SDE - 1

You have been given a square array 'VEC' of integers of size 'N' rows and 'N' columns. Your task is to find the minimum sum of a falling path through the square array. The number of rows and columns in the given array will be the same.

A falling path starts at any element in the first row and chooses one element from each row. The next row's choice must be in a column that is different from the previous row's column by at most one.

Example:

VEC[][]= {{5, 10}, {25, 15}}      

All the rectangles denote the possible falling paths. The rectangle with red filler is the minimum falling path with the minimum falling path sum of 20 (5+15). 

You are given an array 'arr' containing 'n' non-negative integers.

Your task is to partition this array into two subsets such that the absolute difference between subset sums is minimum.

You just need to find the minimum absolute difference considering any valid division of the array elements.

Note:

1. Each array element should belong to exactly one of the subsets.

2. Subsets need not always be contiguous.
For example, for the array : [1, 2, 3], some of the possible divisions are 
   a) {1,2} and {3}
   b) {1,3} and {2}.

3. Subset-sum is the sum of all the elements in that subset. 

Example:

Input: 'n' = 5, 'arr' = [3, 1, 5, 2, 8].

Ouput: 1

Explanation: We can partition the given array into {3, 1, 5} and {2, 8}. 
This will give us the minimum possible absolute difference i.e. (10 - 9 = 1).

Given a rod of length ‘N’ units. The rod can be cut into different sizes and each size has a cost associated with it. Determine the maximum cost obtained by cutting the rod and selling its pieces.

Note:

1. The sizes will range from 1 to ‘N’ and will be integers.

2. The sum of the pieces cut should be equal to ‘N’.

3. Consider 1-based indexing.

You are given a string ‘S’ of length ‘N’ representing an integer.

Beauty of a string is the difference between the frequency of the most frequently occurring character and the least frequently occurring character.

You must return the sum of beauty of all substrings of string ‘S’.

Note:

A substring is a string formed after deleting zero or more characters from both ends of a string.

Example:

Input:
S = “hello"

Output:
5

Explanation: The following substring ‘hell’, ‘ell’, ‘llo’, ‘ello’, and ‘hello’ has the beauty of 1. Hence we return 5.

You are given a string 'str' of length 'N'.

Your task is to reverse the original string word by word.

There can be multiple spaces between two words and there can be leading or trailing spaces but in the output reversed string you need to put a single space between two words, and your reversed string should not contain leading or trailing spaces.

Example :

If the given input string is "Welcome to Coding Ninjas", then you should return "Ninjas Coding to Welcome" as the reversed string has only a single space between two words and there is no leading or trailing space.