c550c22001-04-30Martin Stjernholm /* An implementation of a threaded red/black balanced binary tree. * * Created 2001-04-27 by Martin Stjernholm * * $Id: rbtree.h,v 1.1 2001/04/30 17:30:25 mast Exp $ */ #ifndef RBTREE_H #define RBTREE_H /* A red/black tree is a binary tree with one extra bit of info in * each node - the color of it. The following properties holds: * * o Every node is either red or black. * o A NULL leaf is considered black. * o If a node is red, its children must be black. * o Every path from a node down to all its leafs have the same * number of black nodes. * * The longest possible path in a given tree thus have alternating red * and black nodes, and the shortest possible path in it have only * black nodes. Therefore it's guaranteed that the longest path is at * most twice the length as the shortest one. */ struct rb_node_hdr { struct rb_node_hdr *prev, *next; unsigned INT16 flags; /* Overlays svalue type field in * rb_node_ind and rb_node_indval. */ }; /* Note: Don't access the ind svalue (or at least not its type field) * in the following directly, since the flags above overlay that. Use * assign_rb_node_ind_no_free() instead. */ struct rb_node_ind { struct rb_node_ind *prev, *next; /* Must be first. */ struct svalue ind; }; struct rb_node_indval { struct rb_node_indval *prev, *next; /* Must be first. */ struct svalue ind, val; }; union rb_node { struct rb_node_hdr h; struct rb_node_ind i; struct rb_node_indval iv; }; #define RB_RED 0x2000 #define RB_THREAD_PREV 0x4000 #define RB_THREAD_NEXT 0x8000 #define RB_FLAG_MASK 0xe000 /* The thread flags indicate whether the prev/next pointers are thread * pointers. A thread pointer is used whenever the pointer would * otherwise be NULL to point to next smaller/bigger element. More * specifically, the next thread pointer points to the closest parent * node whose prev pointer subtree contains it, and vice versa for the * prev thread pointer: * * p <. .> p * / . . \ * / . . \ * a . . a * / \ . . / \ * \ . . / * b . . b * / \ . <- next prev -> . / \ * ... . thread pointer . ... * \ . . / * c . . c * / \.. ../ \ */ #define RB_FLAG_MARKER 0x1000 #define RB_IND_FLAG_MASK 0xf000 /* The flag marker is set to nail direct uses of the ind type field. */ /* Operations: * * insert: * Adds a new entry only if one with the same index doesn't exist * already, replaces it otherwise. If a node was added it's * returned, otherwise zero is returned. * * add: * Adds a new entry, even if one with the same index already * exists. Returns the newly created node. * * add_after: * Adds a new entry after the given one. Returns the newly created * node. * * delete: * Deletes an arbitrary entry with the specified index, if one * exists. Returns nonzero in that case, zero otherwise. * * delete_node: * Deletes the given node from the tree. Useful to get the right * entry when several have the same index. The node is assumed to * exist in the tree. Note that it's a linear search to get the * right node among several with the same index. * * find_eq: * Returns an arbitrary entry which have the given index, or zero * if none exists. * * find_lt, find_gt, find_le, find_ge: * find_lt and find_le returns the biggest entry which satisfy the * condition, and vice versa for the other two. This means that * e.g. rb_next when used on the