Assignment 2 Done

src/assignments/assignment02/small_exercises.rs

@@ -1,23 +1,29 @@
 //! Small problems.
 
-use std::iter;
+use std::{cmp::min, iter};
 
 const FAHRENHEIT_OFFSET: f64 = 32.0;
 const FAHRENHEIT_SCALE: f64 = 5.0 / 9.0;
 
 /// Converts Fahrenheit to Celsius temperature degree.
 pub fn fahrenheit_to_celsius(degree: f64) -> f64 {
-    todo!()
+    (degree - 32.0) * 5.0 / 9.0
 }
 
 /// Capitalizes English alphabets (leaving the other characters intact).
 pub fn capitalize(input: String) -> String {
-    todo!()
+    input.to_ascii_uppercase()
 }
 
 /// Returns the sum of the given array. (We assume the absence of integer overflow.)
 pub fn sum_array(input: &[u64]) -> u64 {
-    todo!()
+    let mut result = 0;
+
+    for i in input {
+        result += i;
+    }
+
+    result
 }
 
 /// Given a non-negative integer, say `n`, return the smallest integer of the form `3^m` that's
@@ -25,13 +31,27 @@ pub fn sum_array(input: &[u64]) -> u64 {
 ///
 /// For instance, up3(6) = 9, up3(9) = 9, up3(10) = 27. (We assume the absence of integer overflow.)
 pub fn up3(n: u64) -> u64 {
-    todo!()
+    let mut value = 1;
+
+    while value < n {
+        value *= 3;
+    }
+
+    value
 }
 
 /// Returns the greatest common divisor (GCD) of two non-negative integers. (We assume the absence
 /// of integer overflow.)
 pub fn gcd(lhs: u64, rhs: u64) -> u64 {
-    todo!()
+    let (mut a, mut b) = if lhs >= rhs { (lhs, rhs) } else { (rhs, lhs) };
+
+    while b != 0 {
+        let r = a % b;
+        a = b;
+        b = r;
+    }
+
+    a
 }
 
 /// Returns the array of nC0, nC1, nC2, ..., nCn, where nCk = n! / (k! * (n-k)!). (We assume the
@@ -40,7 +60,24 @@ pub fn gcd(lhs: u64, rhs: u64) -> u64 {
 /// Consult <https://en.wikipedia.org/wiki/Pascal%27s_triangle> for computation of binomial
 /// coefficients without integer overflow.
 pub fn chooses(n: u64) -> Vec<u64> {
-    todo!()
+    let mut result = vec![1];
+
+    for k in 1..=n {
+        let last = *result.last().unwrap();
+        let numerator = n + 1 - k;
+
+        let new_value = if numerator % k == 0 {
+            last * ((numerator) / k)
+        } else if last % k == 0 {
+            (last / k) * numerator
+        } else {
+            let gcd_last = gcd(last, k);
+            (last / gcd_last) * (numerator / (k / gcd_last))
+        };
+        result.push(new_value);
+    }
+
+    result
 }
 
 /// Returns the "zip" of two vectors.
@@ -48,5 +85,12 @@ pub fn chooses(n: u64) -> Vec<u64> {
 /// For instance, `zip(vec![1, 2, 3], vec![4, 5])` equals to `vec![(1, 4), (2, 5)]`. Here, `3` is
 /// ignored because it doesn't have a partner.
 pub fn zip(lhs: Vec<u64>, rhs: Vec<u64>) -> Vec<(u64, u64)> {
-    todo!()
+    let length = min(lhs.len(), rhs.len());
+    let mut result: Vec<(u64, u64)> = Vec::new();
+
+    for i in 0..length {
+        result.push((lhs[i], rhs[i]));
+    }
+
+    result
 }

src/assignments/assignment02/vec_and_mat.rs

@@ -44,7 +44,12 @@ impl Mul<Mat2> for Mat2 {
 
     /// Consult <https://www.mathsisfun.com/algebra/matrix-multiplying.html>
     fn mul(self, rhs: Mat2) -> Self::Output {
-        todo!()
+        Mat2 {
+            a: self.a * rhs.a + self.b * rhs.c,
+            b: self.a * rhs.b + self.b * rhs.d,
+            c: self.c * rhs.a + self.d * rhs.c,
+            d: self.c * rhs.b + self.d * rhs.d,
+        }
     }
 }
 
@@ -55,21 +60,30 @@ impl Mul<Vec2> for Mat2 {
     ///
     /// Consult <https://www.mathsisfun.com/algebra/matrix-multiplying.html>
     fn mul(self, rhs: Vec2) -> Self::Output {
-        todo!()
+        Vec2 {
+            a: self.a * rhs.a + self.b * rhs.b,
+            b: self.c * rhs.a + self.d * rhs.b,
+        }
     }
 }
 
 impl Mat2 {
     /// Calculates the power of matrix.
     fn power(self, power: u64) -> Mat2 {
-        todo!()
+        let mut result = Mat2::new();
+
+        for i in 0..power {
+            result = result * self;
+        }
+
+        result
     }
 }
 
 impl Vec2 {
     /// Gets the upper value of vector.
     fn get_upper(self) -> u64 {
-        todo!()
+        self.a
     }
 }
 
@@ -120,7 +134,14 @@ impl FMat2 {
     /// );
     /// ```
     pub fn inverse(self) -> Self {
-        todo!()
+        let det = self.a * self.d - self.b * self.c;
+
+        FMat2 {
+            a: self.d / det,
+            b: -self.b / det,
+            c: -self.c / det,
+            d: self.a / det,
+        }
     }
 }