Distinct Matrix | Starters 81 Codechef

Problem

You are given an integer $�$ . Generate a matrix of size $� \times �$ such that:

Each element of the matrix is either 0 or 1;
All rows (from left to right) and all columns (from top to bottom) are distinct.
In other words, the $2 \cdot �$ strings, that are obtained from the rows and columns of the matrix, are all distinct.

If multiple such matrices exist, print any. If no such matrix exists, print $- 1$ instead.

Input Format

The first line of input will contain a single integer $�$ , denoting the number of test cases.
Each test case consists of a single integer $�$ , the length of the row and column of matrix.

Output Format

For each test case, output $�$ lines, where each line contains a binary string of length $�$ , such that the matrix satisfies the given conditions.

If no such matrix exists, print $- 1$ .

Constraints

$1 \leq � \leq 100$
$2 \leq � \leq 1000$
The sum of $�$ over all test cases won't exceed $6000$ .

Sample 1:

Input

Output

Explanation:

Test case $1$ : The rows of the matrix are ${1010, 1110, 1001, 1011}$ . The columns of the matrix are ${1111, 0100, 1101, 0011}$ .
The set of all rows and columns are ${1010, 1110, 1001, 1011, 1111, 0100, 1101, 0011}$ . Note that all elements of the set containing all rows and columns are distinct. Thus, the matrix satisfies the conditions.

Test case $2$ : It can be proven that no binary matrix of size $2 \times 2$ is valid.

Solution :

Make a matrix like this

100000...00  
110000...00  
111000...00  
...  
111111...10  
111111...11

Now analyze which row and column are same.


#include <bits/stdc++.h>

using namespace std;

#define int            long long int
#define F              first
#define S              second
#define pb             push_back
#define si             set <int>
#define vi             vector <int>
#define pii            pair <int, int>
#define vpi            vector <pii>
#define vpp            vector <pair<int, pii>>
#define mii            map <int, int>
#define mpi            map <pii, int>
#define spi            set <pii>
#define endl           "\n"
#define sz(x)          ((int) x.size())
#define all(p)         p.begin(), p.end()
#define double         long double
#define que_max        priority_queue <int>
#define que_min        priority_queue <int, vi, greater<int>>
#define bug(...)       __f (#__VA_ARGS__, __VA_ARGS__)
#define print(a)       for(auto x : a) cout << x << " "; cout << endl
#define print1(a)      for(auto x : a) cout << x.F << " " << x.S << endl
#define print2(a,x,y)  for(int i = x; i < y; i++) cout<< a[i]<< " "; cout << endl

inline int power(int a, int b)
{
  int x = 1;
  while (b)
  {
    if (b & 1) x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}

template <typename Arg1>
void __f (const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << endl; }
template <typename Arg1, typename... Args>
void __f (const char* names, Arg1&& arg1, Args&&... args)
{
  const char* comma = strchr (names + 1, ',');
  cout.write (names, comma - names) << " : " << arg1 << " | "; __f (comma + 1, args...);
}

const int N = 200005;

void solve() {

int n;
cin>>n;

if(n<=2){
    cout<<-1<<endl;
    return;
}

vector<vi>ans;

for (int i = 0; i < n; i++)
{
    vi temp;
    for (int j = 0; j < n; j++)
    {
        if(j<=i)temp.push_back(1);
        else temp.pb(0);
    }
    ans.pb(temp);
}
ans[1][0]=0;

//print the answer
for (int i = 0; i < n; i++)
{
    for (int j = 0; j < n; j++)
    {
        cout<<ans[i][j];
    }
    cout<<endl;
}

}

int32_t main()
{
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);


  clock_t z = clock();

  int t = 1;
  cin >> t; 
  while (t--) solve();



  return 0;
}