returned node from find_le never * returns an entry with the same index. * * If cmp_less is nonzero, it's a function pointer used as `< to * compare the entries. If it's zero the internal set order is used. * All destructive operations might change the tree root. */ /* Functions for handling nodes with index only. */ PMOD_EXPORT struct rb_node_ind *rb_ind_insert (struct rb_node_ind **tree, struct svalue *ind, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_ind *rb_ind_add (struct rb_node_ind **tree, struct svalue *ind, struct svalue *cmp_less); PMOD_EXPORT int rb_ind_delete (struct rb_node_ind **tree, struct svalue *ind, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_ind *rb_ind_copy (struct rb_node_ind *tree); PMOD_EXPORT void rb_ind_free (struct rb_node_ind *tree); /* Functions for handling nodes with index and value. */ PMOD_EXPORT struct rb_node_indval *rb_indval_insert (struct rb_node_indval **tree, struct svalue *ind, struct svalue *val, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_indval *rb_indval_add (struct rb_node_indval **tree, struct svalue *ind, struct svalue *val, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_indval *rb_indval_add_after (struct rb_node_indval **tree, struct rb_node_indval *node, struct svalue *ind, struct svalue *val, struct svalue *cmp_less); PMOD_EXPORT int rb_indval_delete (struct rb_node_indval **tree, struct svalue *ind, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_indval *rb_indval_delete_node (struct rb_node_indval **tree, struct rb_node_indval *node, struct svalue *cmp_less); PMOD_EXPORT struct rb_node_indval *rb_indval_copy (struct rb_node_indval *tree); PMOD_EXPORT void rb_indval_free (struct rb_node_indval *tree); /* Functions for handling both types of nodes. */ PMOD_EXPORT union rb_node *rb_find_eq (union rb_node *tree, struct svalue *key, struct svalue *cmp_less); PMOD_EXPORT union rb_node *rb_find_lt (union rb_node *tree, struct svalue *key, struct svalue *cmp_less); PMOD_EXPORT union rb_node *rb_find_gt (union rb_node *tree, struct svalue *key, struct svalue *cmp_less); PMOD_EXPORT union rb_node *rb_find_le (union rb_node *tree, struct svalue *key, struct svalue *cmp_less); PMOD_EXPORT union rb_node *rb_find_ge (union rb_node *tree, struct svalue *key, struct svalue *cmp_less); /* Functions for handling any type of node. */ PMOD_EXPORT struct rb_node_hdr *rb_first (struct rb_node_hdr *tree); PMOD_EXPORT struct rb_node_hdr *rb_last (struct rb_node_hdr *tree); PMOD_EXPORT struct rb_node_hdr *rb_prev (struct rb_node_hdr *node); PMOD_EXPORT struct rb_node_hdr *rb_next (struct rb_node_hdr *node); #define RB_IND_FIND_FUNC(func, tree, key, cmp_less) \ ((struct rb_node_ind *) func ((union rb_node *) (tree), (key), (cmp_less))) #define RB_IND_STEP_FUNC(func, tree) \ ((struct rb_node_ind *) func ((struct rb_node_hdr *) (tree))) #define rb_ind_find_eq(tree, key, cmp_less) \ RB_IND_FIND_FUNC (rb_find_eq, tree, key, cmp_less) #define rb_ind_find_lt(tree, key, cmp_less) \ RB_IND_FIND_FUNC (rb_find_lt, tree, key, cmp_less) #define rb_ind_find_gt(tree, key, cmp_less) \ RB_IND_FIND_FUNC (rb_find_gt, tree, key, cmp_less) #define rb_ind_find_le(tree, key, cmp_less) \ RB_IND_FIND_FUNC (rb_find_le, tree, key, cmp_less) #define rb_ind_find_ge(tree, key, cmp_less) \ RB_IND_FIND_FUNC (rb_find_ge, tree, key, cmp_less) #define