• Heap
• Stack
• Queue
• Linked List
• Tree
  • Binary Search Tree
• Union Find
  • UnionFind基础操作
  • UnionFind follow up
• Trie
  • applications:
  • why not using a hashmap to store string?
  • Model
  • sample peoblems
  • 考点
• Graph
• Array
  • Array
• Sort
  • Quick Sort
• Collections
  • methods
  • ArrayList
• Hash
  • HashSet
• Basics
  • Math
  • String
  • Bit Manipulation
• DP
  • Dynamic Programming
• Double Sequence
• Search
  • Breadth-first Search
  • Depth-first Search
• Backtracking
• Fancy
• Approach
  • Recursion
• Data Structure
• Problem Sets
  • Two Pointer
  • Min/Max Heap

• peek(), pop(), push()
• Stack stack = new Stack<>();

• 用来暂且保存有效信息
• 翻转stack
• stack优化DFS, 变成非递归

• 找每个元素左边或者右边 第一个比它自身小/大的元素
• 用单调栈来维护
• 维护monotonous stack 是题目需要, 而不是stack本身性质. 比如, 题目需要stack.peek() O(1), 加上需要单调递增/递减的性质, 就用起来了stack.

MaxTree, Largest Rectangle In Histogram, Maximal Rectangle (in 2D array)

• Functions: peek(), poll(), add()/offer(), remove(object)
• queue = new LinkedList<...>()
• PriorityQueue: new Comparator 很重要
• 看到Min/Max就要想到heap. 如果给出的数组没有排序, 先排序, 然后用heap. PrioirtyQueue是用Binary Heap做出来的
• 看到median 想到heap

• No concept of size(), it's all pointers: node.next.next
• how to set head/dummy, and return dummy.next as result.
• iterate over linked list
• Don't get mixed up with Java LinkedList. Here we are talking about linked list concept, not the Java data structure LinkedList

• If BST not given, can use TreeSet
• All left nodes are less than current node.val; all right nodes are greater than curr node.val
• Use DFS to traverse: divide and conquer. Similarly, usually can convert the DFS solution to interative solution.
• Use stack to traverse iteratively

Binary Indexed Tree

Segment Tree

• 集合合并，查找元素在集合里面
• Find and Union functions
• Time Complexity: log(n)
• 在UnionFind function里维护不同的状态, expose with public helper functions

• 查询两个元素是否在同一个集合内
• 合并两个元素所在的集合

• 查询某个元素所在集合的元素个数
• 查询当前集合的个数

一个字母一个字母查找，快速判断前缀

• Autocomplete
• Spell check
• IP routing
• T9 text prediction (old NOKIA phone)
• solve world game

• Trie can help find all strings with prefix
• Trie can enumerate a data set of strings in lexicographical order
• Trie saves space because of the prefix
• Trie can potentially faster than hashMap, when there are logs collisions for the map.

• children map: Map<Character, TrieNode>. Also can use char[26], but it's more scalable to us a map.
• always have isEnd which marks a end of a particular string

• insert
• search
• exist of prefix
• node when the prefix end

• 一个一个字母遍历
• 需要节约空间
• 查找前缀

• linear collection that supports insertion and removal at both ends. Pronounced 'deck'
• It's a queue && stack
• new ArrayDeque()
• head/top: offerFirst(), pollFirst(), peekFirst()
• tail/bottom: offerLast(), pollLast(), peekLast()
• 双端queue: 维护一个候选可能的最大值集合
• ex: Sliding WIndow Maximum

Graph

Topological Sort

• Arrays.asList([1,2,3]);

Two Pointers

• 记得二分的template
• 往往不会有个数组让我们二分, 但是同样是要去找满足某个条件的最大/最小值
• 二分是个思想, 不是简单的array二分公式.
• 有时候在index上二分, mid是index; 但是有时候, 会在数值上二分, 那么mid就是value, 忌讳不要死板地套用nums[mid]

• 按值二分，需要怎么二分性
• 找到可能的解的范围
• 猜答案
• 检验答案 (match/if/else ...)
• 调整搜索范围
• Find Peak Element II

Collections.sort()

Integer[] array = {1, 2, 3}; new ArrayList(Arrays.asList(array))

Map

Hash Table

• contains: O(1)
• set.add(...) returns false if there is duplicate. This operation won't change the existing set.
• Build HashSet set, and the set will automatically compare the equivalence of the lists within at each list element level.

• 转换成string
• % mod, 除法
• Integer.MAX_VALUE, Integer.MIN_VALUE; if overflow, use long
• Integer.valueOf(number), where number is int

• s.toCharArray()
• String.valueOf(charArrary)
• sb = new StringBuffer()
• sb.reverse(), sb.append(), sb.deleteCharAt(), sb.length(), sb.setCharAt(index, char)
• Character.isDigit(x)
• 遇到找string的相关问题: 考虑string的重复性

• Bit OR |, AND &, XOR ^
• Bit shift: <<, >>
• A << 1: binary of A shifted left for 1 bit, which result in value x 2
• A >> 1: divide by integer 2. Note: decimals are ignored in the result.
• bit shift is a lot faster than reqular 'times' operation.
• 32 bit number: leading bit = 1, negative numbjer; leading bit = 0, positive number.

• add leading '1' if the 32 bit number originally has leading '1'.

• Java/python: logical shift >>>, always add leading '0' regardless of the sign of the 32-bit number. That is, it may turn a negative number to positive, if the leading bit is originally '1'
• Because with '( )', make sure to surround the desired operation
• & 0000 = clean up; | ABC = assign ABC
• A^B=C, then A = B^C
• bits可以用来表示不同的状态, 比如2bit可以表示4种状态: 00, 01, 10, 11

Optimization problems:

• memoization && subproblems
• Fibonacci
• Shortest paths
• guessing && DAG View

• Sequence problem, have dp[] length of n + 1.
• Look at last index for clues
• Usually can start for loop at index = 0, and we handle the init conditions within the for loop (ex: assign particular value or skip i=0 rows)
• Rolling array (curr, prev pointer) to optimize space; note the rolling dimension should be apply at the top-for loop.

Track queue size, use the queue as in rotation

• Finding all (or some) solutions to some computational problems, notebaly constraint satisfaction problems
• It attemps to build/find all candidates and abandon partial candidate when the candidates appears not to be suitable(backtracking, backing off from wrong candidates)

Memoization

Minimax

Reservoir Sampling

Geometry

Brainteaser

Greedy

Divide and Conquer

• ex: dfs
• always find the entry point or terminating point
• watch out for the return or result of recursed function

Design

• Union Find
• Trie
• Heap: PriorityQueue[Java]. Made of: Binary Heap
• Hash: HashMap[Java]. Made of: HashMap
• TreeMap: TreeMap[Java]. Balanced Binary Tree
• TreeSet: TreeSet[Java]. Balanced Binary Tree

• 见到需要维护一个集合的最小值/最大值的时候要想到用堆
• 第k小的元素，Heap用来维护当前候选集合
• 见到数组要想到先排序

• Monotonous stack的运用: 找左边和右边第一个比它大的元素
• 递归转非递归

• 加一个数
• 删一个数

• 见到区间需要排序就可以考虑扫描线
• 事件往往是以区间的形式存在
• 区间两端代表事件的开始和结束
• 需要排序
• Meeting Room I, II