SDE - 2

You have an integer ‘N’ and an array ‘X’ of ‘N’ integers. You need to maximize the value of the array, which is equal to ⅀ '(X[i] - i)^2' from ‘i’ in the range ‘[0, N-1]’. To do this, you can rearrange the elements of the given array.

Determine the maximum value of the array you can get after rearranging the array ‘X’ elements.

Example:

'N' = 3, ‘X' = [1,2,1] 
If we rearrange our array 'X' to '[2, 1, 1]' .
Then our answer will be (0-2)^2 + (1-1)^2 + (1-2)^2 = 4 + 0 + 1 = 5.
For array ‘[1, 1, 2]’ value will be equal to ‘1 + 0 + 0 = 1’.
For array ‘[1, 2, 1]’ value will be equal to ‘1 + 1 + 1 = 3’.

You are given a graph with ‘N’ nodes and exactly one cycle. You are given a 2-d array ‘EDGES’, where ‘Edges[i]’=[‘node0’, ’node1’], denotes an undirected edge from node0 to node1. The nodes are numbered from 0 to ‘N’-1, where ‘N’ is the number of nodes in the graph.

The distance between two nodes is defined as the number of edges between them.

You must return an array ‘ANSWER’ of size ‘N’, where ‘ANSWER[i]’ is the shortest distance between node ‘i’ and any node present in the cycle.

Note :

The graph is connected.
There is, at most, one edge between any pair of nodes.
There is exactly one cycle in the graph.

Example:

Input: N=7, edges=[[1, 2], [2, 3], [3, 4], [4, 1], [0, 1], [5, 2], [6, 5]]

Output: [1, 0, 0, 0, 0, 1, 2]

Explanation: The Nodes 1, 2, 3, and 4 form a cycle.
The distance between nodes 0 to 1 is 1.
The distance between nodes 1 to 1 is 0.
The distance between nodes 2 to 2 is 0.
The distance between nodes 3 to 3 is 0.
The distance between nodes 4 to 4 is 0.
The distance between nodes 5 to 2 is 1.
The distance between nodes 6 to 2 is 2.

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There are 100 doors in a row, all doors are initially closed. A person walks through all doors multiple times and toggle (if open then close, if close then open) them in the following way: In the first walk, the person toggles every door In the second walk, the person toggles every second door, i.e., 2^nd, 4^th, 6^th, 8^th, … In the third walk, the person toggles every third door, i.e. 3^rd, 6^th, 9^th, … Likewise, In the 100^th walk, the person toggles the 100^th door. 
Which doors are open in the end?