Add sheet4 solution

aufgaben/sheet4/sol1/good.rs

@@ -0,0 +1,57 @@
+/// Prints all happy primes between 1 and 20.
+fn main() {
+    for i in 1..21 {
+        if is_happy_prime(i) {
+            println!("{} is a happy prime!", i);
+        }
+    }
+}
+
+/// Determines whether the given number is a happy number AND a prime number.
+fn is_happy_prime(n: u64) -> bool {
+    is_happy(n) && is_prime(n)
+}
+
+/// Determines whether the given, positive number is a [happy number][1].
+///
+/// [1]: https://en.wikipedia.org/wiki/Happy_number
+fn is_happy(mut number: u64) -> bool {
+    // Either we end as "1" or in a cycle
+    while number > 1 {
+        number = {
+            // Here we compute the sum of squares of all digits. The trick is that
+            // the last digit is `number % 10` and that we can remove the last
+            // digit by dividing number by 10.
+            let mut sum = 0;
+            while number > 0 {
+                let digit = number % 10;
+                sum += digit * digit;
+                number /= 10;
+            }
+
+            sum
+        };
+
+        // We ended up in a cycle -> not happy
+        if number == 4 {
+            return false;
+        }
+    }
+
+    true
+}
+
+/// Determines whether the given, positive, non-zero number is a prime number.
+fn is_prime(n: u64) -> bool {
+    if n == 1 {
+        return false;
+    }
+
+    for divisor in 2..n {
+        if n % divisor == 0 {
+            return false;
+        }
+    }
+
+    true
+}