how backtracks work

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leetCode 50 (N-Queens):
The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

solution: each potentional position for a queen should satisfy no attach, then traverse the 2D grids to find out all good positions; it requires to find all possible combinations, so recursive call will be used also.

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 bool one_queen_visited(int** mat, int n, pair<int, int>& queen_idx)
 {
	 int row = queen_idx.first ;
	 int col = queen_idx.second; 
	 
	 for(int i=0; i<n; i++)
	 {
		for(int j=0; j<n; j++)
		{
			if(mat[row][j] == 0)
				mat[row][j] = 1;
			else if(mat[row][j] == 100)
				return false; 
		}
		
		if(mat[i][col] == 0)
			 mat[i][col] = 1;
		else if(mat[i][col] == 100)
			 return false; 
	 }
		
	 //for left leaning 
	 for(int i=row, j=col; i>=0 && j>=0; i--, j--)
	 {
			if(mat[i][j] == 0)
				mat[i][j] = 1; 
			else if(mat[i][j] == 100)
				return false; 
	 }
	 
	 for(int i=row, j=col; i<n && j<n; i++, j++)
	 {
			if(mat[i][j] == 0)
				mat[i][j] = 1; 
			else if(mat[i][j] == 100)
				return false; 
	 }	
	  
	 //for right leaning 
		//down
	  for(int i=row, j=col; i<n && j>=0; i++, j--)
	 {
			if(mat[i][j] == 0)
				mat[i][j] = 1; 
			else if(mat[i][j] == 100)
				return false; 
	 }
	  //up 
	 for(int i=row, j=col; i>=0 && j<n; i--, j++)
	 {
			if(mat[i][j] == 0)
				mat[i][j] = 1; 
			else if(mat[i][j] == 100)
				return false; 
	 }	
 
	 mat[row][col] = 100;  //queen location marked as 100
	 return true; 
 }
int backtrack = 0; 
	 
void sol(int** mat,  int n, int start_j=0)
 {
	 std::pair<int, int>  idx; 
	 vector<pair<int, int>>   queens; 
	 vector< vector<pair<int, int>> >  queens_v; 
	 if(start_j > n) return ;   //end of recursive 
	 for(int i=0; i<n; i++)
	 {
		 for(int j= ((i==0)? max(start_j, 0) : 0); j<n; j++)
		 {
			 idx =  std::make_pair(i, j); 
			 if(one_queen_visited(mat, n, idx)) // find a fit queen position, store into  queens 
			 {
				 queens.push_back(idx);
			 }
		 }
	 } 
	 	 
	 if(queens.size() == n)
	 {
		 queens_v.push_back(queens);
		int** mat_copy =  new int*[n] ;
		for(int i=0; i<n; i++)
		{
			mat_copy[i] = new  int[n](); 
		}	
	
		for(int i=0; i<queens.size(); i++)
		{
			idx =  queens[i];
			mat_copy[idx.first][idx.second] = 1 ;
		}
	
		for(int i=0; i<n; i++)
		{
			for(int j=0; j<n; j++)
				cout<< mat_copy[i][j] << ' ' ;
			cout << endl;
		}
	 }
		
	clean_mat(mat, n);
	sol(mat, n, ++backtrack); 			
 }

I did actually new memory in C++ as following:

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int** mat = (int**) new(n * sizeof(int*)); 
for(int i=0;  i<n; i++)
	mat[i] = (int*) new( n * sizeof(int));

which failed, then realized only malloc works in this way.