|
| 1 | +/* Bottom-Up Approach |
| 2 | +----------------------------------------- |
| 3 | + Time Complexity : O(n) |
| 4 | + Space Complexity : O(n) |
| 5 | +----------------------------------------*/ |
| 6 | + |
1 | 7 | class Solution { |
2 | | - // 0: 'a', 1: 'e', 2: 'i', 3: 'o', 4: 'u' |
| 8 | + int MOD = (int) 1e9+7; |
3 | 9 |
|
4 | | - private static int MOD = 1_000_000_000 + 7; |
5 | | - |
6 | | - private int getSum(long[] arr) { |
7 | | - long sum = 0; |
8 | | - for(long x: arr) { |
9 | | - sum = sum + x; |
10 | | - sum = sum % MOD; |
| 10 | + public int countVowelPermutation(int n) { |
| 11 | + if (n == 1) { |
| 12 | + return 5; |
11 | 13 | } |
12 | | - return (int) sum; |
13 | | - } |
14 | | - |
15 | | - private long[] getBaseCounts() { |
16 | | - return new long[]{1, 1, 1, 1, 1}; |
17 | | - } |
18 | | - |
19 | | - private Map<Integer, List<Integer>> getNextCountMapping() { |
20 | | - Map<Integer, List<Integer>> map = new HashMap<>(); |
21 | | - |
22 | | - /* 0 1 2 3 4 |
23 | | - a e i o u |
24 | | - |
25 | | - Reverse mapping i.e. "depends on" |
26 | | - {a: [e, i, u]}, {e: [a, i]}, {i: [e, o]}, |
27 | | - {o: [i]}, {u: [i, o]} |
28 | | - */ |
29 | | - |
30 | | - map.put(0, new ArrayList<>(List.of(1, 2, 4))); |
31 | | - map.put(1, new ArrayList<>(List.of(0, 2))); |
32 | | - map.put(2, new ArrayList<>(List.of(1, 3))); |
33 | | - map.put(3, new ArrayList<>(List.of(2))); |
34 | | - map.put(4, new ArrayList<>(List.of(2, 3))); |
35 | | - |
36 | | - return map; |
37 | | - } |
38 | | - |
39 | | - private long[] getNextCounts( |
40 | | - long[] currentCounts, |
41 | | - Map<Integer, List<Integer>> mapNextCounting |
42 | | - ) { |
43 | | - long[] nextCounts = new long[5]; |
44 | | - Arrays.fill(nextCounts, 0); |
45 | | - |
46 | | - // Mapping conversion |
47 | | - for(int key: mapNextCounting.keySet()) { |
48 | | - for(int val: mapNextCounting.get(key)) { |
49 | | - nextCounts[val] += (long) currentCounts[key]; |
50 | | - nextCounts[val] %= MOD; |
51 | | - } |
| 14 | + |
| 15 | + long[][] dp = new long[n + 1][5]; |
| 16 | + for (int j = 0; j < 5; j++) { |
| 17 | + dp[1][j] = 1; |
52 | 18 | } |
53 | | - |
54 | | - return nextCounts; |
| 19 | + |
| 20 | + for (int i = 2; i <= n; i++) { |
| 21 | + dp[i][0] = dp[i - 1][1]; |
| 22 | + dp[i][1] = (dp[i - 1][0] + dp[i - 1][2]) % MOD; |
| 23 | + dp[i][2] = (dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][3] + dp[i - 1][4]) % MOD; |
| 24 | + dp[i][3] = (dp[i - 1][2] + dp[i - 1][4]) % MOD; |
| 25 | + dp[i][4] = dp[i - 1][0]; |
| 26 | + } |
| 27 | + |
| 28 | + long result = 0; |
| 29 | + for (int j = 0; j < 5; j++) { |
| 30 | + result = (result + dp[n][j]) % MOD; |
| 31 | + } |
| 32 | + |
| 33 | + return (int)result; |
55 | 34 | } |
56 | | - |
| 35 | +} |
| 36 | + |
| 37 | +/* Top Down Approach |
| 38 | +----------------------------------------- |
| 39 | + Time Complexity : O(n) |
| 40 | + Space Complexity : O(n) |
| 41 | +----------------------------------------*/ |
| 42 | + |
| 43 | +class Solution { |
| 44 | + HashMap<String, Integer> memo = new HashMap<>(); |
| 45 | + int MOD = (int) 1e9+7; |
| 46 | + |
57 | 47 | public int countVowelPermutation(int n) { |
58 | | - long[] counts = getBaseCounts(); |
59 | | - if(n == 1) { |
60 | | - return getSum(counts); |
61 | | - } |
| 48 | + long ans = 0; |
| 49 | + ans = (ans + dfs('a', n, 1)) % MOD; |
| 50 | + ans = (ans + dfs('e', n, 1)) % MOD; |
| 51 | + ans = (ans + dfs('i', n, 1)) % MOD; |
| 52 | + ans = (ans + dfs('o', n, 1)) % MOD; |
| 53 | + ans = (ans + dfs('u', n, 1)) % MOD; |
| 54 | + return (int)ans; |
| 55 | + } |
| 56 | + |
| 57 | + private int dfs(char c, int n, int l){ |
| 58 | + if(l == n) |
| 59 | + return 1; |
62 | 60 |
|
63 | | - Map<Integer, List<Integer>> mapNextCounting; |
64 | | - mapNextCounting = getNextCountMapping(); |
65 | | - |
66 | | - for(int i=1; i<n; i++) { |
67 | | - counts = getNextCounts(counts, mapNextCounting); |
| 61 | + String key = c + "_" + l; |
| 62 | + if (memo.containsKey(key)) return memo.get(key); |
| 63 | + |
| 64 | + long res = 0; |
| 65 | + if(c == 'a') { |
| 66 | + res = dfs('e', n, l+1); |
| 67 | + } else if(c == 'e') { |
| 68 | + res = (res + dfs('a', n, l+1)) % MOD; |
| 69 | + res = (res + dfs('i', n, l+1)) % MOD; |
| 70 | + } else if(c == 'i') { |
| 71 | + res = (res + dfs('a', n, l+1)) % MOD; |
| 72 | + res = (res + dfs('e', n, l+1)) % MOD; |
| 73 | + res = (res + dfs('o', n, l+1)) % MOD; |
| 74 | + res = (res + dfs('u', n, l+1)) % MOD; |
| 75 | + } else if(c == 'o') { |
| 76 | + res = (res + dfs('i', n, l+1)) % MOD; |
| 77 | + res = (res + dfs('u', n, l+1)) % MOD; |
| 78 | + } else { |
| 79 | + res = dfs('a', n, l+1); |
68 | 80 | } |
69 | | - |
70 | | - return getSum(counts); |
| 81 | + |
| 82 | + memo.put(key, (int)(res % MOD)); |
| 83 | + return (int)(res % MOD); |
71 | 84 | } |
72 | 85 | } |
0 commit comments