Node Depths of BinaryTree

refer to : https://www.algoexpert.io/questions/Node%20Depths

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1. 问题描述。

二叉树的结点的深度（depth）定义为： 当前结点到二叉树的根的距离。 给定一个二叉树，求所有结点的深度的和。

2. 分析

每个结点的深度等于它的上一层结点的深度+ 1

3. recursive method。

# average case: balanced tree
# O(n) time | O(h) space, h is the height of the binary tree

import java.util.*;

class Program {

  public static int nodeDepths(BinaryTree root) {
    return helper(root, 0);
  }
    
  public static int helper(BinaryTree root, int depth){
    if(root == null){
       return 0;
    }
    return helper(root.left, depth + 1) + helper(root.right, depth+1) + depth;
 }

  static class BinaryTree {
    int value;
    BinaryTree left;
    BinaryTree right;

    public BinaryTree(int value) {
      this.value = value;
      left = null;
      right = null;
    }
  }
}

def nodeDepths(root,depth = 0 ):
    if root is None:
        return 0
    return depth + nodeDepths(root.left, depth + 1) + nodeDepths(root.right, depth + 1)
    


# This is the class of the input binary tree.
class BinaryTree:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

4. iterative method

# average case: balanced tree
# O(n) time | O(h) space, h is the height of the binary tree

import java.util.*;

class Program {

  public static int nodeDepths(BinaryTree root) {
    int sumOfDepth = 0;
        List<Level> stack = new ArrayList<Level>();
        stack.add(new Level(root,0));
        while(stack.size()>0){
            Level top = stack.remove(stack.size()-1);
            BinaryTree node = top.root;
            int depth = top.depth;
            if(node == null) continue;
            sumOfDepth += depth;
            stack.add(new Level(node.left, depth + 1));
            stack.add(new Level(node.right, depth + 1));
        }
        return sumOfDepth;
  }
    
    static class Level{
        public BinaryTree root;
        int depth;
        
        public Level(BinaryTree root, int depth){
            this.root = root;
            this.depth = depth;
        }
    }

  static class BinaryTree {
    int value;
    BinaryTree left;
    BinaryTree right;

    public BinaryTree(int value) {
      this.value = value;
      left = null;
      right = null;
    }
  }
}

def nodeDepths(root):
    sumOfDepths = 0
    stack = [{"node":root, "depth":0}]
    while len(stack)>0:
        nodeInfo = stack.pop()
        node, depth = nodeInfo["node"], nodeInfo["depth"]
        if node is None:
            continue
        sumOfDepths += depth
        stack.append({"node":node.left, "depth":depth+1})
        stack.append({"node":node.right, "depth":depth+1})
    return sumOfDepths


# This is the class of the input binary tree.
class BinaryTree:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None