commit 04d31e992a5998800b63b2b81c36ceb55b4223eb
Author: mo8it <mo8it@proton.me>
Date:   Thu Jul 6 16:35:21 2023 +0200

    Initial commit

diff --git a/.gitignore b/.gitignore
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diff --git a/Cargo.lock b/Cargo.lock
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+[package]
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diff --git a/LICENSE.txt b/LICENSE.txt
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index 0000000..21a3458
--- /dev/null
+++ b/LICENSE.txt
@@ -0,0 +1,661 @@
+                    GNU AFFERO GENERAL PUBLIC LICENSE
+                       Version 3, 19 November 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU Affero General Public License is a free, copyleft license for
+software and other kinds of works, specifically designed to ensure
+cooperation with the community in the case of network server software.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+our General Public Licenses are intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  Developers that use our General Public Licenses protect your rights
+with two steps: (1) assert copyright on the software, and (2) offer
+you this License which gives you legal permission to copy, distribute
+and/or modify the software.
+
+  A secondary benefit of defending all users' freedom is that
+improvements made in alternate versions of the program, if they
+receive widespread use, become available for other developers to
+incorporate.  Many developers of free software are heartened and
+encouraged by the resulting cooperation.  However, in the case of
+software used on network servers, this result may fail to come about.
+The GNU General Public License permits making a modified version and
+letting the public access it on a server without ever releasing its
+source code to the public.
+
+  The GNU Affero General Public License is designed specifically to
+ensure that, in such cases, the modified source code becomes available
+to the community.  It requires the operator of a network server to
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+users of that server.  Therefore, public use of a modified version, on
+a publicly accessible server, gives the public access to the source
+code of the modified version.
+
+  An older license, called the Affero General Public License and
+published by Affero, was designed to accomplish similar goals.  This is
+a different license, not a version of the Affero GPL, but Affero has
+released a new version of the Affero GPL which permits relicensing under
+this license.
+
+  The precise terms and conditions for copying, distribution and
+modification follow.
+
+                       TERMS AND CONDITIONS
+
+  0. Definitions.
+
+  "This License" refers to version 3 of the GNU Affero General Public License.
+
+  "Copyright" also means copyright-like laws that apply to other kinds of
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+unpacking, reading or copying.
+
+  7. Additional Terms.
+
+  "Additional permissions" are terms that supplement the terms of this
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+Additional permissions that are applicable to the entire Program shall
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+apply only to part of the Program, that part may be used separately
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+this License without regard to the additional permissions.
+
+  When you convey a copy of a covered work, you may at your option
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+
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+
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+
+  9. Acceptance Not Required for Having Copies.
+
+  You are not required to accept this License in order to receive or
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+
+  10. Automatic Licensing of Downstream Recipients.
+
+  Each time you convey a covered work, the recipient automatically
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+
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+  A "contributor" is a copyright holder who authorizes use under this
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+  A contributor's "essential patent claims" are all patent claims
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+
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+
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+
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+
+  A patent license is "discriminatory" if it does not include within
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+specifically granted under this License.  You may not convey a covered
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+in the business of distributing software, under which you make payment
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+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
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+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+  Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+  12. No Surrender of Others' Freedom.
+
+  If conditions are imposed on you (whether by court order, agreement or
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+not convey it at all.  For example, if you agree to terms that obligate you
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+License would be to refrain entirely from conveying the Program.
+
+  13. Remote Network Interaction; Use with the GNU General Public License.
+
+  Notwithstanding any other provision of this License, if you modify the
+Program, your modified version must prominently offer all users
+interacting with it remotely through a computer network (if your version
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+following paragraph.
+
+  Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
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+License will continue to apply to the part which is the covered work,
+but the work with which it is combined will remain governed by version
+3 of the GNU General Public License.
+
+  14. Revised Versions of this License.
+
+  The Free Software Foundation may publish revised and/or new versions of
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+will be similar in spirit to the present version, but may differ in detail to
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+
+  Each version is given a distinguishing version number.  If the
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+option of following the terms and conditions either of that numbered
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+Foundation.  If the Program does not specify a version number of the
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+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
+versions of the GNU Affero General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
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+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
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+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    pivot-saw
+    Copyright (C) 2023  Mo Bitar (@mo8it)
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Affero General Public License as published
+    by the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Affero General Public License for more details.
