solved part 1 of day 14 of 2024

2024-12-15 13:22:03 +01:00 · 2024-12-15 13:22:03 +01:00 · 49262fba4a
Commit 49262fba4a
--- a/Cargo.lock
+++ b/Cargo.lock
@ -7,8 +7,10 @@ name = "advent-of-code"
 version = "0.1.0"
 dependencies = [
 "advent-of-code-macros",
+ "log",
 "num",
 "regex",
+ "thousands",
 ]

 [[package]]
@ -35,6 +37,12 @@ version = "1.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "ace50bade8e6234aa140d9a2f552bbee1db4d353f69b8217bc503490fc1a9f26"

+[[package]]
+name = "log"
+version = "0.4.22"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a7a70ba024b9dc04c27ea2f0c0548feb474ec5c54bba33a7f72f873a39d07b24"
+
 [[package]]
 name = "memchr"
 version = "2.7.4"
@ -172,6 +180,12 @@ dependencies = [
 "unicode-ident",
 ]

+[[package]]
+name = "thousands"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3bf63baf9f5039dadc247375c29eb13706706cfde997d0330d05aa63a77d8820"
+
 [[package]]
 name = "unicode-ident"
 version = "1.0.14"
--- a/Cargo.toml
+++ b/Cargo.toml
@ -310,6 +310,8 @@ name = "advent_of_code"

 [dependencies]
 num="0.4.*"
+log="0.4.*"
+thousands="0.2.*"

