Create number-of-strings-which-can-be-rearranged-to-contain-substring.cpp

Author: kamyu104

C++/number-of-strings-which-can-be-rearranged-to-contain-substring.cpp

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+// Time:  O(logn)
+// Space: O(1)
+
+// combinatorics, principle of inclusion-exclusion
+class Solution {
+public:
+    int stringCount(int n) {
+        static const int MOD = 1e9 + 7;
+        const auto& powmod = [](uint64_t a, uint64_t b, uint64_t mod) {
+            a %= mod;
+            int64_t result = 1;
+            while (b) {
+                if (b & 1) {
+                    result = (result * a % mod);
+                }
+                a = (a * a % mod);
+                b >>= 1;
+            }
+            return result;
+        };
+    
+        return  ((powmod(26, n, MOD) - 
+                 (25 + 25 + 25 + n) * powmod(25, n - 1, MOD) +                   // no l, t, e, ee
+                 (24 + 24 + 24 + n + n + 0) * powmod(24, n - 1, MOD) -           // no l|t, l|e, t|e, l|ee, t|ee, e|ee
+                 (23 + n + 0 + 0) * powmod(23, n - 1, MOD)) % MOD + MOD) % MOD;  // no l|t|e, l|t|ee, l|e|ee, t|e|ee    
+    }
+};
+
+// Time:  O(2^4 * n) = O(n)
+// Space: O(2^4) = O(1)
+// bitmasks, dp
+class Solution2 {
+public:
+    int stringCount(int n) {
+        static const int MOD = 1e9 + 7;
+
+        enum {L = 1 << 0, E = 1 << 1, EE = 1 << 2, T = 1 << 3};
+        vector<int64_t> dp(1 << 4);
+        dp[0] = 1;
+        for (int _ = 0; _ < n; ++_) {
+            vector<int64_t> new_dp(1 << 4);
+            for (int mask = 0; mask < size(dp); ++mask) {
+                new_dp[mask | L] = (new_dp[mask | L] + dp[mask]) % MOD;
+                if ((mask & E) == 0) {
+                    new_dp[mask | E] = (new_dp[mask|E] + dp[mask]) % MOD;
+                } else {
+                    new_dp[mask | EE] = (new_dp[mask | EE] + dp[mask]) % MOD;
+                }
+                new_dp[mask | T] = (new_dp[mask | T] + dp[mask]) % MOD;
+                new_dp[mask] = (new_dp[mask] + 23 * dp[mask]) % MOD;
+            }
+            dp = move(new_dp);
+        }
+        return dp.back();
+    }
+};