[DFS] Rectify time complexity and add a solution to Word Pattern II

soapyigu · soapyigu · commit dd511ba4a92e · 2018-07-04T16:51:13.000-07:00
diff --git a/DFS/CombinationSumII.swift b/DFS/CombinationSumII.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/combination-sum-ii/
  * Primary idea: Classic Depth-first Search
  * 
- * Time Complexity: O(n!), Space Complexity: O(2^n - 2)
+ * Time Complexity: O(n^n), Space Complexity: O(2^n - 2)
  *
  */
 
diff --git a/DFS/CombinationSumIII.swift b/DFS/CombinationSumIII.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/combination-sum-iii/
  * Primary idea: Classic Depth-first Search
  * 
- * Time Complexity: O(n!), Space Complexity: O(nCk)
+ * Time Complexity: O(n^n), Space Complexity: O(nCk)
  *
  */
 
diff --git a/DFS/Combinations.swift b/DFS/Combinations.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/combinations/
  * Primary idea: Classic Depth-first Search, another version of Subsets
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/ExpressionAddOperators.swift b/DFS/ExpressionAddOperators.swift
@@ -7,7 +7,7 @@
  * 1. String cast to Integer will make character loss, e.g. "05" -> 5
  * 2. Multiplication's priority is higher than addiction
  *
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/GeneralizedAbbreviation.swift b/DFS/GeneralizedAbbreviation.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/generalized-abbreviation/
  * Primary idea: Classic Depth-first Search
  * 
- * Time Complexity: O(n!), Space Complexity: O(2^n)
+ * Time Complexity: O(n^n), Space Complexity: O(2^n)
  *
  */
 
diff --git a/DFS/NQueens.swift b/DFS/NQueens.swift
@@ -3,7 +3,7 @@
  * Primary idea: Classic Depth-first Search, fill out row by row, and check column and 
  *               diagnol for each time
  * 
- * Time Complexity: O(n!), Space Complexity: O(n^2)
+ * Time Complexity: O(n^n), Space Complexity: O(n^2)
  *
  */
 
diff --git a/DFS/NQueensII.swift b/DFS/NQueensII.swift
@@ -3,7 +3,7 @@
  * Primary idea: Classic Depth-first Search, fill out row by row, and check column and 
  *               diagnol for each time, only need to care which column is used
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/PalindromePartitioning.swift b/DFS/PalindromePartitioning.swift
@@ -3,7 +3,7 @@
  * Primary idea: Classic Depth-first Search, use index to track substring, 
  *               and move forward to deeper level only if the substring is a palindrome
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/Permutations.swift b/DFS/Permutations.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/permutations/
  * Primary idea: Classic Depth-first Search, remember backtracking
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/PermutationsII.swift b/DFS/PermutationsII.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/permutations-ii/
  * Primary idea: Classic Depth-first Search, adopt last occurrence to avoid dupliates
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/RemoveInvalidParentheses.swift b/DFS/RemoveInvalidParentheses.swift
@@ -3,7 +3,7 @@
  * Primary idea: Remove ) when the string is invalid, add to result when string is valid, 
  *               and do the same thing for the reversed one
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/Subsets.swift b/DFS/Subsets.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/subsets/
  * Primary idea: Classic Depth-first Search
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/SubsetsII.swift b/DFS/SubsetsII.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/subsets-ii/
  * Primary idea: Classic Depth-first Search, avoid duplicates by adopting the first occurrence
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/DFS/WordPatternII.swift b/DFS/WordPatternII.swift
@@ -0,0 +1,47 @@
+/**
+ * Question Link: https://leetcode.com/problems/word-pattern-ii/
+ * Primary idea: Depth first search, split the string to find possible word to pattern character until find the end
+ * 
+ * Time Complexity: O(n^n), Space Complexity: O(n)
+ *
+ */
+
+class WordPatternII {
+    func wordPatternMatch(_ pattern: String, _ str: String) -> Bool {        
+        return helper(pattern, str, [Character: String]())
+    }
+    
+    fileprivate func helper(_ pattern: String, _ str: String, _ patternToWord: [Character: String]) -> Bool {
+        guard let firstChar = pattern.first, str.count > 0 else {
+            return pattern.isEmpty && str.isEmpty
+        }
+        
+        let newPattern = String(pattern.suffix(pattern.count - 1))
+        
+        if let existingWord = patternToWord[firstChar] {
+            if str.hasPrefix(existingWord) {
+                return helper(newPattern, String(str.suffix(str.count - existingWord.count)), patternToWord)
+            } else {
+                return false
+            }
+        }
+        
+        for i in 0..<str.count {
+            
+            let word = String(str.prefix(i + 1))
+            
+            // word is already used for another pattern
+            if patternToWord.values.contains(word) {
+                continue
+            }
+            
+            var patternToWord = patternToWord
+            patternToWord[firstChar] = word
+            if helper(newPattern, String(str.suffix(str.count - word.count)), patternToWord) {
+                return true
+            }
+        }
+        
+        return false
+    }
+}
diff --git a/DFS/WordSquares.swift b/DFS/WordSquares.swift
@@ -2,7 +2,7 @@
  * Question Link: https://leetcode.com/problems/word-squares/
  * Primary idea: Classic Depth-first Search, fill out row by row, choose correct word with fixed prefix, only need to care which column is used
  * 
- * Time Complexity: O(n!), Space Complexity: O(n)
+ * Time Complexity: O(n^n), Space Complexity: O(n)
  *
  */
 