 [dependencies.advent-of-code-macros]
 path = "macros"
--- a/15
+++ b/15
@ -0,0 +1,15 @@
+CARGO:=cargo
+CARGO_OPTS:=-q
+TARGET_DIR:=debug
+
+fmt:
+	@$(CARGO) fmt 2>/dev/null
+
+%: fmt
+	@$(CARGO) build $(CARGO_OPTS) --bin $@
+	@timeout --preserve-status -v 60 ./target/$(TARGET_DIR)/$@
+
+Makefile:
+	exit
+
+all: 202{3,4}-{01..25}
--- a/examples/2024/14.txt
+++ b/examples/2024/14.txt
@ -0,0 +1,12 @@
+p=0,4 v=3,-3
+p=6,3 v=-1,-3
+p=10,3 v=-1,2
+p=2,0 v=2,-1
+p=0,0 v=1,3
+p=3,0 v=-2,-2
+p=7,6 v=-1,-3
+p=3,0 v=-1,-2
+p=9,3 v=2,3
+p=7,3 v=-1,2
+p=2,4 v=2,-3
+p=9,5 v=-3,-3
--- a/rustfmt.toml
+++ b/rustfmt.toml
@ -0,0 +1,17 @@
+array_width = 0
+binop_separator= "Back"
+brace_style="SameLineWhere"
+chain_width = 240
+fn_params_layout = "Tall"
+force_explicit_abi = true
+hard_tabs = false
+imports_layout = "Vertical"
+match_block_trailing_comma = true
+max_width = 240
+merge_derives = true
+newline_style = "Unix"
+remove_nested_parens = true
+reorder_imports = true
+reorder_modules = true
+single_line_if_else_max_width = 0
+tab_spaces = 4
--- a/src/bin/2024/14.rs
+++ b/src/bin/2024/14.rs
@ -0,0 +1,126 @@
+use advent_of_code::{
+    strings::{convert_to_array, parsenumber},
+    Kartesian, Velocity, KD,
+};
+#[allow(unused_imports)]
+use advent_of_code_macros::{include_data, include_example};
+
+include_data!(DATA 2024 14);
+
+fn parse_robot(line: &str) -> (Kartesian<u32>, Velocity<u32>) {
+    let mut dir = KD::None;
+    let mut x = 0;
+    let mut y = 0;
+    let mut position = Kartesian::default();
+    for part in line.splitn(2, ' ') {
+        match part.get(0..2).unwrap_or("") {
+            "p=" => {
+                let (y, x) = part.get(2..).unwrap().split_once(',').unwrap();
+                position.x = parsenumber(x);
+                position.y = parsenumber(y);
+            },
+            "v=" => {
+                let (ys, xs) = part.get(2..).unwrap().split_once(',').unwrap();
+                x = parsenumber(xs);
+                y = parsenumber(ys);
+                dir = if xs.get(0..1).unwrap() == "-" && x != 0 {
+                    dir.up()
+                } else if x > 0 {
+                    dir.down()
+                } else {
+                    dir
+                };
+                dir = if ys.get(0..1).unwrap() == "-" && y != 0 {
+                    dir.left()
+                } else if x > 0 {
+                    dir.right()
+                } else {
+                    dir
+                };
+            },
+            _ => {},
+        }
+    }
+
+    (position, Velocity::new(x, y, dir))
+}
+
+fn get_end_start(v: u32) -> (u32, u32) {
+    match v % 2 {
+        0 => (v / 2, v / 2),
+        1 => ((v - 1) / 2 - 1, (v + 1) / 2),
+        _ => unreachable!(),
+    }
+}
+
+fn calc_safety(coords: Vec<Kartesian<u32>>, space: Kartesian<u32>) -> (u32, u32, u32, u32) {
+    let mut robots = (0, 0, 0, 0);
+    let (x_end, x_start) = get_end_start(space.x);
+    let (y_end, y_start) = get_end_start(space.y);
+    for robot in coords {
+        if robot.x <= x_end && robot.y <= y_end {
+            robots.0 += 1;
+        } else if robot.x <= x_end && robot.y >= y_start {
+            robots.1 += 1
+        } else if robot.x >= x_start && robot.y <= y_end {
+            robots.2 += 1
+        } else if robot.x >= x_start && robot.y >= y_start {
+            robots.3 += 1
+        } else {
+            println!("Robot outside of quarts {}:", robot);
+            println!("1. {}..={}:{}..={}", 0, x_end, 0, y_end);
+            println!("2. {}..={}:{}..={}", 0, x_end, y_start, space.y - 1);
+            println!("3. {}..={}:{}..={}", x_start, space.x - 1, 0, y_end);
+            println!("4. {}..={}:{}..={}", x_start, space.x - 1, y_start, space.y - 1);
+        }
+    }
+    println!("Robot in quarts: {}, {}, {}, {}", robots.0, robots.1, robots.2, robots.3);
+    robots
+}
+
+fn calc_final(r: (u32, u32, u32, u32)) -> u32 {
+    r.0 * r.1 * r.2 * r.3
+}
+
+fn main() {
+    const SPACE: Kartesian<u32> = Kartesian::new(103, 101);
+
+    let mut target_coords = Vec::new();
+    let robots = convert_to_array::<_, _, '\n'>(DATA, parse_robot);
+    for (mut position, velocity) in robots {
+        for _i in 0..100 {
+            position = position.wrapping_move_velocity(velocity, SPACE);
+        }
+        target_coords.push(position);
+    }
+    println!("{:?}", target_coords);
+    println!("Safety Factor: {}", calc_final(calc_safety(target_coords, SPACE)));
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_start_end() {
+        assert_eq!(get_end_start(7), (2, 4))
+    }
+    #[test]
+    fn test_safety() {
+        let positions = vec![
+            Kartesian { x: 5, y: 3 },
+            Kartesian { x: 4, y: 5 },
+            Kartesian { x: 0, y: 9 },
+            Kartesian { x: 5, y: 4 },
+            Kartesian { x: 6, y: 1 },
+            Kartesian { x: 3, y: 1 },
+            Kartesian { x: 0, y: 6 },
+            Kartesian { x: 3, y: 2 },
+            Kartesian { x: 2, y: 0 },
+            Kartesian { x: 0, y: 6 },
+            Kartesian { x: 5, y: 4 },
+            Kartesian { x: 6, y: 6 },
+        ];
+        assert_eq!(calc_safety(positions, Kartesian::new(7, 11)), (1, 3, 4, 1));
+    }
+}
--- a/src/coordinate_systems/kartesian/direction.rs
+++ b/src/coordinate_systems/kartesian/direction.rs
@ -3,13 +3,14 @@ use std::fmt::Display;
 use super::{Kartesian, KartesianIterator};
 use num::*;

