Q20_lowest_common_ancestor_of_a_binary_tree.cpp

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

// According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

// Example 1:
// Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
// Output: 3
// Explanation: The LCA of nodes 5 and 1 is 3.

// Example 2:
// Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
// Output: 5
// Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

// Example 3:
// Input: root = [1,2], p = 1, q = 2
// Output: 1

#include<bits/stdc++.h>
using namespace std;

struct TreeNode {
    int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode() : val(0), left(nullptr), right(nullptr) {}
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
    TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
};

// Very Important question

class Solution {
private:
    TreeNode* findLCA(TreeNode* root, TreeNode* p, TreeNode* q) {
        if(!root) return NULL;
        if(root->val == p->val || root->val == q->val) return root;

        TreeNode* lca1 = findLCA(root->left, p, q);
        TreeNode* lca2 = findLCA(root->right, p, q);

        if(lca1 && lca2) return root;
        if(lca1) return lca1;
        return lca2;
    }
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        return findLCA(root, p, q);
    }
};

// Time Complexity  : O(n) 
// Space Complexity : O(h)
// where h is the height of the tree