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/*
* Copyright © 2025 Behdad Esfahbod
*
* This is part of HarfBuzz, a text shaping library.
*
* Permission is hereby granted, without written agreement and without
* license or royalty fees, to use, copy, modify, and distribute this
* software and its documentation for any purpose, provided that the
* above copyright notice and the following two paragraphs appear in
* all copies of this software.
*
* IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
* ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
* IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.
*
* THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
* BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
* ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
* PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
*
* Author(s): Behdad Esfahbod
*/
#ifndef HB_DECYCLER_HH
#define HB_DECYCLER_HH
#include "hb.hh"
/*
* hb_decycler_t is an efficient cycle detector for graph traversal.
* It's a simple tortoise-and-hare algorithm with a twist: it's
* designed to detect cycles while traversing a graph in a DFS manner,
* instead of just a linked list.
*
* For Floyd's tortoise and hare algorithm, see:
* https://en.wikipedia.org/wiki/Cycle_detection#Floyd's_tortoise_and_hare
*
* hb_decycler_t is O(n) in the number of nodes in the DFS traversal
* if there are no cycles. Unlike Floyd's algorithm, hb_decycler_t
* can be used in a DFS traversal, where the graph is not a simple
* linked list, but a tree with possible cycles. Like Floyd's algorithm,
* it is constant-memory (~three pointers).
*
* The decycler works by creating an implicit linked-list on the stack,
* of the path from the root to the current node, and apply Floyd's
* algorithm on that list as it goes.
*
* The decycler is malloc-free, and as such, much faster to use than a
* hb_set_t or hb_map_t equivalent.
*
* The decycler detects cycles in the graph *eventually*, not *immediately*.
* That is, it may not detect a cycle until the cycle is fully traversed,
* even multiple times. See Floyd's algorithm analysis for details.
*
* The implementation saves a pointer storage on the stack by combining
* this->u.decycler and this->u.next into a union. This is possible because
* at any point we only need one of those values. The invariant is that
* after construction, and before destruction, of a node, the u.decycler
* field is always valid. The u.next field is only valid when the node is
* in the traversal path, parent to another node.
*
* There are three method's:
*
* - hb_decycler_node_t() constructor: Creates a new node in the traversal.
* The constructor takes a reference to the decycler object and inserts
* itself as the latest node in the traversal path, by advancing the hare
* pointer, and for every other descent, advancing the tortoise pointer.
*
* - ~hb_decycler_node_t() destructor: Restores the decycler object to its
* previous state by removing the node from the traversal path.
*
* - bool visit(uintptr_t value): Called on every node in the graph. Returns
* true if the node is not part of a cycle, and false if it is. The value
* parameter is used to detect cycles. It's the caller's responsibility
* to ensure that the value is unique for each node in the graph.
* The cycle detection is as simple as comparing the value to the value
* held by the tortoise pointer, which is the Floyd's algorithm.
*
* For usage examples see test-decycler.cc.
*/
struct hb_decycler_node_t;
struct hb_decycler_t
{
friend struct hb_decycler_node_t;
private:
bool tortoise_awake = false;
hb_decycler_node_t *tortoise = nullptr;
hb_decycler_node_t *hare = nullptr;
};
struct hb_decycler_node_t
{
hb_decycler_node_t (hb_decycler_t &decycler)
{
u.decycler = &decycler;
decycler.tortoise_awake = !decycler.tortoise_awake;
if (!decycler.tortoise)
{
// First node.
assert (decycler.tortoise_awake);
assert (!decycler.hare);
decycler.tortoise = decycler.hare = this;
return;
}
if (decycler.tortoise_awake)
decycler.tortoise = decycler.tortoise->u.next; // Time to move.
this->prev = decycler.hare;
decycler.hare->u.next = this;
decycler.hare = this;
}
~hb_decycler_node_t ()
{
hb_decycler_t &decycler = *u.decycler;
// Inverse of the constructor.
assert (decycler.hare == this);
decycler.hare = prev;
if (prev)
prev->u.decycler = &decycler;
assert (decycler.tortoise);
if (decycler.tortoise_awake)
decycler.tortoise = decycler.tortoise->prev;
decycler.tortoise_awake = !decycler.tortoise_awake;
}
bool visit (uintptr_t value_)
{
value = value_;
hb_decycler_t &decycler = *u.decycler;
if (decycler.tortoise == this)
return true; // First node; not a cycle.
if (decycler.tortoise->value == value)
return false; // Cycle detected.
return true;
}
private:
union {
hb_decycler_t *decycler;
hb_decycler_node_t *next;
} u = {nullptr};
hb_decycler_node_t *prev = nullptr;
uintptr_t value = 0;
};
#endif /* HB_DECYCLER_HH */