From e02c9f8040c1810ffeaca3dbe3c09b872bf7b38e Mon Sep 17 00:00:00 2001
From: Symbolk <symbolk@163.com>
Date: Tue, 17 Dec 2019 20:52:24 +0800
Subject: [PATCH] Homework for Week08.

---
 Week 08/id_556/LeetCode_127_556.py |  67 +++++++++++++++++
 Week 08/id_556/LeetCode_300_556.py |  64 +++++++++++++++++
 Week 08/id_556/LeetCode_91_556.py  |  48 +++++++++++++
 Week 08/id_556/NOTE.md             | 111 +++++++++++++++++++++++++++++
 4 files changed, 290 insertions(+)
 create mode 100644 Week 08/id_556/LeetCode_127_556.py
 create mode 100644 Week 08/id_556/LeetCode_300_556.py
 create mode 100644 Week 08/id_556/LeetCode_91_556.py

diff --git a/Week 08/id_556/LeetCode_127_556.py b/Week 08/id_556/LeetCode_127_556.py
new file mode 100644
index 000000000..a714a2f66
--- /dev/null
+++ b/Week 08/id_556/LeetCode_127_556.py	
@@ -0,0 +1,67 @@
+from typing import List
+
+
+class Solution(object):
+    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
+        wordSet = set(wordList)
+        if endWord not in wordSet:
+            return 0
+
+        res = 1
+        n = len(beginWord)
+        current = set()
+        current.add(beginWord)
+
+        while current:
+            next_level = set()
+            if endWord in current:
+                return res
+            for cur in current:
+                if cur in wordSet:
+                    wordSet.remove(cur)
+                for i in range(n):
+                    for ch in range(97, 123):
+                        tmp = cur[:i] + chr(ch) + cur[i + 1:]
+                        if tmp in wordSet:
+                            next_level.add(tmp)
+            res += 1
+            current = next_level
+        return 0
+
+    def ladderLength2(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
+        wordSet = set(wordList)
+        if endWord not in wordSet:
+            return 0
+
+        res = 1
+        wordDict = {}
+        for w in wordSet:
+            for i in range(len(w)):
+                new_w = w[:i] + "_" + w[i + 1:]
+                if new_w in wordDict:
+                    wordDict[new_w].append(w)
+                else:
+                    wordDict[new_w] = [w]
+
+        current = [beginWord]
+        next_level = []
+        while current:
+            for w in current:
+                if w == endWord:
+                    return res
+                for i in range(len(w)):
+                    new_w = w[:i] + "_" + w[i + 1:]
+                    if new_w in wordDict:
+                        for t in wordDict[new_w]:
+                            if t not in next_level:
+                                next_level.append(t)
+                        del wordDict[new_w]
+            res += 1
+            current = next_level
+            next_level = []
+        return 0
+
+
+if __name__ == "__main__":
+    solution = Solution()
+    print(solution.ladderLength2("hit", "cog", ["hot", "dot", "dog", "lot", "log", "cog"]))
diff --git a/Week 08/id_556/LeetCode_300_556.py b/Week 08/id_556/LeetCode_300_556.py
new file mode 100644
index 000000000..60025b0e0
--- /dev/null
+++ b/Week 08/id_556/LeetCode_300_556.py	
@@ -0,0 +1,64 @@
+from typing import List
+
+
+# O(n^2)
+def lengthOfLIS(nums: List[int]) -> int:
+    if not nums:
+        return 0
+    n = len(nums)
+    dp = [1] * n
+    for i in range(n):
+        for j in range(i):
+            if nums[j] < nums[i]:
+                dp[i] = max(dp[i], dp[j] + 1)
+            else:
+                continue
+    return max(dp)
+
+
+# O(nlogn)
+def lengthOfLIS2(nums):
+    if not nums:
+        return 0
+    n = len(nums)
+    if n < 2:
+        return n
+    # the min tail element in nums[:i+1]
+    tails = [nums[0]]
+    for i in range(1, n):
+        if nums[i] > tails[-1]:
+            tails.append(nums[i])
+            continue
+        # binary search to find the first tail > nums[i]
+        l, r = 0, len(tails) - 1
+        while l <= r:
+            m = l + ((r - l) >> 1)
+            if tails[m] < nums[i]:
+                l = m + 1
+            else:
+                r = m - 1
+        tails[l] = nums[i]
+    return len(tails)
+
+
+def lengthOfLIS3(nums):
+    n = len(nums)
+    tails, res = [0] * n, 0
+    for num in nums:
+        i, j = 0, res
+        while i < j:
+            m = i + ((j - i) >> 1)
+            if tails[m] < num:
+                i = m + 1
+            else:
+                j = m
+        tails[i] = num
+        if j == res:
+            res += 1
+    return res
+
+
+nums = [10, 9, 2, 5, 3, 7, 101, 18]
+print(lengthOfLIS(nums))
+print(lengthOfLIS2(nums))
+print(lengthOfLIS3(nums))
diff --git a/Week 08/id_556/LeetCode_91_556.py b/Week 08/id_556/LeetCode_91_556.py
new file mode 100644
index 000000000..48c26a3ae
--- /dev/null
+++ b/Week 08/id_556/LeetCode_91_556.py	
@@ -0,0 +1,48 @@
+# O(n) time/space
+def numDecodings(s: str) -> int:
+    n = len(s)
+    if not s or s[0] == "0":
+        return 0
+    # dp[i] denotes the num of decoding for s[:i]
+    dp = [0] * (n + 1)
+    dp[0] = 1
+    dp[1] = 1
+    for i in range(1, n):
+        if s[i] == "0":
+            if s[i - 1] == "1" or s[i - 1] == "2":
+                dp[i + 1] = dp[i - 1]
+            else:
+                return 0
+        else:
+            if s[i - 1] == "1" or (s[i - 1] == "2" and "1" <= s[i] <= "6"):
+                dp[i + 1] = dp[i] + dp[i - 1]
+            else:
+                dp[i + 1] = dp[i]
+    return dp[-1]
+
+
+# O(n) time, O(1) space
+def numDecodings2(s):
+    n = len(s)
+    if not s or s[0] == "0":
+        return 0
+    pre, cur = 1, 1
+    for i in range(1, n):
+        if s[i] == "0":
+            if s[i - 1] == "1" or s[i - 1] == "2":
+                cur = pre
+            else:
+                return 0
+        else:
+            if s[i - 1] == "1" or (s[i - 1] == "2" and "1" <= s[i] <= "6"):
+                tmp = cur
+                cur += pre
+                pre = tmp
+            else:
+                pre = cur
+    return cur
+
+
+print(numDecodings("0"))
+print(numDecodings2("226"))
+print("226"[:2])
diff --git a/Week 08/id_556/NOTE.md b/Week 08/id_556/NOTE.md
index a6321d6e2..f43329d3e 100755
--- a/Week 08/id_556/NOTE.md	
+++ b/Week 08/id_556/NOTE.md	
@@ -2,3 +2,114 @@
 
