Tree 树结构

Case 1st 最少的摄像头——亚马逊面试问题

给定一个二叉树，我们在树的节点上安装摄像头。

节点上的每个摄像机都可以监视其父级、自身及其直接子级。

计算监视树的所有节点所需的最小摄像机数。

例：

Input: [0,0,null,0,0]
Output: 1
Explanation: One camera is enough to monitor all nodes if placed as shown.

了解问题：

由于我们希望尽量减少相机的数量，因此有一点很清楚，我们不会将相机放置在叶节点上。

所以我们可以从叶子到根追溯。这使得DFS成为解决问题的最可能选择。

但是当我们回溯时，我们需要在节点之间交换信息，以查看当前节点是否需要摄像头。

如果上一个节点已经有摄像头，我们不需要摄像头。总而言之，我们需要考虑以下事项：

如果当前节点是叶节点，则我们不需要相机。

如果我们在当前节点上没有摄像头，那么父节点需要它。

如果当前节点具有相机，则其父节点不需要相机。

我们可以分配不同的值来指示这些状态。-1 从孩子的意思是放相机。1 来自任何孩子意味着没有相机。

代码实现：

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def minCameraCover(self, root: TreeNode) -> int:
        def dfs(node):
            l=0
            r=0
            if (node.left is None and node.right is None):
                return -1
            if node.left:
                l = dfs(node.left)
            if node.right:
                r = dfs(node.right)
            if(l == -1 or r == -1):
                self.count += 1
                return 1
            if(l == 0 and r == 0):
                return -1
            if(l == 1 or r == 1):
                return 0
        self.count=0
        cams = dfs(root)
        if(cams == -1):
            self.count += 1
        return self.count

复杂性分析

时间复杂度：O（N），其中 N 是二叉树中的节点数

空间复杂性：递归调用堆栈的空间，可能是 N

Case 2nd 族谱

了解到家族成员的代际关系，我们想透过图的关系信息输入，返回任意某人是第几代？

英伟达和AMD之间是否存在完全竞争？下图显示了黄仁勋和苏丽莎家谱显示他们的关系有多密切？

如何构造恰当的数据结构？

1、构造家庭成员的class类 FamilyMember

2、追加家庭成员的profile信息对应到树连接节点

3、如何输出打印

class类 FamilyMember

class FamilyMember:

    def __init__(self, name, gender, generation):
        self.name = name
        self.gender = gender
        self.generation = generation
        self.children = []
        self.parents = []


# 家族根
root = FamilyMember("John", "Male", 0)

# John 的子女
child1 = FamilyMember("Jane", "Female", 1)
child2 = FamilyMember("Mike", "Male", 1)
root.children.append(child1)
root.children.append(child2)
child1.parents.append(root)
child2.parents.append(root)

#  Jane 和 Mike 的子女
grandchild1 = FamilyMember("Jay", "Male", 2)
grandchild2 = FamilyMember("Joy", "Female", 2)
...
child1.children.append(grandchild1)
child1.children.append(grandchild2)
grandchild1.parents.append(child1)
...

输出：

#递归
def print_family(member):
    print(f"{member.name} - {member.gender} - Generation {member.generation}")
    for child in member.children:
        print(" |--", end="") 
        print_family(child)
        
print_family(root)

2.如何打印输出直观效果的家族树？

我们定义了一个print_family()函数,它能递归地打印指定家庭成员以及其子节点。

通过在每个节点前增加 "| "符号,就能形成一个漂亮的树形结构。关键点是:

递归调用print_family(),打印每个子节点；
在子节点前增加 "|" 和"--"符号,形成一个缩进结构；
打印每个节点的时候,打印其名称、性别和代数信息；

执行print_family(root),就可以打印出整个家族结构。可以看到,使用递归,就可以很简单地打印出一个复杂的树形结构。你可能还想添加更多功能,比如:

查找指定成员
计算指定成员的后代数
统计各代人口数
画出家族结构图

这些都可以基于上述基本功能来实现。通过分解为类、方法和函数,编码家族结构会更加模块化和可扩展。

John - Male - Generation 0
 |--Jane - Female - Generation 1
 |--Jay - Male - Generation 2
 |--Joy - Female - Generation 2
 |--Mike - Male - Generation 1

