需要帮助来了解二叉树的最大深度[Leetcode]

Question

For the following:

var maxDepth = function(root) {
if(!root){
  return 0
}
var leftMax=maxDepth(root.left)
var rightMax=maxDepth(root.right)
return Math.max(leftMax, rightMax)+1};

I don't understand how the variables leftMax and rightMax work in conjunction with Math.max. How is the variables numbers?

For example, lets say the tree looks like this:

     a
   /   
  b
 /
c

So first, it would reach here: var leftMax=maxDepth(root.left), root.left being b. What is leftMax at this point? Is it some number and where is the number from?

Thanks

Answer 1

Maximum depth of a binary tree can be presented as a maximum depth of its subtrees from left or right child plus 1 for the current level. Let the depth of a subtree be 0 if it's empty (no left or right child).

The depth of those subtrees, in turn, can be calculated in the same way.

var leftMax=maxDepth(root.left)
var rightMax=maxDepth(root.right)

So the algorithm divides subtrees until a leaf is reached. Leaves have no children (equivalent to "each child has zero depth"), so its maximum depth of subtrees is zero.

if(!root){  // no child for the parent node
  return 0
}

Now let's add 1 for the current level and get back to the previous call. The same operations for both left and right subtrees are performed, so the algorithm knows about the depth of right and left subtrees at the end of each iteration:

var leftMax=maxDepth(root.left)
var rightMax=maxDepth(root.right)

This means the current tree has a depth of max(subtrees depth) plus 1 for the current level:

return Math.max(leftMax, rightMax)+1};

In your example, the algorithm goes as deep as it can on the left children first and returns to visit righter ones. This strategy is called Depth-first search