Add solution to day 26

05- May/26- Stone Game II/26- Stone Game II (Ahmed Gamal).cpp

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+// Author: Ahmed Gamal
+
+// for this problem, we can use dynamic programming to solve it
+// we will solve the problem from the perspective of the first player (Alex)
+// from the perspective of the first player, in his turn, he will try to maximize the score
+// and in the second player's turn, he will try to minimize the score of the first player
+
+// so, we will use a memoization table to store the maximum score that the first player can get from the ith element in the piles vector
+// and the m value is m
+
+class Solution {
+    // memoization table and it's size
+    static const int N = 101;
+    int memo[N][N][2];
+
+    // dp(idx, m, turn) returns the maximum score that the first player can get from the idx element in the piles vector
+    // and the m value is m and it's the turn of the turn ? the first player : the second player
+    int dp(int idx, int m, int turn, vector<int>& v) {
+        // if the idx is larger than the size of the piles vector, we will return 0
+        if(idx >= v.size()) {
+            return 0;
+        }
+
+        // if the value of the memoization table is not -1, we will return it
+        int& ret = memo[idx][m][turn];
+        if(~ret) {
+            return ret;
+        }
+
+        // if it's the first player's turn, we will try to maximize the score
+        // if it's the second player's turn, we will try to minimize the score
+        ret = turn ? 0 : 2e9;
+
+        // we will try to choose from 1 to 2 * m elements from the piles vector
+        // sum is the sum of the elements that we will choose
+        int sum = 0;
+        for(int i = 0; i < m * 2; i++) {
+            // if the idx + i is larger than the size of the piles vector, we will break
+            if(idx + i >= v.size()) {
+                break;
+            }
+
+            // updating the sum
+            sum += v[idx + i];
+
+            // if it's the first player's turn, we will try to maximize the score
+            if(turn) {
+                ret = max(ret, sum + dp(idx + i + 1, max(m, i + 1), false, v));
+            } else {
+                // if it's the second player's turn, we will try to minimize the score
+                ret = min(ret, dp(idx + i + 1, max(m, i + 1), true, v));
+            }
+        }
+
+        return ret;
+    }
+
+public:
+    int stoneGameII(vector<int>& piles) {
+        // initializing the memoization table with -1
+        memset(memo, -1, sizeof memo);
+
+        // starting the dp from the first element in the piles vector with m = 1 and it's the first player's turn
+        return dp(0, 1, true, piles);
+    }
+};