feat(DP): new dp problems formated

decode-ways/src/ac.cpp

@@ -0,0 +1,56 @@
+#include <bits/stdc++.h>
+
+typedef long long ll;
+using namespace std;
+
+ll numDecodings(string s)
+{
+   if (s[0] == '0')
+      return 0;
+   for (int i = 1; i < s.size(); i++)
+   {
+      if (s[i] == '0' && s[i - 1] == '0')
+         return 0;
+   }
+
+   // each letter can be a part of the message on their on
+   // they can extend the last letter to also form another part of the mesage
+   // let dp[i][{0, 1}] be the number of different messages ending at the i(th) char when the i(th) char
+   // is not concatenated with i-1(th) char or is.
+
+   // if s[i] is between 1 and 26 then it can be added alone, so dp[i][0] = dp[i - 1][0] + dp[i - 1][1]
+   // if s[i] concatenated with s[i - 1] and is between 1 and 26 then they can be added togheter, dp[i][1] = dp[i - 2][0] + dp[i - 2][1]
+
+   // dp[1][0] = 1, dp[1][1] = 0
+
+   int N = s.size();
+   vector<vector<ll>> dp(N + 1, vector<ll>(2, 0));
+   dp[1][0] = 1, dp[1][1] = 0;
+   dp[0][0] = 1;
+   for (int i = 2; i <= N; i++)
+   {
+      char current = s[i - 1], last = s[i - 2];
+      string aux = "";
+      aux += last;
+      aux += current;
+      if (current != '0')
+      {
+         dp[i][0] = dp[i - 1][0] + dp[i - 1][1];
+      }
+
+      int code = stoi(aux);
+      if (10 <= code && code <= 26)
+      {
+         dp[i][1] = dp[i - 2][0] + dp[i - 2][1];
+      }
+   }
+   return dp[N][0] + dp[N][1];
+}
+
+int main()
+{
+   int n; cin >> n;
+   string code; cin >> code;
+   cout << numDecodings(code) << endl;
+   return 0;
+}