diff --git a/README.md b/README.md
@@ -28,7 +28,7 @@
 * [Microsoft](#microsoft)
 
 ## Progress
-[Problem Status](#problem-status) shows the latest progress to all 800+ questions. Currently we have 261 completed solutions. Note: questions with &hearts; mark means that you have to **Subscript to premium membership** of LeetCode to unlock them. Thank you for great contributions from [CharleneJiang](https://github.com/CharleneJiang), [ReadmeCritic](https://github.com/ReadmeCritic), [demonkoo](https://github.com/demonkoo), [DaiYue](https://github.com/DaiYue), [Quaggie](https://github.com/Quaggie) and [jindulys](https://github.com/jindulys).
+[Problem Status](#problem-status) shows the latest progress to all 800+ questions. Currently we have 262 completed solutions. Note: questions with &hearts; mark means that you have to **Subscript to premium membership** of LeetCode to unlock them. Thank you for great contributions from [CharleneJiang](https://github.com/CharleneJiang), [ReadmeCritic](https://github.com/ReadmeCritic), [demonkoo](https://github.com/demonkoo), [DaiYue](https://github.com/DaiYue), [Quaggie](https://github.com/Quaggie) and [jindulys](https://github.com/jindulys).
 
 
 ## Array
@@ -223,31 +223,32 @@
 ## Depth-first search
 | Title | Solution | Difficulty | Time | Space |
 | ----- | -------- | ---------- | ---- | ----- |
-[Permutations](https://leetcode.com/problems/permutations/)| [Swift](./DFS/Permutations.swift)| Medium| O(n!)| O(n)|
-[Permutations II](https://leetcode.com/problems/permutations-ii/)| [Swift](./DFS/PermutationsII.swift)| Medium| O(n!)| O(n)|
-[Subsets](https://leetcode.com/problems/subsets/)| [Swift](./DFS/Subsets.swift)| Medium| O(n!)| O(n)|
-[Subsets II](https://leetcode.com/problems/subsets-ii/)| [Swift](./DFS/SubsetsII.swift)| Medium| O(n!)| O(n)|
-[Combinations](https://leetcode.com/problems/combinations/)| [Swift](./DFS/Combinations.swift)| Medium| O(n!)| O(n)|
+[Permutations](https://leetcode.com/problems/permutations/)| [Swift](./DFS/Permutations.swift)| Medium| O(n^n)| O(n)|
+[Permutations II](https://leetcode.com/problems/permutations-ii/)| [Swift](./DFS/PermutationsII.swift)| Medium| O(n^n)| O(n)|
+[Subsets](https://leetcode.com/problems/subsets/)| [Swift](./DFS/Subsets.swift)| Medium| O(n^n)| O(n)|
+[Subsets II](https://leetcode.com/problems/subsets-ii/)| [Swift](./DFS/SubsetsII.swift)| Medium| O(n^n)| O(n)|
+[Combinations](https://leetcode.com/problems/combinations/)| [Swift](./DFS/Combinations.swift)| Medium| O(n^n)| O(n)|
 [Combination Sum](https://leetcode.com/problems/combination-sum/)| [Swift](./DFS/CombinationSum.swift)| Medium| O(n^n)| O(2^n - 1)|
-[Combination Sum II](https://leetcode.com/problems/combination-sum-ii/)| [Swift](./DFS/CombinationSumII.swift)| Medium| O(n!)| O(2^n - 2)|
-[Combination Sum III](https://leetcode.com/problems/combination-sum-iii/)| [Swift](./DFS/CombinationSumIII.swift)| Medium| O(n!)| O(nCk)|
+[Combination Sum II](https://leetcode.com/problems/combination-sum-ii/)| [Swift](./DFS/CombinationSumII.swift)| Medium| O(n^n)| O(2^n - 2)|
+[Combination Sum III](https://leetcode.com/problems/combination-sum-iii/)| [Swift](./DFS/CombinationSumIII.swift)| Medium| O(n^n)| O(nCk)|
 [Letter Combinations of a Phone Number](https://leetcode.com/problems/letter-combinations-of-a-phone-number/)| [Swift](./DFS/LetterCombinationsPhoneNumber.swift)| Medium| O(mn)| O(n)|
