二叉树排序(前序、中序、后序)

理论

前序、中序、后序主要根据遍历时根结点的顺序来决定。

  • 前序遍历(根结点在前面)
    先遍历根结点,然后遍历左子树,最后遍历右子树
  • 中序遍历(根结点在中间)
    先遍历左子树,再遍历根结点,最后遍历右子树
  • 后序遍历(根结点在后面)
    先遍历左子树,再遍历右子树,最后遍历根结点

理解

有一个二叉树如下图:


二叉树
  • 前序遍历结果:ABCDEFGHIJ
  • 中序遍历结果:CBEDFAHGIJ
  • 后序遍历结果:CEFDBHJIGA

实战

  • 前序递归遍历
from typing import List


class TreeNode:
    def __init__(self, val='', left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
class Solution:
    def preorderTraversal(self, root: TreeNode) -> List[int]:
        def preorder(root: TreeNode):
            if not root:
                return []
            res.append(root.val)
            preorder(root.left)
            preorder(root.right)

        res = []
        preorder(root)
        return res


e = TreeNode('e')
f = TreeNode('f')
d = TreeNode('d', e, f)
c = TreeNode('c')
b = TreeNode('b', c, d)
h = TreeNode('h')
j = TreeNode('j')
i = TreeNode('i', right=j)
g = TreeNode('g', h, i)
a = TreeNode('a', b, g)

solu = Solution()
res = solu.preorderTraversal(a)
print(res)

打印结果:

['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
  • 中序递归遍历
from typing import List

class TreeNode:
    def __init__(self, val='', left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
class Solution:
    def preorderTraversal(self, root: TreeNode) -> List[int]:
        def preorder(root: TreeNode):
            if not root:
                return []

            preorder(root.left)
            res.append(root.val)
            preorder(root.right)

        res = []
        preorder(root)
        return res

e = TreeNode('e')
f = TreeNode('f')
d = TreeNode('d', e, f)
c = TreeNode('c')
b = TreeNode('b', c, d)
h = TreeNode('h')
j = TreeNode('j')
i = TreeNode('i', right=j)
g = TreeNode('g', h, i)
a = TreeNode('a', b, g)

solu = Solution()
res = solu.preorderTraversal(a)
print(res)

打印结果:

['c', 'b', 'e', 'd', 'f', 'a', 'h', 'g', 'i', 'j']
  • 后序递归遍历
from typing import List

class TreeNode:
    def __init__(self, val='', left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
class Solution:
    def preorderTraversal(self, root: TreeNode) -> List[int]:
        def preorder(root: TreeNode):
            if not root:
                return []

            preorder(root.left)
            preorder(root.right)
            res.append(root.val)

        res = []
        preorder(root)
        return res

e = TreeNode('e')
f = TreeNode('f')
d = TreeNode('d', e, f)
c = TreeNode('c')
b = TreeNode('b', c, d)
h = TreeNode('h')
j = TreeNode('j')
i = TreeNode('i', right=j)
g = TreeNode('g', h, i)
a = TreeNode('a', b, g)

solu = Solution()
res = solu.preorderTraversal(a)
print(res)

打印结果:

['c', 'e', 'f', 'd', 'b', 'h', 'j', 'i', 'g', 'a']

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