当我们想了解某个家族成员处于族谱中的第几代，如何构造算法？

def count_gen(Familytree, person):
    prev = set()
    for r in Familytree:
        while r not in prev:
            prev.add(r)
            r = tree[r]
    return len(skils)

致所有受到时间约束的工程师的任务清单

对于那些正在找工作的时间有限的工程师,这里有一份列出各类型问题中最好的LeetCode题目的列表,它可以教你每个类别/类型问题的核心概念和技巧!

许多其他LeetCode题目都是这些个别题目技巧的混合。在我上一个求职过程中,我使用这个列表只做重要的题目。

如下:


•Arrays - Two Sum
•Strings - Longest Substring Without Repeating Characters
•Linked Lists - Reverse a Linked List
•Stacks - Validate Stack Sequences
•Queues - Implement Queue using Stacks
•Trees - Binary Tree Inorder Traversal
•Binary Search - Search Insert Position
•Sorting - Merge Sort
•Hash Tables - Two Sum
•Dynamic Programming - Climbing Stairs
•Greedy Algorithms - Maximum Units on a Truck
•Depth First Search - Number of Islands
•Breadth First Search - Clone Graph
•Bit Manipulation - Single Number
•Backtracking - Permutations
•Sliding Window - Maximum Sum Subarray of Size K
•Divide and Conquer - Merge Sorted Array
•Recursion - Reverse a String
•Binary Search Tree - Lowest Common Ancestor of a Binary Tree
•Heaps - Merge K Sorted Lists
•Trie - Implement Trie (Prefix Tree) （

Array

Two Sum - https://leetcode.com/problems/two-sum/
Best Time to Buy and Sell Stock - https://leetcode.com/problems/best-time-to-buy-and-sell-stock/
Contains Duplicate - https://leetcode.com/problems/contains-duplicate/
Product of Array Except Self - https://leetcode.com/problems/product-of-array-except-self/
Maximum Subarray - https://leetcode.com/problems/maximum-subarray/
Maximum Product Subarray - https://leetcode.com/problems/maximum-product-subarray/
Find Minimum in Rotated Sorted Array - https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/
Search in Rotated Sorted Array - https://leetcode.com/problems/search-in-rotated-sorted-array/
3Sum - https://leetcode.com/problems/3sum/
Container With Most Water - https://leetcode.com/problems/container-with-most-water/

Binary

Sum of Two Integers - https://leetcode.com/problems/sum-of-two-integers/
Number of 1 Bits - https://leetcode.com/problems/number-of-1-bits/
Counting Bits - https://leetcode.com/problems/counting-bits/
Missing Number - https://leetcode.com/problems/missing-number/
Reverse Bits - https://leetcode.com/problems/reverse-bits/

Dynamic Programming

Climbing Stairs - https://leetcode.com/problems/climbing-stairs/
Coin Change - https://leetcode.com/problems/coin-change/
Longest Increasing Subsequence - https://leetcode.com/problems/longest-increasing-subsequence/
Longest Common Subsequence -
Word Break Problem - https://leetcode.com/problems/word-break/
Combination Sum - https://leetcode.com/problems/combination-sum-iv/
House Robber - https://leetcode.com/problems/house-robber/
House Robber II - https://leetcode.com/problems/house-robber-ii/
Decode Ways - https://leetcode.com/problems/decode-ways/
Unique Paths - https://leetcode.com/problems/unique-paths/
Jump Game - https://leetcode.com/problems/jump-game/

Graph

Clone Graph - https://leetcode.com/problems/clone-graph/
Course Schedule - https://leetcode.com/problems/course-schedule/
Pacific Atlantic Water Flow - https://leetcode.com/problems/pacific-atlantic-water-flow/
Number of Islands - https://leetcode.com/problems/number-of-islands/
Longest Consecutive Sequence - https://leetcode.com/problems/longest-consecutive-sequence/
Alien Dictionary (Leetcode Premium) - https://leetcode.com/problems/alien-dictionary/
Graph Valid Tree (Leetcode Premium) - https://leetcode.com/problems/graph-valid-tree/
Number of Connected Components in an Undirected Graph (Leetcode Premium) - https://leetcode.com/problems/number-of-connected-components-in-an-undirected-graph/

