[Algorithm] Given the root to a binary tree, return the deepest node

By given a binary tree, and a root node, find the deepest node of this tree.

We have way to create node:

function createNode(val, left = null, right = null) {
  return {
    val,
    left,
    addLeft(leftKey) {
      return (this.left = leftKey ? createNode(leftKey) : null);
    },
    right,
    addRight(rightKey) {
      return (this.right = rightKey ? createNode(rightKey) : null);
    }
  };
}

Way to create tree:

function createBT(rootKey) {
  const root = createNode(rootKey);
  return {
    root,
    deepest(node) {
      // code goes here
    }
  };
}

Way to construct tree:

const tree = createBT("root");
const root = tree.root;
const left = root.addLeft("left");
root.addRight("right");

const leftleft = left.addLeft("left.left");
const leftleftleft = leftleft.addLeft("left.left.left");
const leftright = left.addRight("left.right");
leftright.addLeft("left.right.left");

The way to solve the problem is recursive calling the 'deepest' function for node's left and right leaf, until we reach the base case, which is the node that doesn't contian any left or right leaf.

function createNode(val, left = null, right = null) {
  return {
    val,
    left,
    addLeft(leftKey) {
      return (this.left = leftKey ? createNode(leftKey) : null);
    },
    right,
    addRight(rightKey) {
      return (this.right = rightKey ? createNode(rightKey) : null);
    }
  };
}

function createBT(rootKey) {
  const root = createNode(rootKey);
  return {
    root,
    deepest(node) {
      function helper(node, depth) {
        if (node && !node.left && !node.right) {
          return {
            depth,
            node
          };
        }

        if (node.left) {
          return helper(node.left, depth + 1);
        } else if (node.right) {
          return helper(node.right, depth + 1);
        }
      }

      const { depth: ld, node: ln } = helper(root.left, 1);
      const { depth: rd, node: rn } = helper(root.right, 1);

      const max = Math.max(ld, rd);
      if (max === ld) {
        return { depth: ld, node: ln.val };
      } else {
        return { depth: rd, node: rn.val };
      }
    }
  };
}

const tree = createBT("root");
const root = tree.root;
const left = root.addLeft("left");
root.addRight("right");

const leftleft = left.addLeft("left.left");
const leftleftleft = leftleft.addLeft("left.left.left");
const leftright = left.addRight("left.right");
leftright.addLeft("left.right.left");

console.log(tree.deepest(root)); // {depth: 3, node: "left.left.left"}