SDE - 1

You are given an 'N * N' matrix of integers where each row and each column is sorted in increasing order. You are given a target integer 'X'.

Find the position of 'X' in the matrix. If it exists then return the pair {i, j} where 'i' represents the row and 'j' represents the column of the array, otherwise return {-1,-1}

For example:

If the given matrix is:
[ [1, 2, 5],
  [3, 4, 9],
  [6, 7, 10]] 
We have to find the position of 4. We will return {1,1} since A[1][1] = 4.

You are given a binary search tree (BST) and a key value 'K'. You need to delete the node with value 'K'. It is guaranteed that a node has the value 'K'.

A binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree whose internal nodes each store a key greater than all the keys in the node's left subtree and less than those in its right subtree.

Note:

All the elements of the binary search tree are unique.

You are given two arrays, ‘A’ and ‘B’, with the same elements in a different order. Your task is to make ‘B’ identical to the ‘A’ by swapping the elements in array ‘B’. You have to find out the minimum number of swaps required.

For Example:

For the first test case, ‘A’ = [5, 6, 4, 10], ‘B’ = [4, 6, 10, 5], here in the ‘B’ we can swap 4 with 10 to form [10, 6, 4, 5] and we can then swap 10 with 5 to form the array [5, 6, 4, 10] which is identical to ‘A’. Hence the answer is 2.

You are given a square matrix of non-negative integers of size 'N x N'. Your task is to rotate that array by 90 degrees in an anti-clockwise direction without using any extra space.

For example:

For given 2D array :

    [    [ 1,  2,  3 ],
         [ 4,  5,  6 ],
         [ 7,  8,  9 ]  ]

After 90 degree rotation in anti clockwise direction, it will become:

    [   [ 3,  6,  9 ],
        [ 2,  5,  8 ],
        [ 1,  4,  7 ]   ]

Given a sequence of ‘N’ space-separated non-negative integers A[1],A[2],A[3],......A[i]…...A[n]. Where each number of the sequence represents the height of the line drawn at point 'i'. Hence on the cartesian plane, each line is drawn from coordinate ('i',0) to coordinate ('i', 'A[i]'), here ‘i’ ranges from 1 to ‘N’. Find two lines, which, together with the x-axis forms a container, such that the container contains the most area of water.

Note :

1. You can not slant the container i.e. the height of the water is equal to the minimum height of the two lines which define the container.

2. Do not print anything, you just need to return the area of the container with maximum water.

Example

For the above Diagram, the first red marked line is formed between coordinates (2,0) and (2,10), and the second red-marked line is formed between coordinates (5,0) and (5,9). The area of water contained between these two lines is (height* width) = (5-2)* 9 = 27, which is the maximum area contained between any two lines present on the plane. So in this case, we will return 3* 9=27.

Ninja and his friend are playing a game. They are having ‘N’ piles and each pile contains ‘A[i]’ amount of stones in it. Ninja will make the first move.

In each move, a player can choose any pile and remove any number of stones ( at least one ) from that pile. The player who cannot make a move loses the game.

Assuming both players play optimally, output 1 if Ninja wins the game and 0 if Ninja loses the game.

Example :

N = 3
A = [ 3, 4, 5 ]

Explanation : 

One of the optimal ways to play the game is : 

Ninja removes 3 stones from the first pile : [ 0, 4, 5 ].
Friend removes 3 stones from the second pile : [ 0, 1, 5 ].
Ninja removes 3 stones from the third pile : [ 0, 1, 1 ].
Friend removes 1 stone from the second pile : [ 0, 0, 1 ].
Ninja removes 1 stones from the third pile : [ 0, 0, 0 ].

Thus Ninja wins the game here.

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