# Exhaustive Search - 窮竭搜索
窮竭搜索又稱暴力搜索，指代將所有可能性列出來，然后再在其中尋找滿足題目條件的解。常用求解方法和工具有：
1. 遞歸函數
1. 棧
1. 隊列
1. 深度優先搜索([DFS](# "Depth-First Search, 深度優先搜索"), Depth-First Search)，又常稱為回溯法
1. 廣度優先搜索([BFS](# "Breadth-First Search, 廣度優先搜索"), Breadth-First Search)
1, 2, 3 往往在深搜或者廣搜中體現。
### [DFS](# "Depth-First Search, 深度優先搜索")
[DFS](# "Depth-First Search, 深度優先搜索") 通常從某個狀態開始，根據特定的規則轉移狀態，直至無法轉移(節點為空)，然后回退到之前一步狀態，繼續按照指定規則轉移狀態，直至遍歷完所有狀態。
回溯法包含了多類問題，模板類似。
排列組合模板->搜索問題(是否要排序，哪些情況要跳過)
使用回溯法的一般步驟：
1. 確定所給問題的解空間：首先應明確定義問題的解空間，解空間中至少包含問題的一個解。
1. 確定結點的擴展搜索規則
1. 以深度優先方式搜索解空間，并在搜索過程中用剪枝函數避免無效搜索。
### [BFS](# "Breadth-First Search, 廣度優先搜索")
[BFS](# "Breadth-First Search, 廣度優先搜索") 從某個狀態開始，搜索**所有可以到達的狀態**，轉移順序為『初始狀態->只需一次轉移就可到達的所有狀態->只需兩次轉移就可到達的所有狀態->...』，所以對于同一個狀態，[BFS](# "Breadth-First Search, 廣度優先搜索") 只搜索一次，故時間復雜度為 O(states×transfer_methods)O(states \times transfer\_methods)O(states×transfer_methods). [BFS](# "Breadth-First Search, 廣度優先搜索") 通常配合隊列一起使用，搜索時先將狀態加入到隊列中，然后從隊列頂端不斷取出狀態，再把從該狀態可轉移到的狀態中尚未訪問過的部分加入隊列，知道隊列為空或已找到解。因此 [BFS](# "Breadth-First Search, 廣度優先搜索") 適合用于『由近及遠』的搜索，比較適合用于求解最短路徑、最少操作之類的問題。
### Reference
- 《挑戰程序設計競賽》Chaper 2.1 p26 最基礎的“窮竭搜索”
- [Steven Skiena: Lecture15 - Backtracking](#)
- [全面解析回溯法：算法框架與問題求解 - 五岳 - 博客園](http://www.cnblogs.com/wuyuegb2312/p/3273337.html)
- [五大常用算法之四：回溯法 - 紅臉書生 - 博客園](http://www.cnblogs.com/steven_oyj/archive/2010/05/22/1741376.html)
- [演算法筆記 - Backtracking](http://www.csie.ntnu.edu.tw/~u91029/Backtracking.html)
- Preface
- Part I - Basics
- Basics Data Structure
- String
- Linked List
- Binary Tree
- Huffman Compression
- Queue
- Heap
- Stack
- Set
- Map
- Graph
- Basics Sorting
- Bubble Sort
- Selection Sort
- Insertion Sort
- Merge Sort
- Quick Sort
- Heap Sort
- Bucket Sort
- Counting Sort
- Radix Sort
- Basics Algorithm
- Divide and Conquer
- Binary Search
- Math
- Greatest Common Divisor
- Prime
- Knapsack
- Probability
- Shuffle
- Basics Misc
- Bit Manipulation
- Part II - Coding
- String
- strStr
- Two Strings Are Anagrams
- Compare Strings
- Anagrams
- Longest Common Substring
- Rotate String
- Reverse Words in a String
- Valid Palindrome
- Longest Palindromic Substring
- Space Replacement
- Wildcard Matching
- Length of Last Word
- Count and Say
- Integer Array
- Remove Element
- Zero Sum Subarray
- Subarray Sum K
- Subarray Sum Closest
- Recover Rotated Sorted Array
- Product of Array Exclude Itself
- Partition Array
- First Missing Positive
- 2 Sum
- 3 Sum
- 3 Sum Closest
- Remove Duplicates from Sorted Array
- Remove Duplicates from Sorted Array II
- Merge Sorted Array
- Merge Sorted Array II
- Median
- Partition Array by Odd and Even
- Kth Largest Element
- Binary Search
- Binary Search
- Search Insert Position
- Search for a Range
- First Bad Version
- Search a 2D Matrix
- Search a 2D Matrix II
- Find Peak Element
- Search in Rotated Sorted Array
- Search in Rotated Sorted Array II
- Find Minimum in Rotated Sorted Array
- Find Minimum in Rotated Sorted Array II
- Median of two Sorted Arrays
- Sqrt x
- Wood Cut
- Math and Bit Manipulation
- Single Number
- Single Number II
- Single Number III
- O1 Check Power of 2
- Convert Integer A to Integer B
- Factorial Trailing Zeroes
- Unique Binary Search Trees
- Update Bits
- Fast Power
- Hash Function
- Count 1 in Binary
- Fibonacci
- A plus B Problem
- Print Numbers by Recursion
- Majority Number
- Majority Number II
- Majority Number III
- Digit Counts
- Ugly Number
- Plus One
