Minimum Absolute Difference in a Binary Search Tree

To compute the minimum absolute difference between values in a binary search tree, leverage the property that an in-order traversal yields a sorted sequence. By tracking the previous node during traversal, differences can be calculatde efficiently.

class Solution {
    TreeNode previous = null;
    int minDiff = Integer.MAX_VALUE;

    public int getMinDiff(TreeNode node) {
        if (node == null) return 0;

        getMinDiff(node.left);
        if (previous != null) {
            minDiff = Math.min(minDiff, node.val - previous.val);
        }
        previous = node;
        getMinDiff(node.right);

        return minDiff;
    }
}

Finding Modes in a Binary Search Tree

Approach 1: Using a Map

Traevrse the tree to collect values, then use a frequency map to identify the most common values.

class Solution {
    public int[] findModes(TreeNode root) {
        List<Integer> values = new ArrayList<>();
        inorderCollect(root, values);
        Map<Integer, Integer> freqMap = new HashMap<>();
        for (int val : values) {
            freqMap.put(val, freqMap.getOrDefault(val, 0) + 1);
        }
        int maxFreq = 0;
        List<Integer> result = new ArrayList<>();
        for (Map.Entry<Integer, Integer> entry : freqMap.entrySet()) {
            if (entry.getValue() > maxFreq) {
                maxFreq = entry.getValue();
                result.clear();
                result.add(entry.getKey());
            } else if (entry.getValue() == maxFreq) {
                result.add(entry.getKey());
            }
        }
        return result.stream().mapToInt(i -> i).toArray();
    }

    private void inorderCollect(TreeNode node, List<Integer> list) {
        if (node == null) return;
        inorderCollect(node.left, list);
        list.add(node.val);
        inorderCollect(node.right, list);
    }
}

Approach 2: In-Place Traversal

Perform an in-order traversal while maintaining counts to find modes with out extra storage for all values.

class Solution {
    TreeNode prev = null;
    int currentCount = 0;
    int maxCount = 0;
    List<Integer> modes = new ArrayList<>();

    public int[] findModes(TreeNode root) {
        traverse(root);
        int[] result = new int[modes.size()];
        for (int i = 0; i < modes.size(); i++) {
            result[i] = modes.get(i);
        }
        return result;
    }

    private void traverse(TreeNode node) {
        if (node == null) return;
        traverse(node.left);
        if (prev == null || prev.val != node.val) {
            currentCount = 1;
        } else {
            currentCount++;
        }
        if (currentCount > maxCount) {
            maxCount = currentCount;
            modes.clear();
            modes.add(node.val);
        } else if (currentCount == maxCount) {
            modes.add(node.val);
        }
        prev = node;
        traverse(node.right);
    }
}

Lowest Common Ancestor in a Binary Tree

To find the lowest common ancestor of two nodes in a binary tree, use a post-order traversal to search from the bottom up. The algorithm recursively checks each node to determine if it contains the target nodes in its subtrees.

class Solution {
    public TreeNode findLCA(TreeNode node, TreeNode p, TreeNode q) {
        if (node == null) return null;
        if (node == p || node == q) return node;

        TreeNode leftResult = findLCA(node.left, p, q);
        TreeNode rightResult = findLCA(node.right, p, q);

        if (leftResult != null && rightResult != null) {
            return node;
        }
        if (leftResult != null) return leftResult;
        if (rightResult != null) return rightResult;
        return null;
    }
}