System Engineer

You have been given a 9x9 2d integer matrix 'MAT' representing a Sudoku puzzle. The empty cells of the Sudoku are filled with zeros, and the rest of the cells are filled with integers from 1 to 9. Your task is to fill all the empty cells such that the final matrix represents a Sudoku solution.

Note:

A Sudoku solution must satisfy all the following conditions-
1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9, 3x3 sub-grids of the grid.

You can also assume that there will be only one sudoku solution for the given matrix.

You are given a 0-indexed n x n grid, where n is always an odd number. Each cell in the grid contains a value of 0, 1, or 2.

A "Letter Y" shape is defined on this grid by three sets of cells:

1) The main diagonal from the top-left (0,0) to the grid's center.
2) The anti-diagonal from the top-right (0, n-1) to the grid's center.
3) The vertical line from the grid's center down to the bottom edge.

The grid is considered to have a "Letter Y" written on it if it meets three conditions:

1) All cells belonging to the Y shape have the same value.
2) All cells not belonging to the Y shape have the same value.
3) The value of the Y cells is different from the value of the non-Y cells.

In one operation, you can change the value of any single cell to 0, 1, or 2. Your task is to find the minimum number of operations required to make the grid satisfy the "Letter Y" conditions.

You are given an array 'ARR' of 'N' distinct positive integers. You are also given a non-negative integer 'B'.

Your task is to return all unique combinations in the array whose sum equals 'B'. A number can be chosen any number of times from the array 'ARR'.

Elements in each combination must be in non-decreasing order.

For example:

Let the array 'ARR' be [1, 2, 3] and 'B' = 5. Then all possible valid combinations are-

(1, 1, 1, 1, 1)
(1, 1, 1, 2)
(1, 1, 3)
(1, 2, 2)
(2, 3)

Ninja is observing an array of ‘N’ numbers and wants to make as many unique subsets as possible. Can you help the Ninja to find all the unique subsets?

Note: Two subsets are called same if they have same set of elements.For example {3,4,1} and {1,4,3} are not unique subsets.

You are given an array ‘ARR’ having N elements. Your task is to print all unique subsets.

For Example

For the given if ARR = [1,1,3],the answer will be [ ],[1],[1,1],[1,3],[3],[1,1,3].

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