2096. Step-By-Step Directions From a Binary Tree Node to Another

Description

You are given the root of a binary tree with n nodes. Each node is uniquely assigned a value from 1 to n. You are also given an integer startValue representing the value of the start node s, and a different integer destValue representing the value of the destination node t.

Find the shortest path starting from node s and ending at node t. Generate step-by-step directions of such path as a string consisting of only the uppercase letters 'L', 'R', and 'U'. Each letter indicates a specific direction:

• 'L' means to go from a node to its left child node.
• 'R' means to go from a node to its right child node.
• 'U' means to go from a node to its parent node.

Return the step-by-step directions of the shortest path from node s to node t.

 

Example 1:

Input: root = [5,1,2,3,null,6,4], startValue = 3, destValue = 6
Output: "UURL"
Explanation: The shortest path is: 3 → 1 → 5 → 2 → 6.

Example 2:

Input: root = [2,1], startValue = 2, destValue = 1
Output: "L"
Explanation: The shortest path is: 2 → 1.

 

Constraints:

• The number of nodes in the tree is n.
• 2 <= n <= 105
• 1 <= Node.val <= n
• All the values in the tree are unique.
• 1 <= startValue, destValue <= n
• startValue != destValue

 

Solutions

Solution: Depth-First Search

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} startValue
 * @param {number} destValue
 * @return {string}
 */
const getDirections = function (root, startValue, destValue) {
  const getStepPath = (node, target, path = '') => {
    if (!node) return '';
    if (node.val === target) return path;

    const { left, right } = node;
    const leftPath = getStepPath(left, target, `${path}L`);

    if (leftPath) return leftPath;
    return getStepPath(right, target, `${path}R`);
  };

  const startPath = getStepPath(root, startValue);
  const endPath = getStepPath(root, destValue);
  let start = 0;

  while (startPath[start] === endPath[start]) start += 1;

  return 'U'.repeat(startPath.length - start) + endPath.slice(start);
};