- Linked List
- Remove Duplicates from Sorted List
- Remove Duplicates from Sorted List II
- Remove Duplicates from Unsorted List
- Partition List
- Two Lists Sum
- Two Lists Sum Advanced
- Remove Nth Node From End of List
- Linked List Cycle
- Linked List Cycle II
- Reverse Linked List
- Reverse Linked List II
- Merge Two Sorted Lists
- Merge k Sorted Lists
- Reorder List
- Copy List with Random Pointer
- Sort List
- Insertion Sort List
- Check if a singly linked list is palindrome
- Delete Node in the Middle of Singly Linked List
- Rotate List
- Swap Nodes in Pairs
- Remove Linked List Elements
- Binary Tree
- Binary Tree Preorder Traversal
- Binary Tree Inorder Traversal
- Binary Tree Postorder Traversal
- Binary Tree Level Order Traversal
- Binary Tree Level Order Traversal II
- Maximum Depth of Binary Tree
- Balanced Binary Tree
- Binary Tree Maximum Path Sum
- Lowest Common Ancestor
- Invert Binary Tree
- Diameter of a Binary Tree
- Construct Binary Tree from Preorder and Inorder Traversal
- Construct Binary Tree from Inorder and Postorder Traversal
- Subtree
- Binary Tree Zigzag Level Order Traversal
- Binary Tree Serialization
- Binary Search Tree
- Insert Node in a Binary Search Tree
- Validate Binary Search Tree
- Search Range in Binary Search Tree
- Convert Sorted Array to Binary Search Tree
- Convert Sorted List to Binary Search Tree
- Binary Search Tree Iterator
- Exhaustive Search
- Subsets
- Unique Subsets
- Permutations
- Unique Permutations
- Next Permutation
- Previous Permuation
- Unique Binary Search Trees II
- Permutation Index
- Permutation Index II
- Permutation Sequence
- Palindrome Partitioning
- Combinations
- Combination Sum
- Combination Sum II
- Minimum Depth of Binary Tree
- Word Search
- Dynamic Programming
- Triangle
- Backpack
- Backpack II
- Minimum Path Sum
- Unique Paths
- Unique Paths II
- Climbing Stairs
- Jump Game
- Word Break
- Longest Increasing Subsequence
- Palindrome Partitioning II
- Longest Common Subsequence
- Edit Distance
- Jump Game II
- Best Time to Buy and Sell Stock
- Best Time to Buy and Sell Stock II
- Best Time to Buy and Sell Stock III
- Best Time to Buy and Sell Stock IV
- Distinct Subsequences
- Interleaving String
- Maximum Subarray
- Maximum Subarray II
- Longest Increasing Continuous subsequence
- Longest Increasing Continuous subsequence II
- Graph
- Find the Connected Component in the Undirected Graph
- Route Between Two Nodes in Graph
- Topological Sorting
- Word Ladder
- Bipartial Graph Part I
- Data Structure
- Implement Queue by Two Stacks
- Min Stack
- Sliding Window Maximum
- Longest Words
- Heapify
- Problem Misc
- Nuts and Bolts Problem
- String to Integer
- Insert Interval
- Merge Intervals
- Minimum Subarray
- Matrix Zigzag Traversal
- Valid Sudoku
- Add Binary
- Reverse Integer
- Gray Code
- Find the Missing Number
- Minimum Window Substring
- Continuous Subarray Sum
- Continuous Subarray Sum II
- Longest Consecutive Sequence
- Part III - Contest
- Google APAC
- APAC 2015 Round B
- Problem A. Password Attacker
- Microsoft
- Microsoft 2015 April
- Problem A. Magic Box
- Problem B. Professor Q's Software
- Problem C. Islands Travel
- Problem D. Recruitment
- Microsoft 2015 April 2
- Problem A. Lucky Substrings
- Problem B. Numeric Keypad
- Problem C. Spring Outing
- Microsoft 2015 September 2
- Problem A. Farthest Point
- Appendix I Interview and Resume
- Interview
- Resume