8888. Distance Between 2 Nodes in BST

Write a function that given a BST, it will return the distance (number of edges) between 2 nodes.

For example, given this tree

         5
        / 
       3   6
      /    
     2   4   7
    /         
   1           8

The distance between 1 and 4 is 3: [1 -> 2 -> 3 -> 4]

The distance between 1 and 8 is 6: [1 -> 2 -> 3 -> 5 -> 6 -> 7 -> 8]

public int bstDistance(TreeNode root, int node1, int node2) {
    if (root == null) return -1;
    TreeNode lca = lca(root, node1, node2);
    return getDistance(lca, node1) + getDistance(lca, node2);
}

private int getDistance(TreeNode src, int dest) {
    if (src.val == dest) return 0;
    TreeNode node = src.left;
    if (src.val < dest) {
        node = src.right;
    }
    return 1 + getDistance(node, dest);
}

private TreeNode lca(TreeNode root, int node1, int node2) {
    while (true) {
        if (root.val > node1 && root.val > node2) {
            root = root.left;
        } else if (root.val < node1 && root.val < node2) {
            root = root.right;
        } else {
            return root;
        }
    }
}

Java solution:
Time complexity: O(h), where h is the height of the tree.
Space complexity: O(h).

找到LCA---计算LCA到两个node的距离并相加

class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if(root == null || root == p || root == q) return root;
        
        
        TreeNode left = lowestCommonAncestor(root.left, p, q);//尝试在左边找p和q
        TreeNode right = lowestCommonAncestor(root.right, p, q);//尝试在右边找q和q
        
        if(left != null && right != null) return root;//如果p、q在左右两侧，说明root是LCA
        
        return left != null ? left : right;
        //如果p和q都在右边（left == null）就返回right，right会返回p和q中首先发现的，就一定是LCA了
        //如果p和q都在左边（right == null），和上面情况类似。
    }
}

lca的另一种查找方法

static int distanceFromRoot(Node root, int x)  
{  
    if (root.key == x)  
        return 0;  
    else if (root.key > x)  
        return 1 + distanceFromRoot(root.left, x);  
    return 1 + distanceFromRoot(root.right, x);  
}  

计算distance的另一种写法