rb_ind_first(tree) RB_IND_STEP_FUNC (rb_first, tree) #define rb_ind_last(tree) RB_IND_STEP_FUNC (rb_last, tree) #define rb_ind_prev(tree) RB_IND_STEP_FUNC (rb_prev, tree) #define rb_ind_next(tree) RB_IND_STEP_FUNC (rb_next, tree) #define RB_INDVAL_FIND_FUNC(func, tree, key, cmp_less) \ ((struct rb_node_indval *) func ((union rb_node *) (tree), (key), (cmp_less))) #define RB_INDVAL_STEP_FUNC(func, tree) \ ((struct rb_node_indval *) func ((struct rb_node_hdr *) (tree))) #define rb_indval_find_eq(tree, key, cmp_less) \ RB_INDVAL_FIND_FUNC (rb_find_eq, tree, key, cmp_less) #define rb_indval_find_lt(tree, key, cmp_less) \ RB_INDVAL_FIND_FUNC (rb_find_lt, tree, key, cmp_less) #define rb_indval_find_gt(tree, key, cmp_less) \ RB_INDVAL_FIND_FUNC (rb_find_gt, tree, key, cmp_less) #define rb_indval_find_le(tree, key, cmp_less) \ RB_INDVAL_FIND_FUNC (rb_find_le, tree, key, cmp_less) #define rb_indval_find_ge(tree, key, cmp_less) \ RB_INDVAL_FIND_FUNC (rb_find_ge, tree, key, cmp_less) #define rb_indval_first(tree) RB_INDVAL_STEP_FUNC (rb_first, tree) #define rb_indval_last(tree) RB_INDVAL_STEP_FUNC (rb_last, tree) #define rb_indval_prev(tree) RB_INDVAL_STEP_FUNC (rb_prev, tree) #define rb_indval_next(tree) RB_INDVAL_STEP_FUNC (rb_next, tree) /* Accessing the index svalue in a node. */ #define assign_rb_node_ind_no_free(to, node) do { \ struct svalue *_rb_node_to = (to); \ *_rb_node_to = (node)->ind; \ _rb_node_to->type &= ~RB_IND_FLAG_MASK; \ add_ref_svalue (_rb_node_to); \ } while (0) #define assign_rb_node_ind(to, node) do { \ struct svalue *_rb_node_to2 = (to); \ free_svalue (_rb_node_to2); \ assign_rb_node_ind_no_free (_rb_node_to2, (node)); \ } while (0) #define push_rb_node_ind(node) do { \ assign_rb_node_ind_no_free (Pike_sp, (node)); \ Pike_sp++; \ } while (0) #define use_rb_node_ind(node, var) \ (var = (node)->ind, var.type &= ~RB_IND_FLAG_MASK, var) /* Low-level tools, for use with arbitrary data. These only requires * that the nodes begin with the rb_node_hdr struct. */ /* A sliced stack is used to track the way down in a tree, so we can * back up again easily while rebalancing it. The first slice is * allocated on the C stack. */ #define STACK_SLICE_SIZE 20 /* This is in the worst possible case enough for trees of size * 2^(20/2) = 1024 before allocating another slice, but in the typical * case it's enough for trees with up to about 2^(20-1) = 524288 * elements. */ struct rb_stack_slice { struct rb_stack_slice *up; struct rb_node_hdr *stack[STACK_SLICE_SIZE]; }; #define RBSTACK_INIT(slice, ssp) \ struct rb_stack_slice PIKE_CONCAT3 (_top_, slice, _); \ struct rb_stack_slice *slice = \ (PIKE_CONCAT3 (_top_, slice, _).up = 0, \ &PIKE_CONCAT3 (_top_, slice, _)); \ size_t ssp = 0 /* Only zero when the stack is empty. */ #define RBSTACK_PUSH(slice, ssp, node) do { \ if (ssp < STACK_SLICE_SIZE) \ slice->stack[ssp++] = (node); \ else { \ struct rb_stack_slice *_new_ = ALLOC_STRUCT (rb_stack_slice); \ _new_->up = slice; \ slice = _new_; \ slice->stack[0] = (node); \ ssp = 1; \ } \ } while (0) #define RBSTACK_POP(slice, ssp, node) do { \ if (ssp) { \ (node) = slice->stack[--ssp]; \ if (!ssp && slice->up) { \ struct rb_stack_slice *_old_ = slice; \ slice = slice->up; \ ssp = STACK_SLICE_SIZE; \ xfree (_old_); \ } \ } \ else (node) = 0; \ } while (0) #define RBSTACK_POP_IGNORE(slice, ssp) do { \ if (ssp && !