Guys I have been working on this problem since morning (4 hours ago) and still couldn’t find a proper answer. Can anyone help me?
problem link: https://codeforces.com/contest/1761/problem/C#
 Problem Explanation:
The problem “Set Construction” from Codeforces requires constructing sets based on a given binary matrix, with certain rules for inclusion and comparison. Let’s break it down:
Problem Explanation

Input:
 You have a binary matrix
b
with dimensionsn x n
, where each element is either 0 or 1.
 You have a binary matrix

Output:
 You need to construct
n
sets ( A_1, A_2, dots, A_n ) consisting of distinct integers from 1 to ( n ).
 You need to construct

Conditions:
 Each set must be nonempty and distinct.
 The matrix
b
indicates the subset relationship between these sets: If
b[i][j] = 1
, then the set ( A_i ) must be a proper subset of ( A_j ).  If
b[i][j] = 0
, then the set ( A_i ) must not be a subset of ( A_j ).
 If

Proper Subset:
 A set ( A_i ) is a proper subset of ( A_j ) if all elements of ( A_i ) are in ( A_j ), and ( A_i ) is strictly smaller (i.e., ( A_i neq A_j )).
Construction of Sets
To create the sets:
 Start with each set containing its index: ( A_i = {i+1} ).
 For each 1 in the matrix
b[i][j]
, add the elements of ( A_i ) to ( A_j ).
Example
For instance, if the matrix b
is:
0 1 0
0 0 1
0 0 0
 It indicates ( A_1 ) should be a proper subset of ( A_2 ), and ( A_2 ) should be a proper subset of ( A_3 ). Thus, you might have:
 ( A_1 = {1} )
 ( A_2 = {1, 2} )
 ( A_3 = {1, 2, 3} )
This ensures the proper subset relationships as indicated by the matrix b
.
Implementation Notes
The solution involves iterating over the matrix and ensuring that the sets are constructed according to the proper subset relationships. For each 1 in the matrix, the corresponding set relationships are established. If a zero is encountered, the corresponding sets must not have a subset relationship.
Example:
 Input
2
4
0001
1001
0001
0000
3
011
001
 Output
3 1 2 3
2 1 3
2 2 4
4 1 2 3 4
1 1
2 1 2
3 1 2 3
 My C# code is here:
int t = int.Parse(Console.ReadLine());
for (int i = 0; i < t; i++)
{
int n = int.Parse(Console.ReadLine());
int[,] b = new int[n, n]; // nxn size, 2d array def
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
b[j, k] = int.Parse(Console.ReadLine());
}
}
List<HashSet<int>> sets = new List<HashSet<int>>();
for (int j = 0; j < n; j++)
{
HashSet<int> set = new HashSet<int>();
for (int k = 0; k < n; k++)
{
set.Add(k+1);
if(b[j, k] == 1) {
set.Remove(j+1);
}
}
sets.Add(set);
}
}
What should I do after that?
I have tried to solve the problem but I couldn’t find a valid solution for the problem. I am expecting **help **for a *proper *and *valid *solution.