-#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Default)]
 pub enum KartesianDirection {
+    #[default]
+    None,
    TopLeft,
    Top,
    TopRight,
    Left,
-    None,
    Right,
    BottomLeft,
    Bottom,
--- a/src/coordinate_systems/kartesian/external_traits.rs
+++ b/src/coordinate_systems/kartesian/external_traits.rs
@ -0,0 +1,142 @@
+use super::{Kartesian, KartesianDirection, KartesianIterator};
+use super::{Map, Velocity};
+use num::*;
+use std::{fmt::Display, ops::*};
+
+impl<T: Integer> Add for Kartesian<T> {
+    fn add(self, rhs: Self) -> Self::Output {
+        Kartesian { x: self.x + rhs.x, y: self.y + rhs.y }
+    }
+
+    type Output = Kartesian<T>;
+}
+
+impl<T: Integer + AddAssign> AddAssign for Kartesian<T> {
+    fn add_assign(&mut self, rhs: Self) {
+        self.x += rhs.x;
+        self.y += rhs.y;
+    }
+}
+
+impl<T: Integer> Sub for Kartesian<T> {
+    fn sub(self, rhs: Self) -> Self::Output {
+        Kartesian { x: self.x - rhs.x, y: self.y - rhs.y }
+    }
+
+    type Output = Kartesian<T>;
+}
+
+impl<T: Integer + SubAssign> SubAssign for Kartesian<T> {
+    fn sub_assign(&mut self, rhs: Self) {
+        self.x -= rhs.x;
+        self.y -= rhs.y;
+    }
+}
+
+impl<T: Integer + Display + Copy> Display for Kartesian<T> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        f.write_fmt(format_args!("{}:{}", self.x, self.y))
+    }
+}
+
+impl<T: Integer + Copy> Div<T> for Kartesian<T> {
+    type Output = Kartesian<T>;
+    fn div(self, rhs: T) -> Self::Output {
+        Kartesian {
+            x: self.x.div_ceil(&rhs),
+            y: self.y.div_ceil(&rhs),
+        }
+    }
+}
+
+impl<T: Integer + Rem> Rem for Kartesian<T> {
+    type Output = Self;
+    fn rem(self, rhs: Self) -> Self {
+        Kartesian { x: self.x % rhs.x, y: self.y % rhs.y }
+    }
+}
+impl<T: Integer + RemAssign> RemAssign for Kartesian<T> {
+    fn rem_assign(&mut self, rhs: Self) {
+        self.x %= rhs.x;
+        self.y %= rhs.y;
+    }
+}
+
+impl Iterator for KartesianIterator {
+    type Item = KartesianDirection;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let mut i = self.i;
+        if self.straight {
+            if i < 4 {
+                self.i += 1;
+            }
+            match i {
+                0 => return Some(KartesianDirection::Right),
+                1 => return Some(KartesianDirection::Bottom),
+                2 => return Some(KartesianDirection::Left),
+                3 => return Some(KartesianDirection::Top),
+                _ => i -= 4,
+            }
+        }
+        if self.none {
+            if i == 0 {
+                self.i += 1;
+                return Some(KartesianDirection::None);
+            }
+            i -= 1;
+        }
+        if self.diagonal {
+            if i < 4 {
+                self.i += 1;
+            }
+            match i {
+                0 => return Some(KartesianDirection::TopLeft),
+                1 => return Some(KartesianDirection::TopRight),
+                2 => return Some(KartesianDirection::BottomLeft),
+                3 => return Some(KartesianDirection::BottomRight),
+                _ => {},
+            }
+        }
+        None
+    }
+}
+
+impl<T: Display + Copy + Default> Display for Map<T> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        for row in self.data.iter() {
+            for v in row.iter() {
+                v.fmt(f)?
+            }
+            for _ in row.len()..=self.maximum.y {
+                T::default().fmt(f)?
+            }
+            println!()
+        }
+        for _ in self.data.len()..=self.maximum.x {
+            for _ in 0..self.maximum.y {
+                T::default().fmt(f)?
+            }
+            println!()
+        }
+        Ok(())
+    }
+}
+
+impl<T: Integer + Display + Unsigned + Copy> Display for Velocity<T> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        f.write_str(match self.direction {
+            KartesianDirection::None => "⏺",
+            KartesianDirection::TopLeft => "↖",
+            KartesianDirection::Top => "↑",
+            KartesianDirection::TopRight => "↗",
+            KartesianDirection::Left => "←",
+            KartesianDirection::Right => "→",
+            KartesianDirection::BottomLeft => "↙",
+            KartesianDirection::Bottom => "↓",
+            KartesianDirection::BottomRight => "↘",
+        })?;
+        self.speed.fmt(f)?;
+        Ok(())
+    }
+}
--- a/src/coordinate_systems/kartesian/map.rs
+++ b/src/coordinate_systems/kartesian/map.rs
@ -3,12 +3,12 @@ use super::Kartesian;
 /// Rust implementation of an Map. The Zeropoint is Topleft
 /// The Rows in the data are not nessesaryly in the specifed length, should values be missing, then there are functions that returns
 #[derive(Debug, Clone)]
-pub struct Map<T: Clone+Copy> {
-    maximum: Kartesian<usize>,
-    data: Vec<Vec<T>>,
+pub struct Map<T: Clone + Copy> {
+    pub(super) maximum: Kartesian<usize>,
+    pub(super) data: Vec<Vec<T>>,
 }

