binary_tree_levels.js

let nodes = [] // list of nodes

const ROOT //binary tree with getChildren function implemented

getNodes(ROOT.getChildren()) // start recursion with no level_index so default is used

function getNodes(level, level_index = 0) { 
  level.forEach(node => { // loop threw nodes in the level
    if (Array.isArray(nodes[level_index])) { 
      nodes[level_index].push(node) // if node already in this level then add
    } else {
      nodes[level_index] = [node] // first node in this level so create array
    }
    // repeat with this nodes children and descend 1 level
    getNodes(node.getChildren(), level_index + 1)
  });
}

nodes[2].join(",") // return list of values from nodes on the 3rd level with comma delimiter 

Problem with this algorithm is it is all or nothing. We cannot ask it to find nodes only up to level 2. It must traverse the whole tree to return the levels.

https://en.wikipedia.org/wiki/Breadth-first_search is the correct implementation which allows you to exit early once you've reached the level you want.

The algorithm unintentionally implemented is known as https://en.wikipedia.org/wiki/Depth-first_search.

demo script using this algorithm can be found here

demo script implementing Breadth-first search algorithm can be seen here.