SDE - 1

On a 2-D plane, we place 'n' stones at some integer coordinate points. Each coordinate point may have at most one stone.

A stone can be removed if it shares either the same row or the same column as another stone that has not been removed.

You are given an array 'stones' of length 'n' where 'stones[i]' = '[ri, ci]' represent the ith stone’s location i.e 'ri' is the row coordinate of the 'ith' stone and 'ci' is the column coordinate of the 'ith' stone. Your task is to return the largest possible number of stones that can be removed.

Example:

Input: 'stones' = [[0,1] [1,0] [0,0]]

Output: 2

Explanation:
We can remove the 1st stone at [0,1] as it has the same row as the 3rd stone [0, 0]. And remove the 2nd stone because it has the same column [0,1] as the 3rd stone.

You are given an array 'A' of length 'N' containing integers.

Determine if there exist three indices 'i', 'j', and 'k' such that 0 <= 'i' < 'j' < 'k' < 'N' and 'A[i]' < 'A[k]' < 'A[j]'.

For Example :

Let 'N' = 5, 'A' = [1, 5, 2, 4, 3].
Here, if we take 'i' = 0, 'j' = 1, and 'k' = 3, then 'i' < 'j' < 'k' (0 < 1 < 3) and 'A[i]' < 'A[k]' < 'A[j]' (1 < 4 < 5).
Therefore, the answer is True.

You are given the number of machines 'N', an array 'M' of length 'N' where 'M[i]' represents the number of days the i-th machine takes to produce one item, and the total number of items 'O' that need to be ordered.

Return the minimum number of days required for all machines working in parallel to complete the order.

For Example :

Let 'N' = 2, 'M' = [3, 1], 'O' = 5.
Day 1: Machine 2 produces an item
Day 2: Machine 2 produces an item
Day 3: Both Machine 1 and Machine 2 produce an item
Day 4: Machine 2 produces an item
Total items produced = 1 + 1 + 2 + 1 = 5 items.
Therefore, the answer is 4 days.

You are given an integer ‘N’, which denotes there are ‘N’ friends. You are supposed to form some pairs them satisfying the following conditions:

1. Each friend can be paired with some other friend or remain single.

2. Each friend can be a part of at most one pair.

You are supposed to find the total number of ways in which the pairing can be done satisfying both conditions. Since the number of ways can be quite large, you should find the answer modulo 1000000007(10^9+7).

Note:

1. Return the final answer by doing a mod with 10^9 + 7.
2. Pairs {A, B} and {B, A} are considered the same.