Binary Tree Postorder Traversal

描述

Given a binary tree, return the postorder traversal of its nodes' values.

For example:Given binary tree {1,#,2,3},

  1.  1
  2.   \
  3.    2
  4.   /
  5.  3

return [3,2,1].

Note: Recursive solution is trivial, could you do it iteratively?

分析

用栈或者Morris遍历。

栈

  1. // Binary Tree Postorder Traversal
  2. // 使用栈，时间复杂度O(n)，空间复杂度O(n)
  3. class Solution {
  4. public:
  5.     vector<int> postorderTraversal(TreeNode *root) {
  6.         vector<int> result;
  7.         stack<const TreeNode *> s;
  8.         /* p，正在访问的结点，q，刚刚访问过的结点*/
  9.         const TreeNode *p = root, *q = nullptr;
  11.         do {
  12.             while (p != nullptr) { /* 往左下走*/
  13.                 s.push(p);
  14.                 p = p->left;
  15.             }
  16.             q = nullptr;
  17.             while (!s.empty()) {
  18.                 p = s.top();
  19.                 s.pop();
  20.                 /* 右孩子不存在或已被访问，访问之*/
  21.                 if (p->right == q) {
  22.                     result.push_back(p->val);
  23.                     q = p; /* 保存刚访问过的结点*/
  24.                 } else {
  25.                     /* 当前结点不能访问，需第二次进栈*/
  26.                     s.push(p);
  27.                     /* 先处理右子树*/
  28.                     p = p->right;
  29.                     break;
  30.                 }
  31.             }
  32.         } while (!s.empty());
  34.         return result;
  35.     }
  36. };

Morris后序遍历

  1. // Binary Tree Postorder Traversal
  2. // Morris后序遍历，时间复杂度O(n)，空间复杂度O(1)
  3. class Solution {
  4. public:
  5.     vector postorderTraversal(TreeNode *root) {
  6.         vector result;
  7.         TreeNode dummy(-1);
  8.         TreeNode *cur, *prev = nullptr;
  9.         std::function < void(const TreeNode*)> visit = 
  10.             [&result](const TreeNode *node){
  11.             result.push_back(node->val); 
  12.         };
  14.         dummy.left = root;
  15.         cur = &dummy;
  16.         while (cur != nullptr) {
  17.             if (cur->left == nullptr) {
  18.                 prev = cur; /* 必须要有 */
  19.                 cur = cur->right;
  20.             } else {
  21.                 TreeNode *node = cur->left;
  22.                 while (node->right != nullptr && node->right != cur)
  23.                     node = node->right;
  25.                 if (node->right == nullptr) { /* 还没线索化，则建立线索 */
  26.                     node->right = cur;
  27.                     prev = cur; /* 必须要有 */
  28.                     cur = cur->left;
  29.                 } else { /* 已经线索化，则访问节点，并删除线索  */
  30.                     visit_reverse(cur->left, prev, visit);
  31.                     prev->right = nullptr;
  32.                     prev = cur; /* 必须要有 */
  33.                     cur = cur->right;
  34.                 }
  35.             }
  36.         }
  37.         return result;
  38.     }
  39. private:
  40.     // 逆转路径
  41.     static void reverse(TreeNode *from, TreeNode *to) {
  42.         TreeNode *x = from, *y = from->right, *z;
  43.         if (from == to) return;
  45.         while (x != to) {
  46.             z = y->right;
  47.             y->right = x;
  48.             x = y;
  49.             y = z;
  50.         }
  51.     }
  53.     // 访问逆转后的路径上的所有结点
  54.     static void visit_reverse(TreeNode* from, TreeNode *to, 
  55.                      std::function< void(const TreeNode*) >& visit) {
  56.         TreeNode *p = to;
  57.         reverse(from, to);
  59.         while (true) {
  60.             visit(p);
  61.             if (p == from)
  62.                 break;
  63.             p = p->right;
  64.         }
  66.         reverse(to, from);
  67.     }
  68. };

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原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/binary-tree/traversal/binary-tree-postorder-traversal.html