+
+    You should have received a copy of the GNU Affero General Public License
+    along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If your software can interact with users remotely through a computer
+network, you should also make sure that it provides a way for users to
+get its source.  For example, if your program is a web application, its
+interface could display a "Source" link that leads users to an archive
+of the code.  There are many ways you could offer source, and different
+solutions will be better for different programs; see section 13 for the
+specific requirements.
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU AGPL, see
+<https://www.gnu.org/licenses/>.
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..e69de29
diff --git a/src/main.rs b/src/main.rs
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--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,124 @@
+use nalgebra::base::{Matrix3, Vector3};
+use rand::{distributions::Uniform, prelude::Distribution, rngs::SmallRng, Rng, SeedableRng};
+use std::collections::HashSet;
+
+type Transformation = Matrix3<i64>;
+type Point = Vector3<i64>;
+
+struct Transformations {
+    ms: Vec<Transformation>,
+    dist: Uniform<usize>,
+}
+
+impl Transformations {
+    pub fn new() -> Self {
+        let len = 23;
+        let mut ms = Vec::with_capacity(len);
+
+        let mut unit_matrix_skipped = false;
+
+        for v0 in [1, -1] {
+            for v1 in [1, -1] {
+                for v2 in [1, -1] {
+                    for ind in 0..3 {
+                        if unit_matrix_skipped {
+                            let mut m = Matrix3::zeros();
+
+                            *m.index_mut((0, ind)) = v0;
+                            *m.index_mut((1, (ind + 1) % 3)) = v1;
+                            *m.index_mut((2, (ind + 2) % 3)) = v2;
+
+                            ms.push(m);
+                        } else {
+                            unit_matrix_skipped = true;
+                        }
+                    }
+                }
+            }
+        }
+
+        debug_assert_eq!(len, ms.len());
+
+        Self {
+            ms,
+            dist: Uniform::new(0, len),
+        }
+    }
+
+    pub fn rand(&self, rng: &mut impl Rng) -> &Transformation {
+        let ind = self.dist.sample(rng);
+
+        unsafe { self.ms.get_unchecked(ind) }
+    }
+}
+
+struct Walk {
+    points: Vec<Point>,
+    new_points: Vec<Point>,
+    pivot_dist: Uniform<usize>,
+    set: HashSet<Point>,
+}
+
+impl Walk {
+    pub fn new(n: usize) -> Self {
+        let max = i64::try_from(n).unwrap();
+
+        let points = (0..max).map(|i| Point::new(i, 0, 0)).collect();
+
+        let new_points = Vec::with_capacity(n - 1);
+
+        let pivot_dist = Uniform::new(0, n - 1);
+
+        let set = HashSet::with_capacity(n);
+
+        Self {
+            points,
+            new_points,
+            pivot_dist,
+            set,
+        }
+    }
+
+    pub fn pivot(&mut self, rng: &mut impl Rng, transformations: &Transformations) {
+        loop {
+            self.set.clear();
+            self.new_points.clear();
+
+            let m = transformations.rand(rng);
+
+            let pivot_ind = self.pivot_dist.sample(rng);
+
+            let (s1, s2) = self.points.split_at_mut(pivot_ind + 1);
+            let pivot = unsafe { s1.get_unchecked(pivot_ind) };
+
+            for point in s2.iter() {
+                self.new_points.push((m * (point - pivot)) + pivot);
+            }
+
+            if s1
+                .iter()
+                .chain(self.new_points.iter())
+                .all(|point| self.set.insert(*point))
+            {
+                for (old_point, new_point) in s2.iter_mut().zip(self.new_points.iter()) {
+                    *old_point = *new_point;
+                }
+
+                return;
+            };
+        }
+    }
+}
+
+fn main() {
+    let transformations = Transformations::new();
+
+    let n = 1_000;
+
+    let seed = 42;
+    let mut rng = SmallRng::seed_from_u64(seed);
+
+    let mut walk = Walk::new(n);
+
+    walk.pivot(&mut rng, &transformations);
+}