--ssp && slice->up) { \ struct rb_stack_slice *_old_ = slice; \ slice = slice->up; \ ssp = STACK_SLICE_SIZE; \ xfree (_old_); \ } \ } while (0) #define RBSTACK_UP(slice, ssp, node) do { \ if (ssp) { \ (node) = slice->stack[--ssp]; \ if (!ssp && slice->up) { \ slice = slice->up; \ ssp = STACK_SLICE_SIZE; \ } \ } \ else (node) = 0; \ } while (0) #define RBSTACK_PEEK(slice, ssp, node) do { \ if (ssp) (node) = slice->stack[ssp - 1]; \ else (node) = 0; \ } while (0) #define RBSTACK_FREE(slice) do { \ while (slice->up) { \ struct rb_stack_slice *_old_ = slice; \ slice = slice->up; \ xfree (_old_); \ } \ } while (0) #define RBSTACK_FREE_SET_ROOT(slice, ssp, node) do { \ if (ssp) { \ while (slice->up) { \ struct rb_stack_slice *_old_ = slice; \ slice = slice->up; \ xfree (_old_); \ } \ (node) = slice->stack[0]; \ } \ } while (0) /* Traverses the tree in depth-first order: * push Run when entering a node. * p_leaf Run when the nodes prev pointer isn't a subtree. * p_sub Run when the nodes prev pointer is a subtree. * between Run after the prev subtree has been recursed and before * the next subtree is examined. * n_leaf Run when the nodes next pointer isn't a subtree. * n_sub Run when the nodes next pointer is a subtree. * pop Run when leaving a node. */ #define LOW_RB_TRAVERSE(label, slice, ssp, node, push, p_leaf, p_sub, between, n_leaf, n_sub, pop) \ do { \ struct rb_node_hdr *low_rb_last_; \ if (node) { \ PIKE_CONCAT (enter_, label): \ {push;} \ if ((node)->flags & RB_THREAD_PREV) \ {p_leaf;} \ else { \ {p_sub;} \ RBSTACK_PUSH (slice, ssp, node); \ (node) = (node)->prev; \ goto PIKE_CONCAT (enter_, label); \ } \ PIKE_CONCAT (between_, label): \ {between;} \ if ((node)->flags & RB_THREAD_NEXT) \ {n_leaf;} \ else { \ {n_sub;} \ RBSTACK_PUSH (slice, ssp, node); \ (node) = (node)->next; \ goto PIKE_CONCAT (enter_, label); \ } \ PIKE_CONCAT (leave_, label): \ while (1) { \ {pop;} \ low_rb_last_ = (node); \ RBSTACK_POP (slice, ssp, node); \ if (!(node)) break; \ if (low_rb_last_ == (node)->prev) \ goto PIKE_CONCAT (between_, label); \ } \ } \ } while (0) #define LOW_RB_DEBUG_TRAVERSE(label, slice, ssp, node, push, p_leaf, p_sub, between, n_leaf, n_sub, pop) \ do { \ size_t PIKE_CONCAT (depth_, label) = 0; \ LOW_RB_TRAVERSE( \ label, slice, ssp, node, \ fprintf (stderr, "%*s%p enter\n", \ PIKE_CONCAT (depth_, label)++, "", node); {push;}, \ fprintf (stderr, "%*s%p prev leaf\n", \ PIKE_CONCAT (depth_, label), "", node); {p_leaf;}, \ fprintf (stderr, "%*s%p prev subtree\n", \ PIKE_CONCAT (depth_, label), "", node); {p_sub;}, \ fprintf (stderr, "%*s%p between\n", \ PIKE_CONCAT (depth_, label) - 1, "", node); {between;}, \ fprintf (stderr, "%*s%p next leaf\n", \ PIKE_CONCAT (depth_, label), "", node); {n_leaf;}, \ fprintf (stderr, "%*s%p next subtree\n", \ PIKE_CONCAT (depth_, label), "", node); {n_sub;}, \ fprintf (stderr, "%*s%p leave\n", \ --PIKE_CONCAT (depth_, label), "", node); {pop;}); \ } while (0) #define LOW_RB_FIND(node, cmp, got_lt, got_eq, got_gt) \ do { \ int cmp_res; \ while (1) { \ DO_IF_DEBUG (if (!node) fatal ("Recursing into null node.