Kth Ancestor of a Tree Node
<p>You are given a tree with <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> in the form of a parent array <code>parent</code> where <code>parent[i]</code> is the parent of <code>i<sup>th</sup></code> node. The root of the tree is node <code>0</code>. Find the <code>k<sup>th</sup></code> ancestor of a given node.</p>

<p>The <code>k<sup>th</sup></code> ancestor of a tree node is the <code>k<sup>th</sup></code> node in the path from that node to the root node.</p>

<p>Implement the <code>TreeAncestor</code> class:</p>

<ul>
	<li><code>TreeAncestor(int n, int[] parent)</code> Initializes the object with the number of nodes in the tree and the parent array.</li>
	<li><code>int getKthAncestor(int node, int k)</code> return the <code>k<sup>th</sup></code> ancestor of the given node <code>node</code>. If there is no such ancestor, return <code>-1</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1400-1499/1483.Kth%20Ancestor%20of%20a%20Tree%20Node/images/1528_ex1.png" style="width: 396px; height: 262px;" />
<pre>
<strong>Input</strong>
[&quot;TreeAncestor&quot;, &quot;getKthAncestor&quot;, &quot;getKthAncestor&quot;, &quot;getKthAncestor&quot;]
[[7, [-1, 0, 0, 1, 1, 2, 2]], [3, 1], [5, 2], [6, 3]]
<strong>Output</strong>
[null, 1, 0, -1]

<strong>Explanation</strong>
TreeAncestor treeAncestor = new TreeAncestor(7, [-1, 0, 0, 1, 1, 2, 2]);
treeAncestor.getKthAncestor(3, 1); // returns 1 which is the parent of 3
treeAncestor.getKthAncestor(5, 2); // returns 0 which is the grandparent of 5
treeAncestor.getKthAncestor(6, 3); // returns -1 because there is no such ancestor</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>parent.length == n</code></li>
	<li><code>parent[0] == -1</code></li>
	<li><code>0 &lt;= parent[i] &lt; n</code> for all <code>0 &lt; i &lt; n</code></li>
	<li><code>0 &lt;= node &lt; n</code></li>
	<li>There will be at most <code>5 * 10<sup>4</sup></code> queries.</li>
</ul>
Tree; Depth-First Search; Breadth-First Search; Design; Binary Search; Dynamic Programming
class TreeAncestor:
    def __init__(self, n: int, parent: List[int]):
        self.p = [[-1] * 18 for _ in range(n)]
        for i, fa in enumerate(parent):
            self.p[i][0] = fa
        for j in range(1, 18):
            for i in range(n):
                if self.p[i][j - 1] == -1:
                    continue
                self.p[i][j] = self.p[self.p[i][j - 1]][j - 1]

    def getKthAncestor(self, node: int, k: int) -> int:
        for i in range(17, -1, -1):
            if k >> i & 1:
                node = self.p[node][i]
                if node == -1:
                    break
        return node


# Your TreeAncestor object will be instantiated and called as such:
# obj = TreeAncestor(n, parent)
# param_1 = obj.getKthAncestor(node,k)
