Associate Software Engineer

You are given ‘n’ items with certain ‘profit’ and ‘weight’ and a knapsack with weight capacity ‘w’.

You need to fill the knapsack with the items in such a way that you get the maximum profit. You are allowed to take one item multiple times.

Example:

Input: 
'n' = 3, 'w' = 10, 
'profit' = [5, 11, 13]
'weight' = [2, 4, 6]

Output: 27

Explanation:
We can fill the knapsack as:

1 item of weight 6 and 1 item of weight 4.
1 item of weight 6 and 2 items of weight 2.
2 items of weight 4 and 1 item of weight 2.
5 items of weight 2.

The maximum profit will be from case 3 = 11 + 11 + 5 = 27. Therefore maximum profit = 27.

Once Kevin is playing a hurdle game in which he has to jump some hurdles to clear a particular level. Each level ‘i’ has ‘i’ hurdles (for example, level 6 has 6 hurdles).

You are provided with the total number of hurdles that Kevin has jumped, you have to tell how many levels he has cleared.

Note :

Kevin has played this game once. He can only reach the level ‘i’ if and only if he has already cleared the level (‘i’ - 1).

You are given a binary tree having 'n' nodes. Each node of the tree has an integer value.

Your task is to find the maximum possible sum of a simple path between any two nodes (possibly the same) of the given tree.

A simple path is a path between any two nodes of a tree, such that no edge in the path is repeated twice. The sum of a simple path is defined as the summation of all node values in a path.