/*
  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;
}

ZIX_PRIVATE 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);
	}
}

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

ZIX_PRIVATE 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
 */
ZIX_PRIVATE 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
 *
 */
ZIX_PRIVATE 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
 *
 */
ZIX_PRIVATE 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
 *
 */
ZIX_PRIVATE 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;
}

ZIX_PRIVATE 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_remove(ZixTree* t, ZixTreeIter* ti)
{
	ZixTreeNode* const n          = ti;
	ZixTreeNode**      pp         = NULL;  // parent pointer
	ZixTreeNode*       to_balance = n->parent;  // lowest node to balance
	int8_t             d_balance  = 0;  // delta(balance) for n->parent

	DEBUG_PRINTF("*** REMOVE %ld\n", (intptr_t)n->data);

	if ((n == t->root) && !n->left && !n->right) {
		t->root = NULL;
		if (t->destroy) {
			t->destroy(n->data);
		}
		free(n);
		--t->size;
		assert(t->size == 0);
		return ZIX_STATUS_SUCCESS;
	}

	// Set pp to the parent pointer to n, if applicable
	if (n->parent) {
		assert(n->parent->left == n || n->parent->right == n);
		if (n->parent->left == n) {  // n is left child
			pp        = &n->parent->left;
			d_balance = 1;
		} else {  // n is right child
			assert(n->parent->right == n);
			pp        = &n->parent->right;
			d_balance = -1;
		}
	}

	assert(!pp || *pp == n);

	int height_change = 0;
	if (!n->left && !n->right) {
		// n is a leaf, just remove it
		if (pp) {
			*pp           = NULL;
			to_balance    = n->parent;
			height_change = (!n->parent->left && !n->parent->right) ? -1 : 0;
		}
	} else if (!n->left) {
		// Replace n with right (only) child
		if (pp) {
			*pp        = n->right;
			to_balance = n->parent;
		} else {
			t->root = n->right;
		}
		n->right->parent = n->parent;
		height_change    = -1;
	} else if (!n->right) {
		// Replace n with left (only) child
		if (pp) {
			*pp        = n->left;
			to_balance = n->parent;
		} else {
			t->root = n->left;
		}
		n->left->parent = n->parent;
		height_change   = -1;
	} else {
		// Replace n with in-order successor (leftmost child of right subtree)
		ZixTreeNode* replace = n->right;
		while (replace->left) {
			assert(replace->left->parent == replace);
			replace = replace->left;
		}

		// Remove replace from parent (replace_p)
		if (replace->parent->left == replace) {
			height_change = replace->parent->right ? 0 : -1;
			d_balance     = 1;
			to_balance    = replace->parent;
			replace->parent->left = replace->right;
		} else {
			assert(replace->parent == n);
			height_change = replace->parent->left ? 0 : -1;
			d_balance     = -1;
			to_balance    = replace->parent;
			replace->parent->right = replace->right;
		}

		if (to_balance == n) {
			to_balance = replace;
		}

		if (replace->right) {
			replace->right->parent = replace->parent;
		}

		replace->balance = n->balance;

		// Swap node to delete with replace
		if (pp) {
			*pp = replace;
		} else {
			assert(t->root == n);
			t->root = replace;
		}
		replace->parent = n->parent;
		replace->left   = n->left;
		n->left->parent = replace;
		replace->right  = n->right;
		if (n->right) {
			n->right->parent = replace;
		}

		assert(!replace->parent
		       || replace->parent->left == replace
		       || replace->parent->right == replace);
	}

	// Rebalance starting at to_balance upwards.
	for (ZixTreeNode* i = to_balance; i; i = i->parent) {
		i->balance += d_balance;
		if (d_balance == 0 || i->balance == -1 || i->balance == 1) {
			break;
		}

		assert(i != n);
		i = zix_tree_rebalance(t, i, &height_change);
		if (i->balance == 0) {
			height_change = -1;
		}

		if (i->parent) {
			if (i == i->parent->left) {
				d_balance = height_change * -1;
			} else {
				assert(i == i->parent->right);
				d_balance = height_change;
			}
		}
	}

	DUMP(t);

	if (t->destroy) {
		t->destroy(n->data);
	}
	free(n);

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

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

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

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

ZIX_API bool
zix_tree_iter_is_rend(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;
}

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

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

		i = i->parent;
	}

	return i;
}
