二叉树的字符串表示形式，找到离树根最远的位置

Question

This is an algorithm that I was given a while ago for a test and I couldn't figure it out. Any ideas?

You are given a recursive notation of a binary tree: each node of a tree is represented as a set of three elements:

1. value of the node
2. left subtree
3. right subtree

So, a tree can be written as (value left_subtree right_subtree) .

If a node doesn't exist then it is represented as an empty set: () .

Your task is to obtain a list of nodes, that are the most distant from the tree root, in the order from left to right.

In the notation of a node its value and subtrees are separated by exactly one space character.

Example:

//             2
//            / \
//           /   \
//          /     \
//         /       \
//        /         \
//       7           5
//      / \           \
//     /   \           \
//    2     6           9
//         / \         /
//        /   \       /
//       5     11    4

tree = "(2 (7 (2 () ()) (6 (5 () ()) (11 () ()))) (5 () (9 (4 () ()) ())))"
treeBottom(tree) // Desired output: [5, 11, 4].

Answer 1

Probably not most sophisticated solution, but it works..

 var tree = "(2 (7 (2 () ()) (6 (5 () ()) (11 () ()))) (5 () (9 (4 () ()) ())))"; var level = 0; var rootLeafs = [] var leaf = -1; var i; var parseToken = { "(": enterLevel, ")": leaveLevel, " ": separate, } function isValidTreeElement() { applyFn = parseToken[tree[i]]||parseNumber; return applyFn() } function enterLevel() { if (i > 0 && tree[i-1] != " ") { alert("Nodes must be separated by space"); return false; } level++; // entering new root leaf if (level == 2) { leaf++; rootLeafs[leaf] = []; } return true; } function leaveLevel() { level--; return true; } function separate() { if (i > 0 && tree[i-1] == " ") { alert("Multiple spaces in row"); return false; } return true; } function parseNumber() { var advance = tree.substring(i).indexOf(" "); if (advance < 1) { alert("Number must followed by space"); return false; } var num = Number(tree.substring(i,i+advance)); if (isNaN(num)) { alert("Expected number, given: " + tree.substring(i,i+advance)); return false; } i += advance - 1; // move index to last char of number // add value to current leaf level if (level > 1) { try { rootLeafs[leaf][level-2].push(num); } catch(e) { rootLeafs[leaf][level-2] = [num]; } } return true; } function walk() { for (i = 0; i < tree.length; i++) { if (!isValidTreeElement()) { return; } } // get last level from each root leaf var results = rootLeafs.reduce(function(a, b) { return a.concat(b.slice(-1)[0]); }, []); console.log('Result: ' + results); } walk();