Create count-vowels-permutation.cpp

Author: kamyu104

C++/count-vowels-permutation.cpp

@@ -0,0 +1,75 @@
+// Time:  O(logn)
+// Space: O(1)
+
+class Solution {
+public:
+    int countVowelPermutation(int n) {
+        vector<vector<int>> T = {{0, 1, 1, 0, 1},
+                                 {1, 0, 1, 0, 0},
+                                 {0, 1, 0, 1, 0},
+                                 {0, 0, 1, 0, 0},
+                                 {0, 0, 1, 1, 0}};
+
+        const auto& result = matrixExpo(T, n - 1);
+        return accumulate(result.cbegin(), result.cend(), 0,
+                          [&](int total, const vector<int>& row) {
+                              return (total + 
+                                      accumulate(row.cbegin(), row.cend(), 0,
+                                                 [&](int sum, int val) {
+                                                     return (sum + val) % MOD;
+                                                 })) % MOD;
+                          });
+    }
+
+private:
+    vector<vector<int>> matrixExpo(const vector<vector<int>>& A, int pow) {
+        vector<vector<int>> result(A.size(), vector<int>(A.size()));
+        vector<vector<int>> A_exp(A);
+        for (int i = 0; i < A.size(); ++i) {
+            result[i][i] = 1;
+        }
+        while (pow) {
+            if (pow % 2 == 1) {
+                result = matrixMult(result, A_exp);
+            }
+            A_exp = matrixMult(A_exp, A_exp);
+            pow /= 2;
+        }
+        return result;
+    }
+
+    vector<vector<int>> matrixMult(const vector<vector<int>>& A, const vector<vector<int>>& B) {
+        vector<vector<int>> result(A.size(), vector<int>(A.size()));
+        for (int i = 0; i < A.size(); ++i) {
+            for (int j = 0; j < B[0].size(); ++j) {
+                int64_t entry = 0;
+                for (int k = 0; k < B.size(); ++k) {
+                    entry = (static_cast<int64_t>(A[i][k]) * B[k][j] % MOD + entry) % MOD;
+                }
+                result[i][j] = static_cast<int>(entry);
+            }
+        }
+        return result;
+    }
+    const int MOD = 1e9 + 7;
+};
+
+// Time:  O(n)
+// Space: O(1)
+class Solution2 {
+public:
+    int countVowelPermutation(int n) {
+        int a = 1, e = 1, i = 1, o = 1, u = 1;
+        for (int x = 1; x < n; ++x) {
+            tie(a, e, i, o, u) = make_tuple(((e + i) % MOD + u) % MOD,
+                                            (a + i) % MOD,
+                                            (e + o) % MOD,
+                                            i,
+                                            (i + o) % MOD);
+        }
+        return (((a + e) % MOD + (i + o) % MOD) % MOD + u) % MOD;
+    }
+    
+private:
+    const int MOD = 1e9 + 7;
+};