http://www.geeksforgeeks.org/lowest-common-ancestor-binary-tree-set-1/
1 #include <iostream> 2 #include <vector> 3 #include <algorithm> 4 #include <queue> 5 #include <stack> 6 #include <string> 7 #include <fstream> 8 #include <map> 9 using namespace std; 10 11 struct node { 12 int data; 13 struct node *left, *right; 14 node() : data(0), left(NULL), right(NULL) { } 15 node(int d) : data(d), left(NULL), right(NULL) { } 16 }; 17 18 bool findpath(node *root, vector<int> &path, int n) { 19 if (!root) return false; 20 path.push_back(root->data); 21 if (root->data == n) return true; 22 if (root->left && findpath(root->left, path, n) || root->right && findpath(root->right, path, n)) return true; 23 path.pop_back(); 24 return false; 25 } 26 27 int LCA(node *root, int n1, int n2) { 28 if (!root) return -1; 29 vector<int> path1, path2; 30 if (!findpath(root, path1, n1) || !findpath(root, path2, n2)) return -1; 31 int i = 0; 32 for (; i < path1.size() && i < path2.size(); i++) { 33 if (path1[i] != path2[i]) break; 34 } 35 return path1[i-1]; 36 } 37 38 int main() { 39 node *root = new node(1); 40 root->left = new node(2); 41 root->right = new node(3); 42 root->left->left = new node(4); 43 root->left->right = new node(5); 44 root->right->left = new node(6); 45 root->right->right = new node(7); 46 cout << "LCA(4, 5) is " << LCA(root, 4, 5) << endl; 47 cout << "LCA(4, 6) is " << LCA(root, 4, 6) << endl; 48 cout << "LCA(3, 4) is " << LCA(root, 3, 4) << endl; 49 cout << "LCA(2, 4) is " << LCA(root, 2, 4) << endl; 50 return 0; 51 }
one traversal
1 #include <iostream> 2 #include <vector> 3 #include <algorithm> 4 #include <queue> 5 #include <stack> 6 #include <string> 7 #include <fstream> 8 #include <map> 9 using namespace std; 10 11 struct node { 12 int data; 13 struct node *left, *right; 14 node() : data(0), left(NULL), right(NULL) { } 15 node(int d) : data(d), left(NULL), right(NULL) { } 16 }; 17 18 node* LCA(node *root, int n1, int n2) { 19 if (!root) return NULL; 20 if (root->data == n1 || root->data == n2) return root; 21 node *l = LCA(root->left, n1, n2); 22 node *r = LCA(root->right, n1, n2); 23 if (l && r) return root; 24 return l? l : r; 25 } 26 27 int main() { 28 node *root = new node(1); 29 root->left = new node(2); 30 root->right = new node(3); 31 root->left->left = new node(4); 32 root->left->right = new node(5); 33 root->right->left = new node(6); 34 root->right->right = new node(7); 35 cout << "LCA(4, 5) is " << LCA(root, 4, 5)->data << endl; 36 cout << "LCA(4, 6) is " << LCA(root, 4, 6)->data << endl; 37 cout << "LCA(3, 4) is " << LCA(root, 3, 4)->data << endl; 38 cout << "LCA(2, 4) is " << LCA(root, 2, 4)->data << endl; 39 return 0; 40 }
上面这段代码有些问题，当n1或者n2不存在时应该回NULL，但是回的是n1或者n2
1 #include <iostream> 2 #include <vector> 3 #include <algorithm> 4 #include <queue> 5 #include <stack> 6 #include <string> 7 #include <fstream> 8 #include <map> 9 using namespace std; 10 11 struct node { 12 int data; 13 struct node *left, *right; 14 node() : data(0), left(NULL), right(NULL) { } 15 node(int d) : data(d), left(NULL), right(NULL) { } 16 }; 17 18 node* _LCA(node *root, int n1, int n2, bool &v1, bool &v2) { 19 if (!root) return NULL; 20 if (root->data == n1) { 21 v1 = true; 22 return root; 23 } 24 if (root->data == n2) { 25 v2 = true; 26 return root; 27 } 28 node *l = _LCA(root->left, n1, n2, v1, v2); 29 node *r = _LCA(root->right, n1, n2, v1, v2); 30 if (l && r) return root; 31 return l? l : r; 32 } 33 34 bool findnode(node *root, int k) { 35 if (!root) return false; 36 return (root->data == k || findnode(root->left, k) || findnode(root->right, k)); 37 } 38 39 node *LCA(node *root, int n1, int n2) { 40 bool v1 = false; 41 bool v2 = false; 42 node *lca = _LCA(root, n1, n2, v1, v2); 43 if (v1 && v2 || v1 && findnode(root, n2) || v2 && findnode(root, n1)) return lca; 44 return NULL; 45 } 46 47 int main() { 48 node *root = new node(1); 49 root->left = new node(2); 50 root->right = new node(3); 51 root->left->left = new node(4); 52 root->left->right = new node(5); 53 root->right->left = new node(6); 54 root->right->right = new node(7); 55 cout << "LCA(4, 5) is " << LCA(root, 4, 5)->data << endl; 56 cout << "LCA(4, 6) is " << LCA(root, 4, 6)->data << endl; 57 cout << "LCA(3, 4) is " << LCA(root, 3, 4)->data << endl; 58 cout << "LCA(2, 4) is " << LCA(root, 2, 4)->data << endl; 59 return 0; 60 }