p->balance == -2);
	assert(q->balance == 0 || q->balance == -1);

	rotate(p, q);

	// p->balance += 1 - MIN(0, q->balance);
	// q->balance += 1 + MAX(0, p->balance);
	++q->balance;
	p->balance = -(q->balance);

	ASSERT_BALANCE(p);
	ASSERT_BALANCE(q);
	return q;
}

/**
 * Rotate left about @a p->left then right about @a p.
 *
 *      p             r
 *     / \           / \
 *    q   D  =>    q     p
 *   / \          / \   / \
 *  A   r        A   B C   D
 *     / \
 *    B   C
 *
 */
static ZixTreeNode*
rotate_left_right(ZixTreeNode* p, int* height_change)
{
	ZixTreeNode* const q = p->left;
	ZixTreeNode* const r = q->right;

	assert(p->balance == -2);
	assert(q->balance == 1);
	assert(r->balance == -1 || r->balance == 0 || r->balance == 1);

	DEBUG_PRINTF("LR %ld  P: %2d  Q: %2d  R: %2d\n",
	             (intptr_t)p->data, p->balance, q->balance, r->balance);

	rotate(q, r);
	rotate(p, r);

	q->balance -= 1 + MAX(0, r->balance);
	p->balance += 1 - MIN(MIN(0, r->balance) - 1, r->balance + q->balance);
	// r->balance += MAX(0, p->balance) + MIN(0, q->balance);

	// p->balance = (p->left && p->right) ? -MIN(r->balance, 0) : 0;
	// q->balance = - MAX(r->balance, 0);
	r->balance = 0;

	*height_change = -1;

	ASSERT_BALANCE(p);
	ASSERT_BALANCE(q);
	ASSERT_BALANCE(r);
	return r;
}

/**
 * Rotate right about @a p->right then right about @a p.
 *
 *    p               r
 *   / \             / \
 *  A   q    =>    p     q
 *     / \        / \   / \
 *    r   D      A   B C   D
 *   / \
 *  B   C
 *
 */
static ZixTreeNode*
rotate_right_left(ZixTreeNode* p, int* height_change)
{
	ZixTreeNode* const q = p->right;
	ZixTreeNode* const r = q->left;

	assert(p->balance == 2);
	assert(q->balance == -1);
	assert(r->balance == -1 || r->balance == 0 || r->balance == 1);

	DEBUG_PRINTF("RL %ld  P: %2d  Q: %2d  R: %2d\n",
	             (intptr_t)p->data, p->balance, q->balance, r->balance);

	rotate(q, r);
	rotate(p, r);

	q->balance += 1 - MIN(0, r->balance);
	p->balance -= 1 + MAX(MAX(0, r->balance) + 1, r->balance + q->balance);
	// r->balance += MAX(0, q->balance) + MIN(0, p->balance);

	// p->balance = (p->left && p->right) ? -MAX(r->balance, 0) : 0;
	// q->balance = - MIN(r->balance, 0);
	r->balance = 0;
	// assert(r->balance == 0);

	*height_change = -1;

	ASSERT_BALANCE(p);
	ASSERT_BALANCE(q);
	ASSERT_BALANCE(r);
	return r;
}

static ZixTreeNode*
zix_tree_rebalance(ZixTree* t, ZixTreeNode* node, int* height_change)
{
#ifdef ZIX_TREE_HYPER_VERIFY
	const size_t old_height = height(node);
#endif
	DEBUG_PRINTF("REBALANCE %ld (%d)\n", (intptr_t)node->data, node->balance);
	*height_change = 0;
	const bool is_root = !node->parent;
	assert((is_root && t->root == node) || (!is_root && t->root != node));
	ZixTreeNode* replacement = node;
	if (node->balance == -2) {
		assert(node->left);
		if (node->left->balance == 1) {
			replacement = rotate_left_right(node, height_change);
		} else {
			replacement = rotate_right(node, height_change);
		}
	} else if (node->balance == 2) {
		assert(node->right);
		if (node->right->balance == -1) {
			replacement = rotate_right_left(node, height_change);
		} else {
			replacement = rotate_left(node, height_change);
		}
	}
	if (is_root) {
		assert(!replacement->parent);
		t->root = replacement;
	}
	DUMP(t);
#ifdef ZIX_TREE_HYPER_VERIFY
	assert(old_height + *height_change == height(replacement));
#endif
	return replacement;
}