\n")); \ {cmp;} \ if (cmp_res > 0) { \ if ((node)->flags & RB_THREAD_NEXT) { \ {got_lt;} \ break; \ } \ (node) = (node)->next; \ } \ else if (cmp_res < 0) { \ if ((node)->flags & RB_THREAD_PREV) { \ {got_gt;} \ break; \ } \ (node) = (node)->prev; \ } \ else { \ {got_eq;} \ break; \ } \ } \ } while (0) /* Tracks the way down a tree to a specific node and updates the stack * as necessary for low_rb_link_* and low_rb_unlink. */ #define LOW_RB_TRACK(slice, ssp, node, cmp, got_lt, got_eq, got_gt) \ LOW_RB_FIND (node, { \ RBSTACK_PUSH (slice, ssp, node); \ {cmp;} \ }, got_lt, got_eq, got_gt) /* Goes to the next node in order while keeping the stack updated. */ #define LOW_RB_TRACK_NEXT(slice, ssp, node) \ do { \ DO_IF_DEBUG ({ \ struct rb_node_hdr *low_rb_stack_top_; \ RBSTACK_PEEK (slice, ssp, low_rb_stack_top_); \ if (node != low_rb_stack_top_) \ fatal ("Given node is not on top of stack.\n"); \ }); \ if (node->flags & RB_THREAD_NEXT) { \ struct rb_node_hdr *low_rb_next_ = node->next; \ while (1) { \ RBSTACK_PEEK (slice, ssp, node); \ if (node == low_rb_next_) break; \ RBSTACK_POP_IGNORE (slice, ssp); \ } \ } \ else { \ node = node->next; \ RBSTACK_PUSH (slice, ssp, node); \ while (!(node->flags & RB_THREAD_PREV)) { \ node = node->prev; \ RBSTACK_PUSH (slice, ssp, node); \ } \ } \ } while (0) typedef int low_rb_cmp_fn (void *key, struct rb_node_hdr *node); /* Used when unlinking nodes. Since an interior node can't be unlinked * we need to move over the data from a leaf node and unlink that * instead. */ typedef void low_rb_move_data_fn (struct rb_node_hdr *to, struct rb_node_hdr *from); typedef struct rb_node_hdr *low_rb_alloc_copy_fn (struct rb_node_hdr *node); void low_rb_init_root (struct rb_node_hdr *new_root); void low_rb_link_at_prev (struct rb_node_hdr **tree, struct rb_stack_slice *slice, size_t ssp, struct rb_node_hdr *new); void low_rb_link_at_next (struct rb_node_hdr **tree, struct rb_stack_slice *slice, size_t ssp, struct rb_node_hdr *new); struct rb_node_hdr *low_rb_unlink (struct rb_node_hdr **tree, struct rb_stack_slice *slice, size_t ssp, low_rb_move_data_fn *move_data); struct rb_node_hdr *low_rb_insert (struct rb_node_hdr **tree, low_rb_cmp_fn *cmpfun, void *key, struct rb_node_hdr *new); void low_rb_add (struct rb_node_hdr **tree, low_rb_cmp_fn *cmpfun, void *key, struct rb_node_hdr *new); void low_rb_add_after (struct rb_node_hdr **tree, low_rb_cmp_fn *cmpfun, void *key, struct rb_node_hdr *new, struct rb_node_hdr *existing); struct rb_node_hdr *low_rb_delete (struct rb_node_hdr **tree, low_rb_cmp_fn *cmpfun, void *key, low_rb_move_data_fn *move_data); struct rb_node_hdr *low_rb_delete_node (struct rb_node_hdr **tree, low_rb_cmp_fn *cmpfun, void *key, low_rb_move_data_fn *move_data, struct rb_node_hdr *node); struct rb_node_hdr *low_rb_copy (struct rb_node_hdr *tree, low_rb_alloc_copy_fn *alloc_copy); struct rb_node_hdr *low_rb_find_eq (struct rb_node_hdr *tree, low_rb_cmp_fn *cmpfun, void *key); struct rb_node_hdr *low_rb_find_lt (struct rb_node_hdr *tree, low_rb_cmp_fn *cmpfun, void *key); struct rb_node_hdr *low_rb_find_gt (struct rb_node_hdr *tree, low_rb_cmp_fn *cmpfun, void *key); struct rb_node_hdr *low_rb_find_le (struct rb_node_hdr *tree, low_rb_cmp_fn *cmpfun, void *key); struct rb_node_hdr *low_rb_find_ge (struct rb_node_hdr *tree, low_rb_cmp_fn *cmpfun, void *key); #ifdef PIKE_DEBUG void debug_check_rb_tree (struct rb_node_hdr *tree); #endif void init_rbtree (void); void exit_rbtree (void); #endif /* RBTREE_H */