/*
* Given an ancestor matrix mat[n][n].
* Construct a Binary Tree from given ancestor matrix where all its values of nodes are from 0 to n-1.
*
* Complexity: O(n*log(n))
*/
public static Ancestor_Matrix_Node BuildTree(int[,] matrix)
{
int n = matrix.GetUpperBound(0) + 1;
Ancestor_Matrix_Node[] nodes = new Ancestor_Matrix_Node[n];
bool[] hasParent = new bool[n];
Tuple <int, int>[] map = new Tuple <int, int> [n];
for (int i = 0; i < n; i++)
{
int sum = 0;
for (int j = 0; j < n; j++)
{
if (matrix[i, j] == 1)
{
sum++;
}
}
map[i] = new Tuple <int, int>(i, sum);
}
Array.Sort(map, (a, b) => { return(a.Item2.CompareTo(b.Item2)); });
Ancestor_Matrix_Node root = null;
foreach (Tuple <int, int> item in map)
{
nodes[item.Item1] = new Ancestor_Matrix_Node(item.Item1);
root = nodes[item.Item1];
if (item.Item2 > 0)
{
for (int j = 0; j < n; j++)
{
if (!hasParent[j] && matrix[item.Item1, j] == 1)
{
if (root.Left == null)
{
root.Left = nodes[j];
}
else
{
root.Right = nodes[j];
}
hasParent[j] = true;
}
}
}
}
return(root);
}
/*
* Given a Binary Tree where all values are from 0 to n-1. Construct an ancestor matrix mat[n][n].
*
* Complexity: O(n).
*/
public static int[,] BuildMatrix(Ancestor_Matrix_Node root)
{
int i = Ancestor_Matrix_Node.CountNodes(root);
int[,] matrix = new int[i, i];
int[] vector = new int[i];
BuildMatrix(root, matrix, vector);
return(matrix);
}
public static int CountNodes(Ancestor_Matrix_Node root)
{
if (root == null)
{
return(0);
}
int i = 1;
i += CountNodes(root.Left);
i += CountNodes(root.Right);
return(i);
}
private static void BuildMatrix(Ancestor_Matrix_Node root, int[,] matrix, int[] vector)
{
if (root == null)
{
return;
}
for (int i = 0; i < vector.Length; i++)
{
if (vector[i] == 1)
{
matrix[i, root.ID] = 1;
}
}
vector[root.ID] = 1;
BuildMatrix(root.Left, matrix, vector);
BuildMatrix(root.Right, matrix, vector);
vector[root.ID] = 0;
return;
}