feat(DP): new problem formated

analise-de-dados/src/ac.cpp

@@ -0,0 +1,68 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+/*
+rollMax[i] = n -> at most n dices of value i consecutive
+
+let dp[i][{1,2,3,4,5,6}] be the number of valid sequences of length i where the last dice was j
+
+we can extend this in the following way
+
+for all k such that k != j
+dp[i + 1][k] += dp[i][j]
+dp[i + 2][k] += dp[i][j]
+...
+dp[i + rollMax[k]][k] += dp[i][j]
+
+dp[0][j] = 1 for all j E {1,2,3,4,5,6}
+
+answer = sum (dp[N][j]) for all j E {1,2,3,4,5,6}
+*/
+const int MOD = 1e9 + 7;
+int dieSimulator(int n, vector<int> &rollMax)
+{
+   vector<vector<long long>> dp(n + 1, vector<long long>(6, 0));
+   for (int i = 0; i < 6; i++)
+   {
+      for (int rolls = 0; rolls <= rollMax[i] && rolls <= n; ++rolls)
+      {
+         dp[rolls][i] = 1;
+      }
+   }
+
+   for (int i = 1; i < n; i++)
+   {
+      for (int j = 0; j < 6; j++)
+      {
+         if (dp[i][j] == 0)
+            continue;
+         for (int k = 0; k < 6; k++)
+         {
+            if (k == j)
+               continue;
+            for (int m = 1; m <= rollMax[k] && i + m <= n; m++)
+            {
+               dp[i + m][k] += dp[i][j];
+               dp[i + m][k] %= MOD;
+            }
+         }
+      }
+   }
+
+   long long ans = 0;
+   for (int i = 0; i < 6; i++)
+      ans += dp[n][i];
+   return ans % MOD;
+}
+
+int main()
+{
+   int n;
+   cin >> n;
+   vector<int> nums(6);
+   for (int i = 0; i < 6; i++)
+      cin >> nums[i];
+   cout << dieSimulator(n, nums) << endl;
+   return 0;
+}