标签：des style blog ar color os 使用 sp on
一、二叉树简介
二叉树节点定义为：
1 struct TreeNode 2 { 3 int val; 4 TreeNode *left; 5 TreeNode *right; 6 TreeNode(int x) : val(x), left(NULL), right(NULL) {} 7 };
有时需要增加parent等其他信息。
二叉树的创建采用输入满二叉树数组的形式，例如 A = [1, -2, -3, 1, 3, 2, NIL, -1], 表示为：
1
-2 -3
1 3 2
-1
由数组A构建一颗二叉树：
1 TreeNode* create_node(int x) 2 { 3 if (x == NIL) /* means null */ 4 return NULL; 5 else 6 return new TreeNode(x); 7 } 8 9 TreeNode* btree_create(TreeNode *root, int va[], int n) 10 { 11 TreeNode *nt = NULL, *pt = NULL; 12 queue<TreeNode *> qtree; 13 int i = 1; 14 15 root = new TreeNode(va[0]); 16 qtree.push(root); 17 while (qtree.size() > 0) 18 { 19 pt = qtree.front(); 20 qtree.pop(); 21 if (pt == NULL) 22 continue; 23 /* create left node */ 24 if (i >= n) 25 break; 26 pt->left = create_node(va[i]); 27 i++; 28 qtree.push(pt->left); 29 /* create right node */ 30 if (i >= n) 31 break; 32 pt->right = create_node(va[i]); 33 i++; 34 qtree.push(pt->right); 35 } 36 return root; 37 }
二、二叉树基本操作
1、min/max depth
int minDepth(TreeNode *root) { if (root == NULL) return 0; int ml = minDepth(root->left); int mr = minDepth(root->right); if (ml == 0) /* the min depth should contain leaf, not only the root node. */ return (mr + 1); if (mr == 0) return (ml + 1); return min(ml, mr) + 1; } int maxDepth(TreeNode *root) { if (root == NULL) return 0; return max(maxDepth(root->left), maxDepth(root->right)) + 1; }
2、二叉树广度优先/深度优先遍历
2.1、BFS
二叉树的bfs记为层次遍历，使用队列做辅助，如下：
a)将root放入队列queue
b)queue不为空，取出队列元素node，并访问
c)node左右节点入队，重复b
1 vector<int> btree_bfs(TreeNode* root) 2 { 3 vector<int> tree_nodes; 4 queue<TreeNode*> qtree; 5 TreeNode* pt = root; 6 7 if (pt == NULL) 8 return tree_nodes; 9 10 qtree.push(pt); 11 while (!qtree.empty()) 12 { 13 pt = qtree.front(); 14 qtree.pop(); 15 tree_nodes.push_back(pt->val); 16 17 if (pt->left != NULL) 18 qtree.push(pt->left); 19 if (pt->right != NULL) 20 qtree.push(pt->right); 21 } 22 23 return tree_nodes; 24 }
2.2 DFS
二叉树深度优先遍历，不妨以左节点优先，即左子树存在则先查询左节点，如下：
a) 当前节点不为空，访问之。并将右节点压栈，继续访问左节点。
b)节点为空，则从栈中取出node，继续a，直至访问完。
1 vector<int> btree_dfs(TreeNode* root) 2 { 3 vector<int> tree_nodes; 4 stack<TreeNode*> stree; 5 TreeNode* pcur = root; 6 7 if (pcur == NULL) 8 return tree_nodes; 9 10 while (!stree.empty() || (pcur != NULL)) 11 { 12 if (pcur != NULL) 13 { 14 tree_nodes.push_back(pcur->val); // visit current 15 if (pcur->right != NULL) 16 stree.push(pcur->right); 17 pcur = pcur->left; 18 } 19 else 20 { 21 pcur = stree.top(); 22 stree.pop(); 23 } 24 } 25 26 return tree_nodes; 27 }
3、pre/in/post order traverse
这三种方式遍历二叉树，递归遍历比较简单，非递归遍历则需要借助queue/stack。
3.1、preorder
1 void preorder(TreeNode *root, vector <int> &ret) 2 { 3 if (root == NULL) 4 return; 5 ret.push_back(root->val); 6 preorder(root->left, ret); 7 preorder(root->right, ret); 8 }
preorder迭代形式和dfs完全一致。
3.2、inorder
void inorder(TreeNode *root, vector <int> &ret) { if (root == NULL) return; inorder(root->left, ret); ret.push_back(root->val); inorder(root->right, ret); }
迭代方式遍历:
a)当前节点不为空，则压栈并访问左子树。
b)否则，出栈并访问元素，再访问右子树，重复a。
1 vector<int> inorderTraversal(TreeNode *root) 2 { 3 vector<int> tree_nodes; 4 stack<TreeNode*> stree; 5 TreeNode* pcur = root; 6 7 while (!stree.empty() || (pcur != NULL)) 8 { 9 if (pcur != NULL) 10 { 11 stree.push(pcur); 12 pcur = pcur->left; //left 13 } 14 else 15 { 16 pcur = stree.top(); 17 stree.pop(); 18 tree_nodes.push_back(pcur->val); 19 pcur = pcur->right; //right 20 } 21 } 22 return tree_nodes; 23 }
3.3 post order
void inorder(TreeNode *root, vector <int> &ret) { if (root == NULL) return; inorder(root->left, ret); inorder(root->right, ret); ret.push_back(root->val); }
后序遍历非递归形式：
a)当前节点pcur不为空，节点入栈，访问左节点
b)否则,获取栈顶节点peek，如果peek->right不为空且不是last_vist_node, pcur变为peek->right
c)否则last_vist_node为栈顶元素，并访问last_vist_node，继续a)
1 vector<int> postorderTraversal(TreeNode *root) 2 { 3 vector<int> tree_nodes; 4 stack<TreeNode *> stree; 5 TreeNode *current = root, *last_visit_node = NULL, *peek_node = NULL; 6 7 while (!stree.empty() || (current != NULL)) 8 { 9 if (current != NULL) 10 { 11 stree.push(current); 12 current = current->left; 13 } 14 else 15 { 16 peek_node = stree.top(); 17 if ((peek_node->right != NULL) && (peek_node->right != last_visit_node)) 18 { // peek‘s right child exists and it‘s not come from last child 19 current = peek_node->right; 20 } 21 else 22 { 23 last_visit_node = peek_node; 24 stree.pop(); 25 tree_nodes.push_back(last_visit_node->val); 26 } 27 } 28 } 29 30 return tree_nodes; 31 }
标签：des style blog ar color os 使用 sp on
原文地址：http://www.cnblogs.com/ym65536/p/4115904.html