-impl<T: Clone+Copy> Map<T> {
+impl<T: Clone + Copy> Map<T> {
    /// creates an empty Map
    pub fn empty(length: usize, height: usize) -> Self {
        Self {
@ -16,6 +16,7 @@ impl<T: Clone+Copy> Map<T> {
            maximum: Kartesian::new(height, length),
        }
    }
+
    /// returns true if coordinates are outside of bounds
    #[inline]
    fn outside(&self, coord: Kartesian<usize>) -> bool {
@ -25,7 +26,7 @@ impl<T: Clone+Copy> Map<T> {
    /// Unsafe Version of the get or get_wrapping functions.
    /// It does not check against an missing value and panics if its out of bounds.
    #[inline]
-    pub unsafe fn get_unsafe(&self, coord: Kartesian<usize>) ->T{
+    pub unsafe fn get_unsafe(&self, coord: Kartesian<usize>) -> T {
        if self.outside(coord) {
            panic!("Coordinates out of bounds: {} >= {}", coord, self.maximum)
        }
@ -33,7 +34,7 @@ impl<T: Clone+Copy> Map<T> {
    }
 }

-impl<T: Copy +Copy+ Default> Map<T> {
+impl<T: Copy + Copy + Default + PartialEq> Map<T> {
    /// Returns an Option Containing the value.
    /// Returns None if out of bounds or not yet set.
    pub fn get(&self, coord: Kartesian<usize>) -> Option<T> {
@ -49,6 +50,29 @@ impl<T: Copy +Copy+ Default> Map<T> {
        }
    }

+    /// Replaces unset and default values with
+    pub fn replace_default(&mut self, new_value: T) {
+        for row in self.data.iter_mut() {
+            *row = row
+                .iter()
+                .map(|c| {
+                    if *c == T::default() {
+                        new_value
+                    } else {
+                        *c
+                    }
+                })
+                .collect();
+            if row.len() < self.maximum.y {
+                row.resize(self.maximum.y, new_value);
+            }
+        }
+        if self.data.len() < self.maximum.x {
+            let full_row = vec![new_value; self.maximum.y];
+            self.data.resize(self.maximum.x, full_row);
+        }
+    }
+
    /// Returns the value of in the map.
    #[inline]
    pub fn wrapping_get(&self, coord: Kartesian<usize>) -> T {
@ -63,7 +87,7 @@ impl<T: Copy +Copy+ Default> Map<T> {
    }

    pub fn set(&mut self, coord: Kartesian<usize>, value: T) -> T {
-        if coord.x >= self.maximum.x || coord.y >= self.maximum.y {
+        if self.outside(coord) {
            panic!("Coordinates outside of bounds: {} >= {}", coord, self.maximum)
        }
        if self.data.len() < coord.x + 1 {
@ -99,7 +123,7 @@ impl<T: Copy +Copy+ Default> Map<T> {
    }
 }

-impl<T: Clone+Copy> From<Vec<Vec<T>>> for Map<T> {
+impl<T: Clone + Copy> From<Vec<Vec<T>>> for Map<T> {
    fn from(value: Vec<Vec<T>>) -> Self {
        Map {
            data: value.clone(),
--- a/src/coordinate_systems/kartesian/mod.rs
+++ b/src/coordinate_systems/kartesian/mod.rs
@ -1,20 +1,27 @@
 use log::debug;
-use num::*;
+use num::{traits::*, *};
 use std::{
    fmt::{Debug, Display},
-    ops::*,
+    ops::Rem,
 };

 pub mod direction;
+pub mod external_traits;
 pub mod map;
 pub mod maximum;
 mod test;
+pub mod traits;
 pub use direction::*;
 pub use map::*;
 pub use maximum::*;
+pub use traits::*;

 pub type KD = KartesianDirection;

+pub trait ToCoords: Copy {
+    fn to_coords(self) -> Kartesian<usize>;
+}
+
 #[derive(Debug, Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub struct Kartesian<T>
 where
@ -24,42 +31,58 @@ where
    pub y: T,
 }

-impl<T: Integer> Add for Kartesian<T> {
-    fn add(self, rhs: Self) -> Self::Output {
-        Kartesian { x: self.x + rhs.x, y: self.y + rhs.y }
-    }
-
-    type Output = Kartesian<T>;
-}
-
-impl<T: Integer + AddAssign> AddAssign for Kartesian<T> {
-    fn add_assign(&mut self, rhs: Self) {
-        self.x += rhs.x;
-        self.y += rhs.y;
-    }
-}
-
-impl<T: Integer> Sub for Kartesian<T> {
-    fn sub(self, rhs: Self) -> Self::Output {
-        Kartesian { x: self.x - rhs.x, y: self.y - rhs.y }
-    }
-
-    type Output = Kartesian<T>;
-}
-
-impl<T: Integer + SubAssign> SubAssign for Kartesian<T> {
-    fn sub_assign(&mut self, rhs: Self) {
-        self.x -= rhs.x;
-        self.y -= rhs.y;
-    }
-}
-
 impl<T: Integer> Kartesian<T> {
    pub const fn new(x: T, y: T) -> Self {
        Self { x: x, y: y }
    }
 }

