LeetCode – Lowest Common Ancestor of a Binary Tree (Java)

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

Java Solution 1

```public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { if(root==null) return null;   if(root==p || root==q) return root;   TreeNode l = lowestCommonAncestor(root.left, p, q); TreeNode r = lowestCommonAncestor(root.right, p, q);   if(l!=null&&r!=null){ return root; }else if(l==null&&r==null){ return null; }else{ return l==null?r:l; } }```

To calculate time complexity, we know that f(n)=2*f(n-1)=2*2*f(n-2)=2^(logn), so time=O(n).

Java Solution 2 - deprecated

Please use the following diagram to walk through the solution.

Since each node is visited in the worst case, time complexity is O(n).

```class Entity{ public int count; public TreeNode node;   public Entity(int count, TreeNode node){ this.count = count; this.node = node; } }   public class Solution { public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { return lcaHelper(root, p, q).node; }   public Entity lcaHelper(TreeNode root, TreeNode p, TreeNode q){ if(root == null) return new Entity(0, null);   Entity left = lcaHelper(root.left, p, q); if(left.count==2) return left;   Entity right = lcaHelper(root.right,p,q); if(right.count==2) return right;   int numTotal = left.count + right.count; if(root== p || root == q){ numTotal++; }   return new Entity(numTotal, root); } }```
Category >> Algorithms
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• nidhi pitroda

Solution 1 doesn’t work for the case when one of the nodes in ancestor of the other. Correct Solution should be as follows :
` `

``` public class Solution { Boolean flag1,flag2; public int lca(TreeNode a, int val1, int val2) { flag1 = flag2 = false; if(a==null) return -1; if(a.left == null && a.right == null) { return (a.val == val1 && val1==val2) ? a.val : -1; } TreeNode temp = find_lca(a,val1,val2); if(flag1 && flag2) return temp.val; else return -1; } public TreeNode find_lca(TreeNode node,int val1,int val2) { TreeNode lca=null; if(node == null) return null; if(node.val == val1) { this.flag1 = true; lca = node; //return node; } if(node.val == val2) { this.flag2 = true; lca = node; // return node; } TreeNode l = find_lca(node.left,val1,val2); TreeNode r = find_lca(node.right,val1,val2); if((l != null && r!=null) || (lca != null)) return node; return l!=null ? l:r; } } ```

• Hooman
• Cherry Zhao

• Ameya Naik

Good catch.. Alternatively, we could have:
``` numTotal += (root == p ? 1 : 0) + (root == q ? 1 : 0); ```

• w4nderlust

Solution 1 doesn’t work in the case of p == q. Should replace

if(root== p || root == q){
numTotal++;
}

with

if (root == p) {
numTotal ++;
}
if (root == q) {
numTotal ++;
}

or add a check at the beginning.

• ryanlr

Tried on leetcode online judge, and it didn’t pass.
``` public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { return findLCA(root, p.val, q.val); } ```

• Ankit Shah

The above code doesn’t seem to work if Btree happens to be BST. Also here is the more simpler one.

``` public class LcaBinaryTree { TreeNode findLCA(TreeNode root, int n1, int n2) { // Base case if (root == null) return null; // If either n1 or n2 matches with root's key, report // the presence by returning root (Note that if a key is // ancestor of other, then the ancestor key becomes LCA if (root.data == n1 || root.data == n2) return root; // Look for keys in left and right subtrees TreeNode left_lca = findLCA(root.left, n1, n2); TreeNode right_lca = findLCA(root.right, n1, n2); // If both of the above calls return Non-NULL, then one key // is present in once subtree and other is present in other, // So this node is the LCA if (left_lca != null && right_lca != null) return root; // Otherwise check if left subtree or right subtree is LCA return (left_lca != null) ? left_lca : right_lca; } public static void main(String[] args) { TreeNode root = new TreeNode(1); root.left = new TreeNode(2); root.right = new TreeNode(3); root.left.left = new TreeNode(4); root.left.right = new TreeNode(5); root.right.left = new TreeNode(6); root.right.right = new TreeNode(7); // BTreePrinter.printNode(root); LcaBinaryTree lca = new LcaBinaryTree(); System.out.println("lca(6 , 7): " + lca.findLCA(root, 6, 7).data); System.out.println("lca(4 , 5): " + lca.findLCA(root, 4, 5).data); System.out.println("lca(2 , 3): " + lca.findLCA(root, 2, 3).data); } } ```

Output of the program:
``` 1 / / 2 3 / / 4 5 6 7 ```

``` ```

```lca(6 , 7): 3 lca(4 , 5): 2 lca(2 , 3): 1 ```

• Sirius

Could you please explain the code and its complexity? Thanks!