SDE - 1

You are given a directed graph of ‘N’ nodes and ‘M’ edges. Also, you have two nodes ‘A’ and ‘B’. Your task is to make at least one valid path from ‘A’ to ‘B’ by doing the below operations a minimum number of times.

Choose two nodes ‘X’ and ‘Y’, such that there exists an edge from ‘X’ to ‘Y’.

Delete edge ‘X’ to ‘Y’.

Add edge ‘Y’ to ‘X’.

You need to print the minimum operations that you have done.

You have been given a 9 X 9 2D matrix 'MATRIX' with some cells filled with digits(1 - 9), and some empty cells (denoted by 0).

You need to find whether there exists a way to fill all the empty cells with some digit(1 - 9) such that the final matrix is a valid Sudoku solution.

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, 3 x 3 sub-matrices of the matrix.

Note

1. There will always be a cell in the matrix which is empty.
2. The given initial matrix will always be consistent according to the rules mentioned in the problem statement.

For a given array with N elements, you need to find the length of the longest subsequence from the array such that all the elements of the subsequence are sorted in strictly increasing order.

Strictly Increasing Sequence is when each term in the sequence is larger than the preceding term.

For example:

[1, 2, 3, 4] is a strictly increasing array, while [2, 1, 4, 3] is not.