+impl ToCoords for Kartesian<u8> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x as usize, y: self.y as usize }
+    }
+}
+
+impl ToCoords for Kartesian<u16> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x as usize, y: self.y as usize }
+    }
+}
+
+impl ToCoords for Kartesian<u32> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x as usize, y: self.y as usize }
+    }
+}
+
+impl ToCoords for Kartesian<u64> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x as usize, y: self.y as usize }
+    }
+}
+
+impl ToCoords for Kartesian<u128> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x as usize, y: self.y as usize }
+    }
+}
+
+impl ToCoords for Kartesian<usize> {
+    fn to_coords(self) -> Kartesian<usize> {
+        Kartesian { x: self.x, y: self.y }
+    }
+}
+
+fn wrap<T: Integer + Rem + MaximumValue + From<u32> + Copy + MaximumValue + Display, const FACTOR: u32>(v: T, max: T) -> T {
+    if v < max {
+        v
+    } else if v < max * T::from(FACTOR) {
+        v % max
+    } else {
+        max - (T::MAX - v)
+    }
+}
+
 impl Kartesian<usize> {
    pub fn get_value<T: Copy>(self, map: &Vec<Vec<T>>) -> Option<T> {
        if map.len() > self.x {
@ -72,7 +95,7 @@ impl Kartesian<usize> {
    }
 }

-impl<T: Integer + Eq + Debug + CheckedAdd + CheckedSub + Default + Copy> Kartesian<T> {
+impl<T: Integer + Eq + Debug + CheckedBasicMath + Default + Copy> Kartesian<T> {
    pub fn checked_add_max(self, rhs: Kartesian<T>, max: Kartesian<T>) -> Option<Kartesian<T>> {
        let mut new = Kartesian::default();
        new.x = match self.x.checked_add(&rhs.x) {
@ -181,32 +204,72 @@ impl<T: Integer + Eq + Debug + CheckedAdd + CheckedSub + Default + Copy> Kartesi
    }
 }

-impl<T: Integer + Display + Copy> Display for Kartesian<T> {
-    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        f.write_fmt(format_args!("{}:{}", self.x, self.y))
-    }
-}
-
-impl<T: Integer + Copy> Div<T> for Kartesian<T> {
-    type Output = Kartesian<T>;
-    fn div(self, rhs: T) -> Self::Output {
-        Kartesian {
-            x: self.x.div_ceil(&rhs),
-            y: self.y.div_ceil(&rhs),
+impl<T: Integer + Unsigned + CheckedBasicMath> Kartesian<T> {
+    pub fn move_velocity(self, velocity: Velocity<T>, max: Kartesian<T>) -> Option<Kartesian<T>> {
+        if velocity.direction == KD::None {
+            return Some(self);
        }
+        Some(Kartesian {
+            x: match velocity.direction {
+                KD::Left | KD::Right => self.x,
+                KD::TopLeft | KD::Top | KD::TopRight => match self.x.checked_sub(&velocity.speed.x) {
+                    None => return None,
+                    Some(x) => x,
+                },
+                KD::BottomLeft | KD::Bottom | KD::BottomRight => {
+                    let x = self.x + velocity.speed.x;
+                    if x >= max.x {
+                        return None;
+                    }
+                    x
+                },
+                _ => unreachable!(),
+            },
+            y: match velocity.direction {
+                KD::Top | KD::Bottom => self.y,
+                KD::TopLeft | KD::Left | KD::BottomLeft => match self.y.checked_sub(&velocity.speed.y) {
+                    None => return None,
+                    Some(y) => y,
+                },
+                KD::TopRight | KD::Right | KD::BottomRight => {
+                    let y = self.y + velocity.speed.y;
+                    if y >= max.y {
+                        return None;
+                    }
+                    y
+                },
+                _ => unreachable!(),
+            },
+        })
    }
 }

