g1201_1300.s1220_count_vowels_permutation.Solution Maven / Gradle / Ivy

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package g1201_1300.s1220_count_vowels_permutation;

// #Hard #Dynamic_Programming #2022_03_11_Time_7_ms_(98.50%)_Space_41.3_MB_(72.81%)

/**
 * 1220 - Count Vowels Permutation\.
 *
 * Hard
 *
 * Given an integer `n`, your task is to count how many strings of length `n` can be formed under the following rules:
 *
 * *   Each character is a lower case vowel (`'a'`, `'e'`, `'i'`, `'o'`, `'u'`)
 * *   Each vowel `'a'` may only be followed by an `'e'`.
 * *   Each vowel `'e'` may only be followed by an `'a'` or an `'i'`.
 * *   Each vowel `'i'` **may not** be followed by another `'i'`.
 * *   Each vowel `'o'` may only be followed by an `'i'` or a `'u'`.
 * *   Each vowel `'u'` may only be followed by an `'a'.`
 *
 * Since the answer may be too large, return it modulo `10^9 + 7.`
 *
 * **Example 1:**
 *
 * **Input:** n = 1
 *
 * **Output:** 5
 *
 * **Explanation:** All possible strings are: "a", "e", "i" , "o" and "u".
 *
 * **Example 2:**
 *
 * **Input:** n = 2
 *
 * **Output:** 10
 *
 * **Explanation:** All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".
 *
 * **Example 3:**
 *
 * **Input:** n = 5
 *
 * **Output:** 68
 *
 * **Constraints:**
 *
 * *   `1 <= n <= 2 * 10^4`
**/
public class Solution {
    public int countVowelPermutation(int n) {
        int mod = (int) 1e9 + 7;
        int prevA = 1;
        int prevE = 1;
        int prevI = 1;
        int prevO = 1;
        int prevU = 1;
        while (n-- > 1) {
            int a = ((prevE + prevI) % mod + prevU) % mod;
            int e = (prevA + prevI) % mod;
            int i = (prevE + prevO) % mod;
            int o = prevI;
            int u = (prevI + prevO) % mod;
            prevA = a;
            prevE = e;
            prevI = i;
            prevO = o;
            prevU = u;
        }
        return ((((prevA + prevE) % mod + prevI) % mod + prevO) % mod + prevU) % mod;
    }
}