Assignment 6 Done

src/assignments/assignment06/semiring.rs

@@ -33,55 +33,55 @@ pub fn from_usize<T: Semiring>(value: usize) -> T {
 
 impl Semiring for u64 {
     fn zero() -> Self {
-        todo!()
+        0
     }
 
     fn one() -> Self {
-        todo!()
+        1
     }
 
     fn add(&self, rhs: &Self) -> Self {
-        todo!()
+        self + rhs
     }
 
     fn mul(&self, rhs: &Self) -> Self {
-        todo!()
+        self * rhs
     }
 }
 
 impl Semiring for i64 {
     fn zero() -> Self {
-        todo!()
+        0
     }
 
     fn one() -> Self {
-        todo!()
+        1
     }
 
     fn add(&self, rhs: &Self) -> Self {
-        todo!()
+        self + rhs
     }
 
     fn mul(&self, rhs: &Self) -> Self {
-        todo!()
+        self * rhs
     }
 }
 
 impl Semiring for f64 {
     fn zero() -> Self {
-        todo!()
+        0.0
     }
 
     fn one() -> Self {
-        todo!()
+        1.0
     }
 
     fn add(&self, rhs: &Self) -> Self {
-        todo!()
+        self + rhs
     }
 
     fn mul(&self, rhs: &Self) -> Self {
-        todo!()
+        self * rhs
     }
 }
 
@@ -105,42 +105,91 @@ pub struct Polynomial<C: Semiring> {
 
 impl<C: Semiring> Semiring for Polynomial<C> {
     fn zero() -> Self {
-        todo!()
+        Self {
+            coefficients: HashMap::new(),
+        }
     }
 
     fn one() -> Self {
-        todo!()
+        Self {
+            coefficients: HashMap::from([(0, C::one())]),
+        }
     }
 
     fn add(&self, rhs: &Self) -> Self {
-        todo!()
+        let mut coefficients = self.coefficients.clone();
+
+        for (deg, coef) in &rhs.coefficients {
+            _ = coefficients
+                .entry(*deg)
+                .and_modify(|value| *value = value.add(coef))
+                .or_insert(coef.clone());
+        }
+
+        coefficients.retain(|_, coef| *coef != C::zero());
+
+        Self { coefficients }
     }
 
     fn mul(&self, rhs: &Self) -> Self {
-        todo!()
+        let mut coefficients: HashMap<u64, C> = HashMap::new();
+
+        for (ldeg, lcoef) in &self.coefficients {
+            for (rdeg, rcoef) in &rhs.coefficients {
+                let coef = lcoef.mul(rcoef);
+                _ = coefficients
+                    .entry(ldeg + rdeg)
+                    .and_modify(|value| *value = value.add(&coef))
+                    .or_insert(coef);
+            }
+        }
+
+        coefficients.retain(|_, coef| *coef != C::zero());
+
+        Self { coefficients }
     }
 }
 
 impl<C: Semiring> Polynomial<C> {
     /// Constructs polynomial `x`.
     pub fn x() -> Self {
-        todo!()
+        Self {
+            coefficients: HashMap::from([(1, C::one())]),
+        }
     }
 
     /// Evaluates the polynomial with the given value.
     pub fn eval(&self, value: C) -> C {
-        todo!()
+        let mut result = C::zero();
+
+        for (deg, coef) in &self.coefficients {
+            let mut xn = C::one();
+            let mut n = 0;
+
+            while n < *deg {
+                xn = xn.mul(&value);
+                n += 1;
+            }
+
+            result = result.add(&coef.mul(&xn));
+        }
+
+        result
     }
 
     /// Constructs polynomial `ax^n`.
     pub fn term(a: C, n: u64) -> Self {
-        todo!()
+        Self {
+            coefficients: HashMap::from([(n, a)]),
+        }
     }
 }
 
 impl<C: Semiring> From<C> for Polynomial<C> {
     fn from(value: C) -> Self {
-        todo!()
+        Self {
+            coefficients: HashMap::from([(0, value)]),
+        }
     }
 }
 
@@ -164,6 +213,30 @@ impl<C: Semiring> std::str::FromStr for Polynomial<C> {
     type Err = (); // Ignore this for now...
 
     fn from_str(s: &str) -> Result<Self, Self::Err> {
-        todo!()
+        let mut coefficients: HashMap<u64, C> = HashMap::new();
+
+        for term in s.split(" + ") {
+            let has_x: bool = term.contains('x');
+            let has_power = term.contains('^');
+
+            let deg: u64 = if has_power {
+                term.split("^").nth(1).unwrap().parse().unwrap()
+            } else if has_x {
+                1
+            } else {
+                0
+            };
+            let coef: usize = if has_x && term.find("x").unwrap() == 0 {
+                1
+            } else if has_x {
+                term.split("x").nth(0).unwrap().parse().unwrap()
+            } else {
+                term.parse().unwrap()
+            };
+
+            let _unused = coefficients.insert(deg, from_usize(coef));
+        }
+
+        Ok(Self { coefficients })
     }
 }