SDE - 1

You are given an array of ‘N’ integers, you need to find the maximum of minimum for every window size. The size of the window should vary from 1 to ‘N’ only.

For example:

ARR = [1,2,3,4]
Minimums of window size 1 = min(1), min(2), min(3), min(4) = 1,2,3,4
Maximum among (1,2,3,4)  is 4

Minimums of window size 2 = min(1,2), min(2,3),   min(3,4) = 1,2,3
Maximum among (1,2,3) is 3

Minimums of window size 3 = min(1,2,3), min(2,3,4) = 1,2
Maximum among (1,2) is 2

Minimums of window size 4 = min(1,2,3,4) = 1
Maximum among them is 1
The output array should be [4,3,2,1].

You are given 'N' stones labeled from 1 to 'N'. The 'i-th' stone has the weight W[i]. There are 'M' colors labeled by integers from 1 to 'M'. The 'i-th' stone has the color C[i] which is an integer between 1 to 'M', both inclusive.

You have been required to fill a Knapsack with these stones. The Knapsack can hold a total weight of 'X'.

You are required to select exactly 'M' stones; one of each color. The sum of the weights of the stones must not exceed 'X'. Since you paid a premium for a Knapsack with capacity 'X', you are required to fill the Knapsack as much as possible.

Write a program to calculate the best way to fill the Knapsack - that is, the unused capacity should be minimized.

You have been given an encoded string. Your task is to decode it back to the original string.

- An encoded string will be of the form <count>[encoded_string], where the 'encoded_string' inside the square brackets is being repeated exactly 'count' times. Note that 'count' is guaranteed to be a positive integer and can be greater than 9.
- There are no extra white spaces and square brackets are well-formed.

For example -

Input: 2[a]
“a” is encoded 2 times, hence the decoded string will be "aa".

Input: 3[a2[b]]
“b” is encoded 2 times, which decodes as 3[abb]. Now, "abb" is encoded 3 times, hence decoded string will be "abbabbabb". 

Given a graph, check whether the graph is bipartite or not. Your function should return true if the given graph's vertices can be divided into two independent sets, ‘U’ and ‘V’ such that every edge (‘u’, ‘v’) either connects a vertex from ‘U’ to ‘V’ or a vertex from ‘V’ to ‘U’.

You are given a 2D array ‘edges’ which contains 0 and 1, where ‘edges[i][j]’ = 1 denotes a bi-directional edge from ‘i’ to ‘j’.

Note:

If edges[i][j] = 1, that implies there is a bi-directional edge between ‘i’ and ‘j’, that means there exists both edges from ‘i’ to ‘j’ and to ‘j’ to ‘i’.

For example

Given:
‘N’ = 3
‘edges’ = [[0, 1, 1], [0, 0, 1], [0,0,0]]. 

You have been given a board where there are '2' rows and 'N' columns. You have an infinite supply of 2x1 tiles, and you can place a tile in the following ways:

1. Horizontally as 1x2 tile
2. Vertically as 2x1 tile

Count the number of ways to tile the given board using the available tiles.

Note :

The number of ways might be large so output your answer modulo 10^9 + 7.

Here an example of tile and board for 'N' = 4 :

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