Create Day 8: Optimal Strategy For A Game.java

April/Day 8: Optimal Strategy For A Game.java

@@ -0,0 +1,31 @@
+class solve
+{
+    //Function to find the maximum possible amount of money we can win.
+    static long countMaximum(int n, int arr[]){
+        int[] sum = new int[n+1];
+        sum[0] = 0;
+        for(int i=0; i<n; i++){
+            sum[i+1] = arr[i] + sum[i];
+        }
+        int[][] dp = new int[n][n];
+        for(int i=0; i<n; i++){
+            dp[i][i] = arr[i];
+        }
+        for(int d=1; d<n; d++){
+            for(int r=0; r<n-d; r++){
+                int c = d+r;
+                //option 1
+                //take arr[c]
+                //sum from r to c-1 inclusive = sum till c-1 - sum till r-1
+                // = sum[c] - sum[r]
+                dp[r][c] = arr[c] + (sum[c] - sum[r]) - dp[r][c-1];
+                //option 2
+                //take arr[r]
+                //sum from r+1 to c inclusive = sum till c - sum till r
+                // = sum[c+1] - sum[r+1];
+                dp[r][c] = Math.max(dp[r][c], arr[r] + (sum[c+1] - sum[r+1]) - dp[r+1][c]);
+            }
+        }
+        return dp[0][n-1];
+    }
+}