problems: add count vowels permutation

Signed-off-by: Matej Focko <mfocko@redhat.com>

problems/count-vowels-permutation.rs

@@ -0,0 +1,104 @@
+use std::collections::HashMap;
+
+type CacheKey = (i32, char);
+struct Cache {
+    cache: HashMap<CacheKey, i32>,
+}
+
+impl Cache {
+    const MODULO: i32 = 1000000007;
+
+    fn new() -> Cache {
+        let mut cache = HashMap::<CacheKey, i32>::new();
+
+        for c in "aeiou".chars() {
+            cache.insert((1, c), 1);
+        }
+
+        Cache { cache: cache }
+    }
+
+    fn is_precomputed(&self, n: i32) -> bool {
+        self.cache.keys().any(|key| key.0 == n)
+    }
+
+    fn get(&self, n: i32) -> i32 {
+        self.cache
+            .keys()
+            .filter(|key| key.0 == n)
+            .fold(0, |acc, key| {
+                // Since the answer may be too large, return it modulo 10^9 + 7.
+                (acc + self.cache.get(key).unwrap_or(&0)) % Self::MODULO
+            })
+    }
+
+    fn precompute(&mut self, n: i32) {
+        if self.is_precomputed(n) {
+            return;
+        }
+
+        if !self.is_precomputed(n - 1) {
+            self.precompute(n - 1);
+        }
+
+        for (current, continuation) in vec![
+            ('a', "e"),
+            ('e', "ai"),
+            ('i', "aeou"),
+            ('o', "iu"),
+            ('u', "a"),
+        ] {
+            self.cache.insert(
+                (n, current),
+                continuation.chars().fold(0, |acc, vowel| {
+                    (acc + self.cache.get(&(n - 1, vowel)).unwrap()) % Self::MODULO
+                }),
+            );
+        }
+    }
+}
+
+struct Solution {}
+impl Solution {
+    pub fn count_vowel_permutation(n: i32) -> i32 {
+        let mut cache = Cache::new();
+        cache.precompute(n);
+
+        cache.get(n)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_example_1() {
+        // Input: n = 1
+        // Output: 5
+        // Explanation: All possible strings are: "a", "e", "i" , "o" and "u".
+        assert_eq!(count_vowel_permutation(1), 5);
+    }
+
+    #[test]
+    fn test_example_2() {
+        // Input: n = 2
+        // Output: 10
+        // Explanation: All possible strings are: All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".
+        assert_eq!(count_vowel_permutation(2), 10);
+    }
+
+    #[test]
+    fn test_example_3() {
+        // Input: n = 5
+        // Output: 68
+        assert_eq!(count_vowel_permutation(5), 68);
+    }
+
+    #[test]
+    fn test_example_4() {
+        // Input: n = 3
+        // Output: 19
+        assert_eq!(count_vowel_permutation(3), 19);
+    }
+}