上周状态太差了，重新振作一下！结果这一part的题目都好难。。。好在虽然不会做，但是心态还不错，没有烦躁。
307. Range Sum Query - Mutable: 做出来一个lowlow的解法，不过也AC了，看了一下tag，原来是segment tree。借这题把segment tree复习一遍。其实这道题完美的利用了segment tree的所有性质，create，update，query。其实segment tree就是在普通tree的基础上记录了更多的信息以便于查询。这里记录的是sum，也可以记录average。
class NumArray(object):
def __init__(self, nums):
"""
:type nums: List[int]
"""
self.root = self.buildTree(nums, 0, len(nums)-1)
def buildTree(self, nums, start, end):
if start > end:
return None
root = SegmentTreeNode(start, end)
if start == end:
root.sum = nums[start] # only one node
else:
mid = start + (end - start) / 2
root.left = self.buildTree(nums, start, mid)
root.right = self.buildTree(nums, mid + 1, end)
root.sum = root.left.sum + root.right.sum
return root
def update(self, i, val):
"""
:type i: int
:type val: int
:rtype: void
"""
self.updateValue(self.root, i, val)
def updateValue(self, root, pos, val):
if root.start == root.end:
root.sum = val
else:
mid = root.start + (root.end - root.start) / 2;
if pos <= mid:
self.updateValue(root.left, pos, val);
else:
self.updateValue(root.right, pos, val);
root.sum = root.left.sum + root.right.sum;
def sumRange(self, i, j):
"""
:type i: int
:type j: int
:rtype: int
"""
return self.sumRangeValue(self.root, i, j)
def sumRangeValue(self, root, start, end):
if root.end == end and root.start == start: # find the current range
return root.sum
else:
mid = root.start + (root.end - root.start) / 2
if end <= mid:
return self.sumRangeValue(root.left, start, end)
elif start >= mid+1:
return self.sumRangeValue(root.right, start, end)
else:
return self.sumRangeValue(root.right, mid+1, end) + self.sumRangeValue(root.left, start, mid)
class SegmentTreeNode(object):
def __init__(self, start, end):
self.start = start
self.end = end
self.left = None
self.right = None
self.sum = 0
# Your NumArray object will be instantiated and called as such:
# obj = NumArray(nums)
# obj.update(i,val)
# param_2 = obj.sumRange(i,j)
309. Best Time to Buy and Sell Stock with Cooldown：这题又是没想出来，虽然之前做过但是还是没什么思路，题目还是要尽力去思考，至少二十分钟没思路再去看答案，不过看过得答案也很快就忘记了。
class Solution(object):
def maxProfit(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
# 这类型的题目是DP问题，DP问题首先就要找到DP问题的state，按照最简易的方法
# 可以找到三个state
# buy[i] means before day i what is the maxProfit for any sequence end with buy
# sell[i] means before day i what is the maxProfit for any sequence end with sell.
# rest[i] means before day i what is the maxProfit for any sequence end with rest.
# 他们之间的逻辑关系是，在买之前必须要rest，在卖之前必须要买。
# buy[i] = max(rest[i-1]-price, buy[i-1])
# sell[i] = max(buy[i-1]+price, sell[i-1])
# rest当天不产生交易，所以由前面的值所决定
# rest[i] = max(sell[i-1], buy[i-1], rest[i-1])
# 同时rest肯定是跟在sell后面的
# rest[i] = sell[i-1]
# 替代入前面的公式，可以推导出buy和sell的关系
# buy[i] = max(sell[i-2]-price, buy[i-1])
# sell[i] = max(buy[i-1]+price, sell[i-1])
# Since states of day i relies only on i-1 and i-2 we can reduce the O(n) space to O(1).
if len(prices) < 2:
return 0
sell, buy, prev_sell, prev_buy = 0, -prices[0], 0, 0
for price in prices:
prev_buy = buy
buy = max(prev_sell - price, prev_buy)
prev_sell = sell
sell = max(prev_buy + price, prev_sell)
return sell
310. Minimum Height Trees: 这题做出了个TLE的版本，就是把每一个节点到其最远的节点的长度找一遍，然后选出最短的那些，看了答案后，有剪枝的方法，很奇妙。
class Solution(object):
def findMinHeightTrees(self, n, edges):
"""
:type n: int
:type edges: List[List[int]]
:rtype: List[int]
"""
if n == 1:
return [0]
adj = [set() for _ in xrange(n)]
for i, j in edges:
adj[i].add(j)
adj[j].add(i)
# 这里有点像topology sort，先找出入度为1的
leaves = [i for i in xrange(n) if len(adj[i]) == 1]
while n > 2: #如果剩余的点超过两个
n -= len(leaves)
newLeaves = []
for i in leaves:
j = adj[i].pop() # 因为len为1，所以pop出来的只能是一个值
adj[j].remove(i) # 然后从这个值的边中删掉进来的node
if len(adj[j]) == 1: # 更新入度为1的值
newLeaves.append(j)
leaves = newLeaves
return leaves
# 这样的值只可能是两个，本质就是找出图中端到端的最长路径，这个最长路径的中间一个点或者两个点就是，找的方法就是从外向内进行bfs剪枝
311. Sparse Matrix Multiplication: 终于写出来了一题。。。都是泪。。。
313. Super Ugly Number: 又手写出来一题yeah！
314. Binary Tree Vertical Order Traversal：level traversal，只是要记录每一个值的degree，root的degree为0，left就减一，right就加一，然后记录到一个hashtable里就可以了
318. Maximum Product of Word Lengths：比较两个字符串是否有重复的字母，就把字符串映射到数字上，26位的bit，用1代表有，0代表无。
319. Bulb Switcher：一道数学证明题，不过要找出其中的规律，把事情说明白也是一个挺绕的过程
320. Generalized Abbreviation: 实在是不会做，连答案都没看懂，明明就是一道backtracking的题目，不过感觉好难
class Solution(object):
def generateAbbreviations(self, word):
"""
:type word: str
:rtype: List[str]
"""
res = []
self.dfs(res, word, 0, "", 0)
return res
def dfs(self, res, word, pos, cur, count):
if pos == len(word):
if count > 0:
cur += str(count)
res.append(cur);
else:
# 缩减当前的字母（也就是说跳过当前的字母），增加pos和count的值
self.dfs(res, word, pos + 1, cur, count + 1) # abbreviate the current character, cur 不变化只增加pos和count
# 如果count大于0那么重新组合cur，保留当前的字母
if count > 0:
cur = cur + str(count) + word[pos]
else:
cur = cur + word[pos]
# 增加pos，重置count为0
self.dfs(res, word, pos + 1, cur, 0) # keep the current character， cur变化但是加上了当前的char，和之前留下的count
322. Coin Change: 这道题还算是简单
