Implementation Optimal strategy for a game (set-1) by dynamic program…(…

…jainaman224#1622) (jainaman224#1985)

* Implementation Optimal strategy for a game (set-1) by dynamic programming

* Changes request jainaman224#1985

* changes request-2 jainaman224#1985

* changes the request jainaman224#1985

Optimal_Strategy_For_A_Game (Set-1)/optimal_strategy_for_a_game_set_1.cpp

@@ -0,0 +1,90 @@
+/*
+OPTIMAL STRATEGY FOR A GAME SET - 1
+Given Problem Statement : Problem statement: Consider a row of n coins of values v1 . . . vn, where n is even.
+We play a game against an opponent by alternating turns. In each turn,
+a player selects either the first or last coin from the row,
+removes it from the row permanently and receives the value of the coin.
+Determine the maximum possible amount of money we can definitely win if we move first.
+Note - Note: The opponent is as clever as the user.
+*/
+// C++ program to find out maximum value from a given sequence of coins
+
+#include <bits/stdc++.h>
+using namespace std;
+
+/*Returns optimal value possible that a player can
+collect from an array of coins of size n. Note
+than n must be even*/
+int optimalStrategyOfGame(int* arr, int n)
+{
+    // Create a table to store solutions of subproblems
+    int table[n][n];
+
+    /*Fill table using above recursive formula.
+    Note that the table is filled in diagonal fashion from
+    diagonal elements to table[0][n-1] which is the result.*/
+    for (int gap = 0; gap < n; ++gap){
+        for (int i = 0, j = gap; j < n; ++i, ++j){
+
+            /*Here x is value of F(i+2, j), y is F(i+1, j-1) and
+            z is F(i, j-2) in above recursive formula*/
+            int x = ((i + 2) <= j) ? table[i + 2][j] : 0;
+            int y = ((i + 1) <= (j - 1)) ? table[i + 1][j - 1] : 0;
+            int z = (i <= (j - 2)) ? table[i][j - 2] : 0;
+            table[i][j] = max(arr[i] + min(x, y), arr[j] + min(y, z));
+        }
+    }
+
+    return table[0][n - 1];
+}
+
+// Driver Code to test above function
+int main()
+{
+     int arr1[1005], n;
+
+    //Number of values in array you want to store
+     cin >> n;
+
+    //Input taken in array
+     for(int i = 0 ; i < n ; i ++ )
+          cin >> arr1[i];
+
+    //function call for calculating it's optimal strategy
+    printf("%d\n", optimalStrategyOfGame(arr1, n));
+
+return 0;
+}
+
+/*
+Input for test case 1:
+4     // n = 4
+8     //input taken in array
+15
+3
+7
+Output for test case 1:
+22
+*/
+/*
+Input for test case 2:
+4     // n = 4
+2     //input taken in array
+2
+2
+2
+Output for test case 2:
+4
+*/
+/*
+Input for test case 3:
+6     // n = 6
+20    //input taken in array
+30
+2
+2
+2
+10
+Output for test case 3:
+42
+*/