SDE - Intern

You and your friend Ninjax are playing a game of coins. Ninjax place the 'N' number of coins in a straight line.

The rule of the game is as follows:

1. Each coin has a value associated with it.

2. It’s a two-player game played against an opponent with alternating turns. 

3. At each turn, the player picks either the first or the last coin from the line and permanently removes it.

4. The value associated with the coin picked by the player adds up to the total amount the player wins. 

Ninjax is a good friend of yours and asks you to start first.

Your task is to find the maximum amount you can definitely win at the end of this game.

Note:

'N' is always even number.

Ninjax is as smart as you, so he will play so as to maximize the amount he wins.

Example 1:

Let the values associated with four coins be: [9, 5, 21, 7] 

Let’s say that initially, you pick 9 and Ninjax picks 7.
Then, you pick 21 and Ninjax picks 5. 
So, you win a total amount of (9+21), i.e. 30.

In case you would have picked up 7 initially and Ninjax would have picked 21 (as he plays optimally). 
Then, you would pick 9 and Ninjax would choose 5. So, you win a total amount of (7+9), i.e. 16, which is not the maximum you can obtain.

Thus, the maximum amount you can win is 30.

Example 2:

Let the values associated with four coins be: [20, 50, 5, 10] 

Let’s say that initially, you pick 10 and Ninjax picks 20.
Then, you pick 50 and Ninjax picks 5. 
So, you win a total amount of (10+50), i.e. 60.

In case you would have picked up 20 initially and Ninjax would have picked 50 (as he plays optimally). 
Then, you would pick 10 and Ninjax would choose 5. So, you win a total amount of (20+10), i.e. 30, which is not the maximum you can obtain.

Thus, the maximum amount you can win is 60.

You have been given a Binary Search Tree of integers. You are supposed to convert it to a greater sum tree such that the value of every node in the given BST is replaced with the sum of the values of all the nodes which are greater than the value of the current node in the tree.

A Binary Search Tree is a tree, whose internal nodes each store a value greater than all the values in the node's left subtree and less than those in its right subtree.

Note :

You need to modify the given tree only. You are not allowed to create a new tree.

For example:

For the given binary search tree

11 will be replaced by {15 + 29 + 35 + 40}, i.e. 119.
2 will be replaced by {7 + 11 + 15 + 29 + 35 + 40}, i.e. 137.
29 will be replaced by {35 + 40}, i.e. 75.
1 will be replaced by {2 + 7 + 11 + 15 + 29 + 35 + 40}, i.e. 139.
7 will be replaced by {11 + 15 + 29 + 35 + 40}, i.e. 130.
15 will be replaced by {15 + 29 + 35 + 40}, i.e. 104.
40 will be replaced by 0 {as there is no node with a value greater than 40}.
35 will be replaced by {40}, i.e. 40.