Interval

Insert Interval - https://leetcode.com/problems/insert-interval/
Merge Intervals - https://leetcode.com/problems/merge-intervals/
Non-overlapping Intervals - https://leetcode.com/problems/non-overlapping-intervals/
Meeting Rooms (Leetcode Premium) - https://leetcode.com/problems/meeting-rooms/
Meeting Rooms II (Leetcode Premium) - https://leetcode.com/problems/meeting-rooms-ii/

Linked List

Reverse a Linked List - https://leetcode.com/problems/reverse-linked-list/
Detect Cycle in a Linked List - https://leetcode.com/problems/linked-list-cycle/
Merge Two Sorted Lists - https://leetcode.com/problems/merge-two-sorted-lists/
Merge K Sorted Lists - https://leetcode.com/problems/merge-k-sorted-lists/
Remove Nth Node From End Of List - https://leetcode.com/problems/remove-nth-node-from-end-of-list/
Reorder List - https://leetcode.com/problems/reorder-list/

Matrix

Set Matrix Zeroes - https://leetcode.com/problems/set-matrix-zeroes/
Spiral Matrix - https://leetcode.com/problems/spiral-matrix/
Rotate Image - https://leetcode.com/problems/rotate-image/
Word Search - https://leetcode.com/problems/word-search/

String

Longest Substring Without Repeating Characters - https://leetcode.com/problems/longest-substring-without-repeating-characters/
Longest Repeating Character Replacement - https://leetcode.com/problems/longest-repeating-character-replacement/
Minimum Window Substring - https://leetcode.com/problems/minimum-window-substring/
Valid Anagram - https://leetcode.com/problems/valid-anagram/
Group Anagrams - https://leetcode.com/problems/group-anagrams/
Valid Parentheses - https://leetcode.com/problems/valid-parentheses/
Valid Palindrome - https://leetcode.com/problems/valid-palindrome/
Longest Palindromic Substring - https://leetcode.com/problems/longest-palindromic-substring/
Palindromic Substrings - https://leetcode.com/problems/palindromic-substrings/
Encode and Decode Strings (Leetcode Premium) - https://leetcode.com/problems/encode-and-decode-strings/

Tree

Maximum Depth of Binary Tree - https://leetcode.com/problems/maximum-depth-of-binary-tree/
Same Tree - https://leetcode.com/problems/same-tree/
Invert/Flip Binary Tree - https://leetcode.com/problems/invert-binary-tree/
Binary Tree Maximum Path Sum - https://leetcode.com/problems/binary-tree-maximum-path-sum/
Binary Tree Level Order Traversal - https://leetcode.com/problems/binary-tree-level-order-traversal/
Serialize and Deserialize Binary Tree - https://leetcode.com/problems/serialize-and-deserialize-binary-tree/
Subtree of Another Tree - https://leetcode.com/problems/subtree-of-another-tree/
Construct Binary Tree from Preorder and Inorder Traversal - https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/
Validate Binary Search Tree - https://leetcode.com/problems/validate-binary-search-tree/
Kth Smallest Element in a BST - https://leetcode.com/problems/kth-smallest-element-in-a-bst/
Lowest Common Ancestor of BST - https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/
Implement Trie (Prefix Tree) - https://leetcode.com/problems/implement-trie-prefix-tree/
Add and Search Word - https://leetcode.com/problems/add-and-search-word-data-structure-design/
Word Search II - https://leetcode.com/problems/word-search-ii/

Heap

Merge K Sorted Lists - https://leetcode.com/problems/merge-k-sorted-lists/
Top K Frequent Elements - https://leetcode.com/problems/top-k-frequent-elements/
Find Median from Data Stream - https://leetcode.com/problems/find-median-from-data-stream/

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