Application 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.

Your friend Ninja has been learning about binary numbers lately. In order to understand binary numbers with perfection, Ninja asks you to generate a list of binary numbers from 1 to ‘N’, which he can use later for reference.

For every integer Ninja gives, your task is to generate all the binary numbers from 1 to ‘N’.

Example:

Consider N = 5,
All the binary numbers from 1 to 5 are: 1, 10, 11, 100, 101.

100 prisoners in jail are standing in a queue facing in one direction. Each prisoner is wearing a hat of color either black or red. A prisoner can see hats of all prisoners in front of him in the queue, but cannot see his hat and hats of prisoners standing behind him. 
The jailer is going to ask color of each prisoner’s hat starting from the last prisoner in queue. If a prisoner tells the correct color, then is saved, otherwise executed. How many prisoners can be saved at most if they are allowed to discuss a strategy before the jailer starts asking colors of their hats. 

You are given a 'Nx3' 2-D array 'Jobs' describing 'N' jobs where 'Jobs[i][0]' denotes the id of 'i-th' job, 'Jobs[i][1]' denotes the deadline of 'i-th' job, and 'Jobs[i][2]' denotes the profit associated with 'i-th job'.

You will make a particular profit if you complete the job within the deadline associated with it. Each job takes 1 unit of time to be completed, and you can schedule only one job at a particular time.

Return the number of jobs to be done to get maximum profit.

Note :

If a particular job has a deadline 'x', it means that it needs to be completed at any time before 'x'.

Assume that the start time is 0.

For Example :

'N' = 3, Jobs = [[1, 1, 30], [2, 3, 40], [3, 2, 10]].

All the jobs have different deadlines. So we can complete all the jobs.

At time 0-1, Job 1 will complete.
At time 1-2, Job 3 will complete.
At time 2-3, Job 2 will complete.

So our answer is [3 80].