ZIX_API
ZixStatus
zix_tree_insert(ZixTree* t, void* e, ZixTreeIter** ti)
{
	DEBUG_PRINTF("**** INSERT %ld\n", (intptr_t)e);
	int          cmp = 0;
	ZixTreeNode* n   = t->root;
	ZixTreeNode* p   = NULL;

	// Find the parent p of e
	while (n) {
		p   = n;
		cmp = t->cmp(e, n->data, t->cmp_data);
		if (cmp < 0) {
			n = n->left;
		} else if (cmp > 0) {
			n = n->right;
		} else if (t->allow_duplicates) {
			n = n->right;
		} else {
			if (ti) {
				*ti = n;
			}
			DEBUG_PRINTF("%ld EXISTS!\n", (intptr_t)e);
			return ZIX_STATUS_EXISTS;
		}
	}

	// Allocate a new node n
	if (!(n = (ZixTreeNode*)malloc(sizeof(ZixTreeNode)))) {
		return ZIX_STATUS_NO_MEM;
	}
	memset(n, '\0', sizeof(ZixTreeNode));
	n->data    = e;
	n->balance = 0;
	if (ti) {
		*ti = n;
	}

	bool p_height_increased = false;

	// Make p the parent of n
	n->parent = p;
	if (!p) {
		t->root = n;
	} else {
		if (cmp < 0) {
			assert(!p->left);
			assert(p->balance == 0 || p->balance == 1);
			p->left = n;
			--p->balance;
			p_height_increased = !p->right;
		} else {
			assert(!p->right);
			assert(p->balance == 0 || p->balance == -1);
			p->right = n;
			++p->balance;
			p_height_increased = !p->left;
		}
	}

	DUMP(t);

	// Rebalance if necessary (at most 1 rotation)
	assert(!p || p->balance == -1 || p->balance == 0 || p->balance == 1);
	if (p && p_height_increased) {
		int height_change = 0;
		for (ZixTreeNode* i = p; i && i->parent; i = i->parent) {
			if (i == i->parent->left) {
				if (--i->parent->balance == -2) {
					zix_tree_rebalance(t, i->parent, &height_change);
					break;
				}
			} else {
				assert(i == i->parent->right);
				if (++i->parent->balance == 2) {
					zix_tree_rebalance(t, i->parent, &height_change);
					break;
				}
			}

			if (i->parent->balance == 0) {
				break;
			}
		}
	}

	DUMP(t);

	++t->size;

#ifdef ZIX_TREE_VERIFY
	if (!verify(t, t->root)) {
		return ZIX_STATUS_ERROR;
	}
#endif

	return ZIX_STATUS_SUCCESS;
}

ZIX_API
ZixStatus
zix_tree_find(const ZixTree* t, const void* e, ZixTreeIter** ti)
{
	ZixTreeNode* n = t->root;
	while (n) {
		const int cmp = t->cmp(e, n->data, t->cmp_data);
		if (cmp == 0) {
			break;
		} else if (cmp < 0) {
			n = n->left;
		} else {
			n = n->right;
		}
	}

	*ti = n;
	return (n) ? ZIX_STATUS_SUCCESS : ZIX_STATUS_NOT_FOUND;
}

ZIX_API
void*
zix_tree_get(ZixTreeIter* ti)
{
	return ti ? ti->data : NULL;
}

ZIX_API
ZixTreeIter*
zix_tree_begin(ZixTree* t)
{
	if (!t->root) {
		return NULL;
	}

	ZixTreeNode* n = t->root;
	while (n->left) {
		n = n->left;
	}
	return n;
}

ZIX_API
ZixTreeIter*
zix_tree_end(ZixTree* t)
{
	return NULL;
}

ZIX_API
bool
zix_tree_iter_is_end(ZixTreeIter* i)
{
	return !i;
}

ZIX_API
ZixTreeIter*
zix_tree_iter_next(ZixTreeIter* i)
{
	if (!i) {
		return NULL;
	}

	if (i->right) {
		i = i->right;
		while (i->left) {
			i = i->left;
		}
	} else {
		while (i->parent && i->parent->right == i) {  // i is a right child
			i = i->parent;
		}

		i = i->parent;
	}

	return i;
}