Q4.7 Find commen ancestor

Q: Design an algorithm and write code to find the first common ancestor of two nodes in a binary tree. Avoid storing additional nodes in a data structure. NOTE: This is not necessarily a binary search tree.

A:不允许额外的空间开销，那么就需要从根开始往下寻找。

因为根节点肯定是其共同的祖先，然后不断往下找，直到找到最后一个两个节点的共同祖先。

#include <iostream>
#include <vector>
using namespace std;const int maxn = 100;struct TreeNode {int val;TreeNode *left;TreeNode *right;TreeNode *parent;TreeNode () {}TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};//初始化数据
TreeNode *dfs(vector<int> &num, int start, int end) {if (start == end) {return NULL;}int mid = start + (end-start)/2;TreeNode *root = new TreeNode(num[mid]);root->left = dfs(num, start, mid);root->right = dfs(num, mid+1, end);return root;
}TreeNode *sortedArrayToBST(vector<int> &num) {const int n = num.size();if (n == 0) {return NULL;}return dfs(num,0,n);
}bool isAncestor(TreeNode *root, TreeNode *dst) {if (!root) {return false;}if (root == dst) {return true;}return isAncestor(root->left, dst) || isAncestor(root->right, dst);
}TreeNode* commonAncestorHelper(TreeNode *root, TreeNode *one, TreeNode *two) {if (!root) {return NULL;}if (root == one || root == two) {return root;}bool is_one_on_left = isAncestor(root->left, one);bool is_two_on_left = isAncestor(root->left, two);if (is_one_on_left != is_two_on_left) {return root;}TreeNode *child = is_one_on_left?root->left:root->right;return commonAncestorHelper(child, one, two);
}TreeNode* commenAncestor(TreeNode *root, TreeNode *one, TreeNode *two) {if (!isAncestor(root, one) || !isAncestor(root, two)) {return NULL;}return commonAncestorHelper(root, one, two);
}TreeNode* search(TreeNode* head, int x){if(head == NULL) return NULL;else if(x == head->val) return head;else if(x <= head->val) search(head->left, x);else search(head->right, x);
}int main(){vector<int> a;for (int i = 1; i < 10; i++) {a.push_back(i);}TreeNode *head = sortedArrayToBST(a);TreeNode *n1 = search(head, 2);TreeNode *n2 = search(head, 4);cout<<n1->val<<" "<<n2->val<<endl;TreeNode *ans = commenAncestor(head, n1, n2);cout<<ans->val<<endl;return 0;
}

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