   
 
+## Week8-19-动态规划
+
+### 基础DP
+
+大部分动态规划最简化的程序往往是动态递推，利用数学归纳法从之前的DP状态循环递推到最终的解。
+
+1. DP状态的定义
+2. 状态转移方程
+3. 最终解位置
+
+动态规划和递归或分治没有本质区别，共性为找重复子问题，关键看有无最优子结构，动规中途可以淘汰次优解
+
+dp[i][j] = min(dp[i-1][j], dp[i-1][j] + A[i][j])
+
+
+### 高级DP
+
+1. 状态拥有更多的维度
+2. 状态方程更为复杂
+3. 本质考察逻辑思维和数学能力等内功
+
+关键需要确定：
+
+1. 维度（定义、压缩）
+2. 状态转移方程
+3. 初始化和边界条件
+
+> 面试中状态定义比较重要，竞赛中递归方程会比较难
+
+> 多练多思考，提升数学能力和抽象思维
+
+#### 实例
+
+##### 9. 股票买卖（121）
+
+三维DP搞定股票买卖系列：
+
+
+##### 10. Edit Distance（72）
+
+
+BFS或双向BFS
+
+字符串变换：（一般使用）二维数组定义DP状态
+
+> 隐含条件：两个字符串的长度在变换中相互靠近；增加和删除是对等的操作
+
+dp[i][j]: word1[0:i]与word[0:j]之间的编辑距离
+
+w1[-1] == w[-1] ?
+
+Y: dp[i][j] = dp[i-1, j-1]
+
+N: min(dp[i-1, j-1] + 1, dp[i-1][j]+1, dp[i, j-1] + 1)
+
+## 字符串算法
+
+字符串可变语言：
+
+C/C++, Ruby, PHP, Swift
+
+字符串不可变语言：
+
+Java, Python, C#, Javascript, Go
+
+### DP+String
+
+1. 编辑距离
+
+dp[i][j] = dp[i-1][j-1] if w1[i]==w2[j] else min(dp[i-1][j-1], dp[i-1]][j], dp[i][j-1])+1
+
+2. 最长公共子序列
+
+dp[i][j] = dp[i-1][j-1] + 1 if s1[i] == s2[j] else max(dp[i-1][j], dp[i][j-1])
+
+3. 最长公共子串
+
+dp[j][j] = dp[i-1][j-1] + 1 if s1[i] == s2[j] else 0
+
+4. 最长回文子序列
+
+- 暴力枚举起点和终点，判断子串是否回文
+- 枚举子串中心的一个字符（奇数长度）或中心两个（偶数长度），判断两边对称的字符长度
+- DP：dp[i][j]=(dp[i+1][j-1] || (j-i)<2) if s[i]==s[j]
+
+5. 正则表达式
+
+
+6. 不同子序列
+
+### 字符串匹配算法 （知道原理可以自己解释即可）
+
+> 给定两个字符串，问其中一个字符串在另一个字符串中出现的起点
+
+1. BrutalForce O(mn)
+
+高级算法都是在暴力枚举的基础上进行优化
+
+2. Rabin-Karp
+
+用hash值先过滤掉不可能相同的子串起点；如果hash值相同，再逐个字符比较
+
+但如果每次都是先取子串再调用系统hash进行计算的话，因hash函数会遍历子串，复杂度其实还是O(mn)
+
+使用滑动窗口进行加速：O(1)来更新hash值，从而整体上平均达到O(n)的复杂度
+
+3. KMP
+
+找已匹配片段最大前缀和最大后缀的最长长度
+
+insight：当知道在某个位置不匹配时，其实已经知道了前面能匹配的子串，可以利用已知匹配往后挪动
\ No newline at end of file