Best Solution completely intuition based: C++, Java and Python Solutions
Intuition\nTo solve this problem, we need to determine the height of the binary tree after a node and its subtree are removed. When a node is removed, there are
# Intuition\nTo solve this problem, we need to determine the height of the binary tree after a node and its subtree are removed. When a node is removed, there are two possibilities:\n1. **The node is not the tallest in its level:** If the removed node does not contribute to the current maximum height at its level, then the height remains unchanged.\n2. **The node is the tallest in its level:** If the removed node contributes to the maximum height at its level, we need to update the height using the second-tallest node\'s height at the same level.\n\n# Approach\n1. **Tree Traversal for Height Calculation:**\n   - Perform a depth-first search (DFS) to compute the height of each node and store this information in a `level` array, where each entry holds the level and height of the node.\n   - While traversing, update the maximum and second-maximum heights at each level using a `maxHeights` array.\n\n2. **Processing Queries:**\n   - For each query, check the node\u2019s height and its level.\n   - If the queried node determines the current maximum height, use the second-highest height at that level as the new maximum height after removal; otherwise, use the original maximum.\n   - Compute the tree height based on the updated maximum height at the level.\n\n# Complexity\n- Time complexity: $$O(n + q)$$, where $$n$$ is the number of nodes in the tree, and $$q$$ is the number of queries. We traverse the tree once for height calculation and then process each query.\n- Space complexity: $$O(n)$$ for storing the level and height information.\n\n# Code\n\n## C++\n\n```cpp []\nclass Solution {\n    int getHeight(TreeNode* root, int lev, vector<pair<int, int>>& level, vector<pair<int, int>>& maxHeights) {\n        if (root == nullptr) return 0;\n        int left = getHeight(root->left, lev + 1, level, maxHeights);\n        int right = getHeight(root->right, lev + 1, level, maxHeights);\n        int currentHeight = max(left, right) + 1;\n        \n        level[root->val] = {lev, currentHeight};\n        \n        auto& [firstMax, secondMax] = maxHeights[lev];\n        if (currentHeight > firstMax) {\n            secondMax = firstMax;\n            firstMax = currentHeight;\n        } else if (currentHeight >= secondMax) {\n            secondMax = currentHeight;\n        }\n        \n        return currentHeight;\n    }\n\npublic:\n    Solution() {\n        std::ios_base::sync_with_stdio(false);\n        std::cin.tie(NULL);\n        std::cout.tie(NULL);\n    }\n\n    vector<int> treeQueries(TreeNode* root, vector<int>& queries) {\n        const int MAX_LEVEL = 1e5 + 7;\n        vector<pair<int, int>> level(MAX_LEVEL);\n        vector<pair<int, int>> maxHeights(MAX_LEVEL, {0, 0});\n        int maxH = getHeight(root, 0, level, maxHeights);\n        vector<int> ans;\n        for (auto& it : queries) {\n            int nodeHeight = level[it].second;\n            int i = level[it].first;\n            auto& [firstMax, secondMax] = maxHeights[i];\n            int maxOtherHeight = (nodeHeight == firstMax && firstMax == secondMax) ? firstMax : \n                                    (nodeHeight == firstMax ? secondMax : firstMax);\n            \n            ans.push_back(i + maxOtherHeight - 1);\n        }\n        \n        return ans;\n    }\n};\n```\n## Java\n\n```java []\n\nclass Solution {\n    private int getHeight(TreeNode root, int lev, Map<Integer, int[]> level, Map<Integer, int[]> maxHeights) {\n        if (root == null) return 0;\n        int left = getHeight(root.left, lev + 1, level, maxHeights);\n        int right = getHeight(root.right, lev + 1, level, maxHeights);\n        int currentHeight = Math.max(left, right) + 1;\n        \n        level.put(root.val, new int[]{lev, currentHeight});\n        \n        int[] heights = maxHeights.getOrDefault(lev, new int[]{0, 0});\n        int firstMax = heights[0], secondMax = heights[1];\n        if (currentHeight > firstMax) {\n            secondMax = firstMax;\n            firstMax = currentHeight;\n        } else if (currentHeight >= secondMax) {\n            secondMax = currentHeight;\n        }\n        \n        maxHeights.put(lev, new int[]{firstMax, secondMax});\n        return currentHeight;\n    }\n\n    public int[] treeQueries(TreeNode root, int[] queries) {\n        final int MAX_LEVEL = 100007;\n        Map<Integer, int[]> level = new HashMap<>();\n        Map<Integer, int[]> maxHeights = new HashMap<>();\n        getHeight(root, 0, level, maxHeights);\n        \n        int[] ans = new int[queries.length];\n        for (int i = 0; i < queries.length; i++) {\n            int nodeHeight = level.get(queries[i])[1];\n            int lev = level.get(queries[i])[0];\n            int[] heights = maxHeights.get(lev);\n            int firstMax = heights[0], secondMax = heights[1];\n            int maxOtherHeight = nodeHeight == firstMax ? secondMax : firstMax;\n            \n            ans[i] = lev + maxOtherHeight - 1;\n        }\n        \n        return ans;\n    }\n}\n\n```\n\n## Python\n\n```python []\nclass Solution:\n    def __init__(self):\n        import sys\n        sys.setrecursionlimit(10**6)\n\n    def getHeight(self, root, lev, level, maxHeights):\n        if root is None:\n            return 0\n        left = self.getHeight(root.left, lev + 1, level, maxHeights)\n        right = self.getHeight(root.right, lev + 1, level, maxHeights)\n        currentHeight = max(left, right) + 1\n        \n        level[root.val] = (lev, currentHeight)\n        \n        firstMax, secondMax = maxHeights[lev]\n        if currentHeight > firstMax:\n            secondMax = firstMax\n            firstMax = currentHeight\n        elif currentHeight >= secondMax:\n            secondMax = currentHeight\n        \n        maxHeights[lev] = (firstMax, secondMax)\n        return currentHeight\n\n    def treeQueries(self, root, queries):\n        MAX_LEVEL = 10**5 + 7\n        level = [None] * MAX_LEVEL\n        maxHeights = [(0, 0)] * MAX_LEVEL\n        self.getHeight(root, 0, level, maxHeights)\n        \n        ans = []\n        for node in queries:\n            nodeHeight = level[node][1]\n            i = level[node][0]\n            firstMax, secondMax = maxHeights[i]\n            maxOtherHeight = firstMax if nodeHeight != firstMax else secondMax\n            ans.append(i + maxOtherHeight - 1)\n        \n        return ans\n\n```\n
['C++']