From 681251203cf431e12e6e259548aa985196d0fce6 Mon Sep 17 00:00:00 2001
From: Sree Vidya <sreevidyapatamsetti@gmail.com>
Date: Wed, 24 Jul 2024 20:47:00 +0530
Subject: [PATCH] 1110-Delete Nodes And Return Forest.md

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+---
+id: delete-nodes-and-return-forest
+title: Delete Nodes And Return Forest
+sidebar_label: Delete Nodes And Return Forest
+tags: [Binary Tree, Depth-First Search, C++, Python, Java]
+description: Solve the problem of deleting nodes from a binary tree and returning the forest of remaining trees using depth-first search.
+---
+
+## Problem Statement
+
+### Problem Description
+
+Given the root of a binary tree, each node in the tree has a distinct value.
+
+After deleting all nodes with a value in `to_delete`, we are left with a forest (a disjoint union of trees).
+
+Return the roots of the trees in the remaining forest. You may return the result in any order.
+
+### Example
+
+**Example 1:**
+```
+Input: root = [1, 2, 3, 4, 5, 6, 7], to_delete = [3, 5]
+Output: [[1, 2, null, 4], [6], [7]]
+```
+
+### Constraints
+
+- The number of nodes in the given tree is at most 1000.
+- Each node has a distinct value between 1 and 1000.
+- `to_delete` contains distinct values between 1 and 1000.
+
+## Solution
+
+### Intuition
+
+The problem can be solved using a depth-first search (DFS) approach. The idea is to traverse the tree and, whenever a node needs to be deleted (i.e., its value is in the `to_delete` list), we handle its children by potentially adding them to the forest if they are not to be deleted. We maintain a set of nodes to be deleted for quick lookup and use a helper function to perform the DFS and manage the forest creation.
+
+### Time Complexity and Space Complexity Analysis
+
+- **Time Complexity**:
+  - The solution involves a single traversal of the tree, making the time complexity $O(n)$, where `n` is the number of nodes in the tree.
+
+- **Space Complexity**:
+  - The space complexity is $O(n)$ due to the recursive call stack and storage for the result list.
+
+### Code
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    vector<TreeNode*> delNodes(TreeNode* root, vector<int>& to_delete) {
+        unordered_set<int> to_delete_set(to_delete.begin(), to_delete.end());
+        vector<TreeNode*> forest;
+        if (!to_delete_set.count(root->val)) {
+            forest.push_back(root);
+        }
+        dfs(root, to_delete_set, forest);
+        return forest;
+    }
+    
+private:
+    TreeNode* dfs(TreeNode* node, unordered_set<int>& to_delete_set, vector<TreeNode*>& forest) {
+        if (!node) return nullptr;
+        node->left = dfs(node->left, to_delete_set, forest);
+        node->right = dfs(node->right, to_delete_set, forest);
+        if (to_delete_set.count(node->val)) {
+            if (node->left) forest.push_back(node->left);
+            if (node->right) forest.push_back(node->right);
+            return nullptr;
+        }
+        return node;
+    }
+};
+```
+#### Python
+```python
+class Solution:
+    def corpFlightBookings(self, bookings: List[List[int]], n: int) -> List[int]:
+        seats = [0] * (n + 1)
+        for booking in bookings:
+            first, last, seats_count = booking
+            seats[first - 1] += seats_count
+            if last < n:
+                seats[last] -= seats_count
+        for i in range(1, n):
+            seats[i] += seats[i - 1]
+        return seats[:-1]
+
+```
+#### Java
+```java
+class Solution {
+    public int[] corpFlightBookings(int[][] bookings, int n) {
+        int[] seats = new int[n + 1];
+        for (int[] booking : bookings) {
+            int first = booking[0];
+            int last = booking[1];
+            int seatsCount = booking[2];
+            seats[first - 1] += seatsCount;
+            if (last < n) {
+                seats[last] -= seatsCount;
+            }
+        }
+        for (int i = 1; i < n; i++) {
+            seats[i] += seats[i - 1];
+        }
+        return Arrays.copyOf(seats, n);
+    }
+}
+```