Step-By-Step Directions From a Binary Tree Node to Another
<p>You are given the <code>root</code> of a <strong>binary tree</strong> with <code>n</code> nodes. Each node is uniquely assigned a value from <code>1</code> to <code>n</code>. You are also given an integer <code>startValue</code> representing the value of the start node <code>s</code>, and a different integer <code>destValue</code> representing the value of the destination node <code>t</code>.</p>

<p>Find the <strong>shortest path</strong> starting from node <code>s</code> and ending at node <code>t</code>. Generate step-by-step directions of such path as a string consisting of only the <strong>uppercase</strong> letters <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;U&#39;</code>. Each letter indicates a specific direction:</p>

<ul>
	<li><code>&#39;L&#39;</code> means to go from a node to its <strong>left child</strong> node.</li>
	<li><code>&#39;R&#39;</code> means to go from a node to its <strong>right child</strong> node.</li>
	<li><code>&#39;U&#39;</code> means to go from a node to its <strong>parent</strong> node.</li>
</ul>

<p>Return <em>the step-by-step directions of the <strong>shortest path</strong> from node </em><code>s</code><em> to node</em> <code>t</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2096.Step-By-Step%20Directions%20From%20a%20Binary%20Tree%20Node%20to%20Another/images/eg1.png" style="width: 214px; height: 163px;" />
<pre>
<strong>Input:</strong> root = [5,1,2,3,null,6,4], startValue = 3, destValue = 6
<strong>Output:</strong> &quot;UURL&quot;
<strong>Explanation:</strong> The shortest path is: 3 &rarr; 1 &rarr; 5 &rarr; 2 &rarr; 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2096.Step-By-Step%20Directions%20From%20a%20Binary%20Tree%20Node%20to%20Another/images/eg2.png" style="width: 74px; height: 102px;" />
<pre>
<strong>Input:</strong> root = [2,1], startValue = 2, destValue = 1
<strong>Output:</strong> &quot;L&quot;
<strong>Explanation:</strong> The shortest path is: 2 &rarr; 1.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is <code>n</code>.</li>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= Node.val &lt;= n</code></li>
	<li>All the values in the tree are <strong>unique</strong>.</li>
	<li><code>1 &lt;= startValue, destValue &lt;= n</code></li>
	<li><code>startValue != destValue</code></li>
</ul>
Tree; Depth-First Search; String; Binary Tree
/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func getDirections(root *TreeNode, startValue int, destValue int) string {
	var lca func(node *TreeNode, p, q int) *TreeNode
	lca = func(node *TreeNode, p, q int) *TreeNode {
		if node == nil || node.Val == p || node.Val == q {
			return node
		}
		left := lca(node.Left, p, q)
		right := lca(node.Right, p, q)
		if left != nil && right != nil {
			return node
		}
		if left != nil {
			return left
		}
		return right
	}
	var dfs func(node *TreeNode, x int, path *[]byte) bool
	dfs = func(node *TreeNode, x int, path *[]byte) bool {
		if node == nil {
			return false
		}
		if node.Val == x {
			return true
		}
		*path = append(*path, 'L')
		if dfs(node.Left, x, path) {
			return true
		}
		(*path)[len(*path)-1] = 'R'
		if dfs(node.Right, x, path) {
			return true
		}
		*path = (*path)[:len(*path)-1]
		return false
	}

	node := lca(root, startValue, destValue)
	pathToStart := []byte{}
	pathToDest := []byte{}
	dfs(node, startValue, &pathToStart)
	dfs(node, destValue, &pathToDest)
	return string(bytes.Repeat([]byte{'U'}, len(pathToStart))) + string(pathToDest)
}