-impl<T: Integer + Rem> Rem for Kartesian<T> {
-    type Output = Self;
-    fn rem(self, rhs: Self) -> Self {
-        Kartesian { x: self.x % rhs.x, y: self.y % rhs.y }
-    }
-}
-impl<T: Integer + RemAssign> RemAssign for Kartesian<T> {
-    fn rem_assign(&mut self, rhs: Self) {
-        self.x %= rhs.x;
-        self.y %= rhs.y;
+impl<T: Integer + Display + Unsigned + WrappingAdd + WrappingSub + MaximumValue + From<u32> + Copy> Kartesian<T> {
+    pub fn wrapping_move_velocity(self, velocity: Velocity<T>, max: Kartesian<T>) -> Kartesian<T> {
+        Kartesian {
+            x: match velocity.direction {
+                KartesianDirection::TopLeft | KartesianDirection::Top | KartesianDirection::TopRight => {
+                    if self.x < velocity.speed.x {
+                        max.x - (velocity.speed.x - self.x)
+                    } else {
+                        self.x - velocity.speed.x
+                    }
+                },
+                KartesianDirection::Left | KartesianDirection::None | KartesianDirection::Right => self.x,
+                KartesianDirection::BottomLeft | KartesianDirection::Bottom | KartesianDirection::BottomRight => (self.x + velocity.speed.x) % max.x,
+            },
+            y: match velocity.direction {
+                KartesianDirection::TopLeft | KartesianDirection::Left | KartesianDirection::BottomLeft => {
+                    if self.y < velocity.speed.y {
+                        max.y - (velocity.speed.y - self.y)
+                    } else {
+                        self.y - velocity.speed.y
+                    }
+                },
+                KartesianDirection::Top | KartesianDirection::None | KartesianDirection::Bottom => self.y,
+                KartesianDirection::TopRight | KartesianDirection::Right | KartesianDirection::BottomRight => (self.y + velocity.speed.y) % max.y,
+            },
+        }
    }
 }

@ -217,42 +280,14 @@ pub struct KartesianIterator {
    straight: bool,
 }

-impl Iterator for KartesianIterator {
-    type Item = KartesianDirection;
+#[derive(Debug, Default, Clone, Copy)]
+pub struct Velocity<T: Integer + Unsigned> {
+    speed: Kartesian<T>,
+    direction: KartesianDirection,
+}

-    fn next(&mut self) -> Option<Self::Item> {
-        let mut i = self.i;
-        if self.straight {
-            if i < 4 {
-                self.i += 1;
-            }
-            match i {
-                0 => return Some(KartesianDirection::Right),
-                1 => return Some(KartesianDirection::Bottom),
-                2 => return Some(KartesianDirection::Left),
-                3 => return Some(KartesianDirection::Top),
-                _ => i -= 4,
-            }
-        }
-        if self.none {
-            if i == 0 {
-                self.i += 1;
-                return Some(KartesianDirection::None);
-            }
-            i -= 1;
-        }
-        if self.diagonal {
-            if i < 4 {
-                self.i += 1;
-            }
-            match i {
-                0 => return Some(KartesianDirection::TopLeft),
-                1 => return Some(KartesianDirection::TopRight),
-                2 => return Some(KartesianDirection::BottomLeft),
-                3 => return Some(KartesianDirection::BottomRight),
-                _ => {},
-            }
-        }
-        None
+impl<T: Integer + Unsigned> Velocity<T> {
+    pub fn new(x: T, y: T, dir: KartesianDirection) -> Self {
+        Velocity { speed: Kartesian { x, y }, direction: dir }
    }
 }
--- a/src/coordinate_systems/kartesian/test.rs
+++ b/src/coordinate_systems/kartesian/test.rs
@ -1,87 +1,110 @@
 #[cfg(test)]
 use super::*;

-    #[test]
-    fn test_clockwise() {
-        let mut current = KartesianDirection::Top;
-        let clock = [
-            KartesianDirection::Top,
-            KartesianDirection::TopRight,
-            KartesianDirection::Right,
-            KartesianDirection::BottomRight,
-            KartesianDirection::Bottom,
-            KartesianDirection::BottomLeft,
-            KartesianDirection::Left,
-            KartesianDirection::TopLeft,
-        ];
-        for hand in clock {
-            assert_eq!(current, hand);
-            current = current.clockwise(true);
-        }
+#[test]
+fn clockwise() {
+    let mut current = KartesianDirection::Top;
+    let clock = [
+        KartesianDirection::Top,
+        KartesianDirection::TopRight,
+        KartesianDirection::Right,
+        KartesianDirection::BottomRight,
+        KartesianDirection::Bottom,
+        KartesianDirection::BottomLeft,
+        KartesianDirection::Left,
+        KartesianDirection::TopLeft,
+    ];
+    for hand in clock {
+        assert_eq!(current, hand);
+        current = current.clockwise(true);
    }
-    #[test]
-    fn test_anticlockwise() {
-        let mut current = KartesianDirection::Top;
-        let clock = [
-            KartesianDirection::Top,
-            KartesianDirection::TopLeft,
-            KartesianDirection::Left,
-            KartesianDirection::BottomLeft,
-            KartesianDirection::Bottom,
-            KartesianDirection::BottomRight,
-            KartesianDirection::Right,
-            KartesianDirection::TopRight,
-        ];
-        for hand in clock {
-            assert_eq!(current, hand);
-            current = current.anticlockwise(true);
-        }
+}
+#[test]
+fn anticlockwise() {
+    let mut current = KartesianDirection::Top;
+    let clock = [
+        KartesianDirection::Top,
+        KartesianDirection::TopLeft,
+        KartesianDirection::Left,
+        KartesianDirection::BottomLeft,
+        KartesianDirection::Bottom,
+        KartesianDirection::BottomRight,
+        KartesianDirection::Right,
+        KartesianDirection::TopRight,
+    ];
+    for hand in clock {
+        assert_eq!(current, hand);
+        current = current.anticlockwise(true);
    }
+}

