SDE - 1

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.

Bob is playing a game where there is a grid of size ‘N’ X ‘M’, where each cell is either 0, 1, or 2.

0 means the cell is empty, 1 means the cell contains a block, and 2 means there is a guard present in that block. A guard can see in all four directions, i.e., left, right, up, down till there is a block or to the end of the grid if there are no blocks present in that direction.

For Example:

0 0
0 0
2 1
In the above grid, if Bob is present at (0,1), he can't move to (0,0) because the cell at (0,0) is seen by the guard present at (2,0).

0 0
1 0
2 1
In the above grid, Bob can move from (0,1) to (0,0) since this cell is not seen by the guard at (2,0) due to the block present at (1,0).

At each step, one can move to any valid adjacent cells that share a common side with the current cell. A cell is valid if it is present inside the grid, empty, and not seen by any of the guards.

Now Bob can enter the grid from any of the four corners of the grid(if it is a valid cell) i.e, (0,0), (N - 1,0), (0,M - 1), (N - 1,M - 1), and he wants to reach a destination cell.

Can you tell whether Bob can reach the destination cell or not?

Note:

If all the corner cells are invalid, then return false.

You have been given a gold mine represented by a 2-d matrix of size ('N' * 'M') 'N' rows and 'M' columns. Each field/cell in this mine contains a positive integer, the amount of gold in kgs.

Initially, the miner is at the first column but can be at any row.

He can move only right, right up, or right down. That is from a given cell and the miner can move to the cell diagonally up towards the right or right or diagonally down towards the right.

Find out the maximum amount of gold he can collect.

Write a program to accept a coordinate point in an XY coordinate system and determine in which quadrant the coordinate point lies.

Print

"1st Quadrant": if  +x,+y
"2nd Quadrant": if -x,+y
"3rd Quadrant": if -x,-y
"4th Quadrant": if +x,-y
"x axis": if x,0
"y axis": if 0,y
"Origin": if 0,0

You are given a positive integer N. Your task is to return a list of integers containing integers from 1 to N (both inclusive) in lexicographically ascending order.

For example:- Given 3 numbers 1, 3 and 10, the lexicographical ascending order will be 1, 10 and 3.

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