To class Tree, add the following methods:

$1-$ nodesInLevel$($int $x)$: it returns number of nodes in a specific level $x.$

for example in this tree, nodesInLevel$(2)$ is $4($assuming that root is in

level $0).$ Hint: this method should call a recursive method.

$2-$ ancestors$($ int k$)$: it prints all ancestor of the node with key $k$ starting

by the parent toward the root.

For example ancestors$(31),$ it prints: $43,19,11.$

Hint: you need to use a stack.

$3-$ printByLevel$()$ which prints all nodes in the tree level by level, it prints all nodes in a specific level

before moving to the nodes at the next depth level. For example this tree should be printed as

follows:

$11,6,19,4,8,17,43,5,10,31,49$

Hint: you need to use a queue.