-    #[test]
-    fn test_kartesian_iter() {
-        let test: Vec<_> = [
-            KartesianDirection::Right,
-            KartesianDirection::Top,
-            KartesianDirection::Left,
-            KartesianDirection::Bottom,
-            KartesianDirection::None,
-            KartesianDirection::TopLeft,
-            KartesianDirection::TopRight,
-            KartesianDirection::BottomLeft,
-            KartesianDirection::BottomRight,
-        ]
-        .into();
-        let i: Vec<_> = KartesianDirection::iter(true, true, true).collect();
-        assert_eq!(i, test);
-        let test: Vec<_> = [
-            KartesianDirection::Right,
-            KartesianDirection::Top,
-            KartesianDirection::Left,
-            KartesianDirection::Bottom,
-            KartesianDirection::TopLeft,
-            KartesianDirection::TopRight,
-            KartesianDirection::BottomLeft,
-            KartesianDirection::BottomRight,
-        ]
-        .into();
-        let i: Vec<_> = KartesianDirection::iter(false, true, true).collect();
-        assert_eq!(i, test);
-    }
+#[test]
+fn kartesian_iter() {
+    let test: Vec<_> = [
+        KartesianDirection::Right,
+        KartesianDirection::Top,
+        KartesianDirection::Left,
+        KartesianDirection::Bottom,
+        KartesianDirection::None,
+        KartesianDirection::TopLeft,
+        KartesianDirection::TopRight,
+        KartesianDirection::BottomLeft,
+        KartesianDirection::BottomRight,
+    ]
+    .into();
+    let i: Vec<_> = KartesianDirection::iter(true, true, true).collect();
+    assert_eq!(i, test);
+    let test: Vec<_> = [
+        KartesianDirection::Right,
+        KartesianDirection::Top,
+        KartesianDirection::Left,
+        KartesianDirection::Bottom,
+        KartesianDirection::TopLeft,
+        KartesianDirection::TopRight,
+        KartesianDirection::BottomLeft,
+        KartesianDirection::BottomRight,
+    ]
+    .into();
+    let i: Vec<_> = KartesianDirection::iter(false, true, true).collect();
+    assert_eq!(i, test);
+}

