feat: solve No.2096

Author: BaffinLee

2001-2100/2096. Step-By-Step Directions From a Binary Tree Node to Another.md

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+# 2096. Step-By-Step Directions From a Binary Tree Node to Another
+
+- Difficulty: Medium.
+- Related Topics: String, Tree, Depth-First Search, Binary Tree.
+- Similar Questions: Path Sum II, Lowest Common Ancestor of a Binary Tree, Binary Tree Paths, Find Distance in a Binary Tree.
+
+## Problem
+
+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:
+
+![](https://assets.leetcode.com/uploads/2021/11/15/eg1.png)
+
+```
+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:
+
+![](https://assets.leetcode.com/uploads/2021/11/15/eg2.png)
+
+```
+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`
+
+
+
+## Solution
+
+```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}
+ */
+var getDirections = function(root, startValue, destValue) {
+    var findLCA = function(node) {
+        if (!node) return false;
+        if (node.val === startValue || node.val === destValue) {
+            return node;
+        }
+        var left = findLCA(node.left);
+        var right = findLCA(node.right);
+        return (left && right) ? node : (left || right || false);
+    };
+    var findStart = function(node) {
+        if (!node) return null;
+        if (node.val === startValue) return '';
+
+        var left = findStart(node.left);
+        if (left !== null) return left + 'U';
+
+        var right = findStart(node.right);
+        if (right !== null) return right + 'U';
+
+        return null;
+    };
+    var findDest = function(node) {
+        if (!node) return null;
+        if (node.val === destValue) return '';
+
+        var left = findDest(node.left);
+        if (left !== null) return 'L' + left;
+
+        var right = findDest(node.right);
+        if (right !== null) return 'R' + right;
+
+        return null;
+    };
+    var LCA = findLCA(root);
+    var startPath = findStart(LCA);
+    var destPath = findDest(LCA);
+    return startPath + destPath;
+};
+```
+
+**Explain:**
+
+nope.
+
+**Complexity:**
+
+* Time complexity : O(n).
+* Space complexity : O(n).