Lowest Common Ancestor III

ID: 578; medium

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Solution 1 (Java)

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */


public class Solution {

    private class Result {
        public boolean hasA, hasB;
        public Result(boolean hasA, boolean hasB) {
            this.hasA = hasA;
            this.hasB = hasB;
        }
    }

    private TreeNode res = null;

    /*
     * @param root: The root of the binary tree.
     * @param A: A TreeNode
     * @param B: A TreeNode
     * @return: Return the LCA of the two nodes.
     */
    public TreeNode lowestCommonAncestor3(TreeNode root, TreeNode A, TreeNode B) {
        dfs(root, A, B);
        return res;
    }

    private Result dfs(TreeNode root, TreeNode A, TreeNode B) {
        if (root == null)
            return new Result(false, false);
        
        Result left = dfs(root.left, A, B);
        Result right = dfs(root.right, A, B);

        boolean a = left.hasA || right.hasA || root == A;
        boolean b = left.hasB || right.hasB || root == B;

        if (a && b && res == null)
            res = root;

        return new Result(a, b);
    }
}

Notes

• We use the Result class to keep track of the status of A and B in the tree.

• If a and b are both true, which means the current root is already is LCA, then we set res only when it is null. This if statement is true for the LCA and its ancestors, but we are guaranteed to have the LCA. The reason is that we are doing a DFS and the LCA appears first. Once we set res to the LCA, we do not update it and do not care about its ancestors.