 [Factor Combinations](https://leetcode.com/problems/factor-combinations/)| [Swift](./DFS/FactorCombinations.swift)| Medium| O(n^n))| O(2^n - 1)|
 [Strobogrammatic Number II](https://leetcode.com/problems/strobogrammatic-number-ii/)| [Swift](./DFS/StrobogrammaticNumberII.swift)| Medium| O(m^n)| O(n)|
-[Generalized Abbreviation](https://leetcode.com/problems/generalized-abbreviation/)| [Swift](./DFS/GeneralizedAbbreviation.swift)| Medium| O(n!)| O(2^n)|
-[Palindrome Partitioning](https://leetcode.com/problems/palindrome-partitioning/)| [Swift](./DFS/PalindromePartitioning.swift)| Medium| O(n!)| O(n)|
+[Generalized Abbreviation](https://leetcode.com/problems/generalized-abbreviation/)| [Swift](./DFS/GeneralizedAbbreviation.swift)| Medium| O(n^n)| O(2^n)|
+[Palindrome Partitioning](https://leetcode.com/problems/palindrome-partitioning/)| [Swift](./DFS/PalindromePartitioning.swift)| Medium| O(n^n)| O(n)|
 [Is Graph Bipartite](https://leetcode.com/problems/is-graph-bipartite/)| [Swift](./DFS/IsGraphBipartite.swift)| Medium| O(n)| O(n)|
 [Number of Islands](https://leetcode.com/problems/number-of-islands/)| [Swift](./DFS/NumberofIslands.swift)| Medium| O((mn)^2)| O(1)|
-[Walls and Gates](https://leetcode.com/problems/walls-and-gates/)| [Swift](./DFS/WallsGates.swift)| Medium| O(n!)| O(2^n)|
+[Walls and Gates](https://leetcode.com/problems/walls-and-gates/)| [Swift](./DFS/WallsGates.swift)| Medium| O(n^n)| O(2^n)|
 [Word Search](https://leetcode.com/problems/word-search/)| [Swift](./DFS/WordSearch.swift)| Medium| O((mn * 4 ^ (k - 1))| O(mn)|
 [Word Search II](https://leetcode.com/problems/word-search-ii/)| [Swift](./DFS/WordSearchII.swift)| Hard| O(((mn)^2))| O(n^2)|
 [Add and Search Word - Data structure design](https://leetcode.com/problems/add-and-search-word-data-structure-design/)| [Swift](./DFS/WordDictionary.swift)| Medium| O(n)| O(n)|
-[N-Queens](https://leetcode.com/problems/n-queens/)| [Swift](./DFS/NQueens.swift)| Hard| O((n!))| O(n^2)|
-[N-Queens II](https://leetcode.com/problems/n-queens-ii/)| [Swift](./DFS/NQueensII.swift)| Hard| O((n!))| O(n)|
-[Word Squares](https://leetcode.com/problems/word-squares/)| [Swift](./DFS/WordSquares.swift)| Hard| O((n!))| O(n)|
+[N-Queens](https://leetcode.com/problems/n-queens/)| [Swift](./DFS/NQueens.swift)| Hard| O((n^n))| O(n^2)|
+[N-Queens II](https://leetcode.com/problems/n-queens-ii/)| [Swift](./DFS/NQueensII.swift)| Hard| O((n^n))| O(n)|
+[Word Squares](https://leetcode.com/problems/word-squares/)| [Swift](./DFS/WordSquares.swift)| Hard| O((n^n))| O(n)|
+[Word Pattern II](https://leetcode.com/problems/word-pattern-ii/)| [Swift](./DFS/WordPatternII.swift)| Hard| O(n^n)| O(n)|
 [Sudoku Solver](https://leetcode.com/problems/sudoku-solver/)| [Swift](./DFS/SudokuSolver.swift)| Hard| O(n^4)| O(1)|
-[Remove Invalid Parentheses](https://leetcode.com/problems/remove-invalid-parentheses/)| [Swift](./DFS/RemoveInvalidParentheses.swift)| Hard| O(n!)| O(n)|
-[Expression Add Operators](https://leetcode.com/problems/expression-add-operators/)| [Swift](./DFS/ExpressionAddOperators.swift)| Hard| O(n!)| O(n)|
+[Remove Invalid Parentheses](https://leetcode.com/problems/remove-invalid-parentheses/)| [Swift](./DFS/RemoveInvalidParentheses.swift)| Hard| O(n^n)| O(n)|
+[Expression Add Operators](https://leetcode.com/problems/expression-add-operators/)| [Swift](./DFS/ExpressionAddOperators.swift)| Hard| O(n^n)| O(n)|
 