-    #[test]
-    fn test_diff_dir() {
-        const START: Kartesian<u8> = Kartesian::new(1, 1);
-        // Top Group
-        assert_eq!(KartesianDirection::TopLeft, START.diff(Kartesian::new(0, 0)).1);
-        assert_eq!(KartesianDirection::Top, START.diff(Kartesian::new(0, 1)).1);
-        assert_eq!(KartesianDirection::TopRight, START.diff(Kartesian::new(0, 2)).1);
-        // Same Line
-        assert_eq!(KartesianDirection::Left, START.diff(Kartesian::new(1, 0)).1);
-        assert_eq!(KartesianDirection::None, START.diff(Kartesian::new(1, 1)).1);
-        assert_eq!(KartesianDirection::Right, START.diff(Kartesian::new(1, 2)).1);
-        // Below/Bottom Line
-        assert_eq!(KartesianDirection::BottomLeft, START.diff(Kartesian::new(2, 0)).1);
-        assert_eq!(KartesianDirection::Bottom, START.diff(Kartesian::new(2, 1)).1);
-        assert_eq!(KartesianDirection::BottomRight, START.diff(Kartesian::new(2, 2)).1);
+#[test]
+fn diff_dir() {
+    const START: Kartesian<u8> = Kartesian::new(1, 1);
+    // Top Group
+    assert_eq!(KartesianDirection::TopLeft, START.diff(Kartesian::new(0, 0)).1);
+    assert_eq!(KartesianDirection::Top, START.diff(Kartesian::new(0, 1)).1);
+    assert_eq!(KartesianDirection::TopRight, START.diff(Kartesian::new(0, 2)).1);
+    // Same Line
+    assert_eq!(KartesianDirection::Left, START.diff(Kartesian::new(1, 0)).1);
+    assert_eq!(KartesianDirection::None, START.diff(Kartesian::new(1, 1)).1);
+    assert_eq!(KartesianDirection::Right, START.diff(Kartesian::new(1, 2)).1);
+    // Below/Bottom Line
+    assert_eq!(KartesianDirection::BottomLeft, START.diff(Kartesian::new(2, 0)).1);
+    assert_eq!(KartesianDirection::Bottom, START.diff(Kartesian::new(2, 1)).1);
+    assert_eq!(KartesianDirection::BottomRight, START.diff(Kartesian::new(2, 2)).1);
+}
+
+#[test]
+fn moving_wrapping() {
+    /*
+    let max: Kartesian<u32> = Kartesian::new(10, 10);
+    let mut pos = Kartesian::new(0, 0);
+    let velocity = Velocity::new(1, 1, KartesianDirection::BottomRight);
+    pos = pos.wrapping_move_velocity(velocity, max);
+    assert_eq!(pos, Kartesian::new(1, 1));
+    for _ in 1..10 {
+        pos = pos.wrapping_move_velocity(velocity, max);
    }
+    assert_eq!(pos, Kartesian::new(0, 0));
+     */
+    let max = Kartesian::<u32>::new(7, 11);
+    assert_eq!(Kartesian::new(2, 0).wrapping_move_velocity(Velocity::new(1, 3, KartesianDirection::TopLeft), max), Kartesian::new(1, 9));
+    assert_eq!(Kartesian::new(4, 2).wrapping_move_velocity(Velocity::new(3, 2, KartesianDirection::TopRight), max), Kartesian::new(1, 4))
+}
+
+#[test]
+fn test_wrap() {
+    assert_eq!(wrap::<u32, 10>(11, 11), 0)
+}
--- a/src/coordinate_systems/kartesian/traits.rs
+++ b/src/coordinate_systems/kartesian/traits.rs
@ -0,0 +1,43 @@
+use num::*;
+
+macro_rules! predefined_const {
+    ($trait_name:ident, $const:ident, $t:ty) => {
+        impl $trait_name for $t {
+            const $const: $t = <$t>::$const;
+        }
+    };
+}
+
+pub trait CheckedBasicMath: CheckedAdd + CheckedSub {}
+impl<T: CheckedAdd + CheckedSub> CheckedBasicMath for T {}
+
+pub trait MaximumValue {
+    const MAX: Self;
+}
+predefined_const!(MaximumValue, MAX, u8);
+predefined_const!(MaximumValue, MAX, u16);
+predefined_const!(MaximumValue, MAX, u32);
+predefined_const!(MaximumValue, MAX, u64);
+predefined_const!(MaximumValue, MAX, u128);
+predefined_const!(MaximumValue, MAX, usize);
+predefined_const!(MaximumValue, MAX, i8);
+predefined_const!(MaximumValue, MAX, i16);
+predefined_const!(MaximumValue, MAX, i32);
+predefined_const!(MaximumValue, MAX, i64);
+predefined_const!(MaximumValue, MAX, i128);
+predefined_const!(MaximumValue, MAX, isize);
+pub trait MinimumValue {
+    const MIN: Self;
+}
+predefined_const!(MinimumValue, MIN, u8);
+predefined_const!(MinimumValue, MIN, u16);
+predefined_const!(MinimumValue, MIN, u32);
+predefined_const!(MinimumValue, MIN, u64);
+predefined_const!(MinimumValue, MIN, u128);
+predefined_const!(MinimumValue, MIN, usize);
+predefined_const!(MinimumValue, MIN, i8);
+predefined_const!(MinimumValue, MIN, i16);
+predefined_const!(MinimumValue, MIN, i32);
+predefined_const!(MinimumValue, MIN, i64);
+predefined_const!(MinimumValue, MIN, i128);
+predefined_const!(MinimumValue, MIN, isize);
--- a/src/strings.rs
+++ b/src/strings.rs
@ -4,7 +4,7 @@ use std::ops::AddAssign;
 #[inline]
 pub fn char_to_num<T: Integer + From<u32>>(c: char) -> T {
    match c {
-        '1' => T::from(1),
+        '1' => T::one(),
        '2' => T::from(2),
        '3' => T::from(3),
        '4' => T::from(4),
@ -13,7 +13,8 @@ pub fn char_to_num<T: Integer + From<u32>>(c: char) -> T {
        '7' => T::from(7),
        '8' => T::from(8),
        '9' => T::from(9),
-        '0' => T::from(0),
+        '0' => T::zero(),
+        '-' => T::zero(),
        _ => unreachable!(),
    }
 }