 ## Breadth-first search
 | Title | Solution | Difficulty | Time | Space |

Original file line number	Diff line number	Diff line change
`@@ -2,7 +2,7 @@`
`2`	`2`	`* Question Link: https://leetcode.com/problems/combination-sum-ii/`
`3`	`3`	`* Primary idea: Classic Depth-first Search`
`4`	`4`	`*`
`5`		`- * Time Complexity: O(n!), Space Complexity: O(2^n - 2)`
	`5`	`+ * Time Complexity: O(n^n), Space Complexity: O(2^n - 2)`
`6`	`6`	`*`
`7`	`7`	`*/`
`8`	`8`
Original file line number	Diff line number	Diff line change
`@@ -7,7 +7,7 @@`
`7`	`7`	`* 1. String cast to Integer will make character loss, e.g. "05" -> 5`
`8`	`8`	`* 2. Multiplication's priority is higher than addiction`
`9`	`9`	`*`
`10`		`- * Time Complexity: O(n!), Space Complexity: O(n)`
	`10`	`+ * Time Complexity: O(n^n), Space Complexity: O(n)`
`11`	`11`	`*`
`12`	`12`	`*/`
`13`	`13`
Original file line number	Diff line number	Diff line change
`@@ -3,7 +3,7 @@`
`3`	`3`	`* Primary idea: Classic Depth-first Search, fill out row by row, and check column and`
`4`	`4`	`* diagnol for each time`
`5`	`5`	`*`
`6`		`- * Time Complexity: O(n!), Space Complexity: O(n^2)`
	`6`	`+ * Time Complexity: O(n^n), Space Complexity: O(n^2)`
`7`	`7`	`*`
`8`	`8`	`*/`
`9`	`9`
Original file line number	Diff line number	Diff line change
`@@ -3,7 +3,7 @@`
`3`	`3`	`* Primary idea: Classic Depth-first Search, fill out row by row, and check column and`
`4`	`4`	`* diagnol for each time, only need to care which column is used`
`5`	`5`	`*`
`6`		`- * Time Complexity: O(n!), Space Complexity: O(n)`
	`6`	`+ * Time Complexity: O(n^n), Space Complexity: O(n)`
`7`	`7`	`*`
`8`	`8`	`*/`
`9`	`9`
Original file line number	Diff line number	Diff line change
`@@ -3,7 +3,7 @@`
`3`	`3`	`* Primary idea: Classic Depth-first Search, use index to track substring,`
`4`	`4`	`* and move forward to deeper level only if the substring is a palindrome`
`5`	`5`	`*`
`6`		`- * Time Complexity: O(n!), Space Complexity: O(n)`
	`6`	`+ * Time Complexity: O(n^n), Space Complexity: O(n)`
`7`	`7`	`*`
`8`	`8`	`*/`
`9`	`9`
Original file line number	Diff line number	Diff line change
`@@ -3,7 +3,7 @@`
`3`	`3`	`* Primary idea: Remove ) when the string is invalid, add to result when string is valid,`
`4`	`4`	`* and do the same thing for the reversed one`
`5`	`5`	`*`
`6`		`- * Time Complexity: O(n!), Space Complexity: O(n)`
	`6`	`+ * Time Complexity: O(n^n), Space Complexity: O(n)`
`7`	`7`	`*`
`8`	`8`	`*/`
`9`	`9`