和树有关的题目求深度 -> 可以利用层序遍历 -> 用到层序遍历就想到使用BFS
896. 单调数列 - 水题
class Solution:
def isMonotonic(self, A) -> bool:
if sorted(A) == A or sorted(A, reverse=True) == A:
return True
return False
690. 员工的重要性 - 简单BFS
class Solution:
def getImportance(self, employees, id):
"""
:type employees: Employee
:type id: int
:rtype: int
"""
s = 0
Q = []
for i in employees:
if i.id == id:
Q.append(i)
while len(Q) != 0:
boss = Q.pop(0)
importance = boss.importance
subordinate = boss.subordinates
s += importance
for i in employees:
if i.id in subordinate:
Q.append(i)
return s
# e1 = Employee(1, 5, [2, 3])
# e2 = Employee(2, 3, [])
# e3 = Employee(3, 3, [])
# Employ = [e1, e2, e3]
# print(Solution().getImportance(Employ, 1))
111. 二叉树的最小深度 - 简单BFS
"""
BFS就是对树的层序遍历，发现的第一个叶子节点一定是深度最小的
"""
class Solution:
def minDepth(self, root: TreeNode) -> int:
if root == None:
return 0
Q = [(root, 1)]
while len(Q) != 0:
node, deepth = Q.pop(0)
if node.left == None and node.right == None:
return deepth
if node.left:
Q.append((node.left, deepth+1))
if node.right:
Q.append((node.right, deepth+1))
559. N叉树的最大深度 - 和楼上找最小深度思路一样
"""
BFS结束后肯定是到了这个树的最后一层，设置一个层数标志位，不断更新标志位，则BFS退出后标志位的值就是最后一层的层数。
"""
class Solution:
def maxDepth(self, root) -> int:
if root == None:
return 0
Q = [(root, 1)]
m = 0
while len(Q) != 0:
node, deepth = Q.pop(0)
m = deepth
for i in node.children:
Q.append((i, deepth+1))
return m
993. 二叉树的堂兄弟节点
"""
BFS - 记录每个节点的深度和父节点，再去比较题目中给定的x和y的深度与父节点
"""
class Solution:
def isCousins(self, root: TreeNode, x: int, y: int) -> bool:
if root == None:
return False
# 节点，层数，父节点
Q = [(root, 1, None)]
checkOver = 0
d = []
par = []
while len(Q) != 0:
node, depth, parent = Q.pop(0)
if node == None:
break
if node.val == x or node.val == y:
checkOver += 1
d.append(depth)
if parent:
par.append(parent.val)
else:
par.append(-10000)
if checkOver == 2:
break
if node.left:
Q.append((node.left, depth+1, node))
if node.right:
Q.append((node.right, depth+1, node))
if d[0] == d[1] and par[0] != par[1]:
return True
return False
102. 二叉树的层次遍历
"""
BFS - 利用set来记录层数
"""
class Solution:
def levelOrder(self, root: TreeNode):
if root == None:
return []
Q = [(root, 1)]
deepSet = set()
deepSet.add(1)
tmp = []
result = []
while len(Q) != 0:
node, deepth = Q.pop(0)
if deepth not in deepSet:
deepSet.add(deepth)
result.append(tmp)
tmp = []
tmp.append(node.val)
if node.left:
Q.append((node.left, deepth+1))
if node.right:
Q.append((node.right, deepth+1))
result.append(tmp)
return result
103. 二叉树的锯齿形层次遍历 - 和二叉树遍历完全一致
"""
两者代码的唯一不同在于锯齿形的遍历编号从0开始的奇数行需要逆转一下
"""
class Solution:
def zigzagLevelOrder(self, root: TreeNode):
if root == None:
return []
Q = [(root, 1)]
deepSet = set()
deepSet.add(1)
tmp = []
result = []
while len(Q) != 0:
node, deepth = Q.pop(0)
if deepth not in deepSet:
deepSet.add(deepth)
result.append(tmp)
tmp = []
tmp.append(node.val)
if node.left:
Q.append((node.left, deepth+1))
if node.right:
Q.append((node.right, deepth+1))
result.append(tmp)
# 唯一的差别就在这里
for i in range(len(result)):
if i % 2 == 1:
result[i] = result[i][::-1]
return result
127. 单词接龙 - 双向BFS
"""
使用最普通BFS模板会超时（暂无解决办法），本题可以思考为一棵树，根节点就是beginWord，它的子节点就是变换一个单词后的单词，子节点的子节点就是子节点变换一个单词... 然后在那一层发现了目标节点，返回该层的层数
"""
class Solution:
def ladderLength(self, beginWord: str, endWord: str, wordList) -> int:
if beginWord == endWord:
return 0
Q = []
for i in wordList:
if self.OneDefferent(i, beginWord):
Q.append((i, 1))
s = set()
while len(Q) != 0:
word, step = Q.pop(0)
# print(word)
if word == endWord:
return step+1
if word in wordList:
wordList.remove(word)
for i in wordList:
if self.OneDefferent(i, word):
Q.append((i, step+1))
return 0
def OneDefferent(self,str1, str2):
str1 = list(str1); str2 = list(str2)
check = 0
for i in range(len(str2)):
if str1[i] != str2[i]:
check += 1
if check > 1 :
return False
if check == 1:
return True
"""
评论中提到的双向BFS(还在理解中)：
当某层数量过大的时候，BFS会耗时很多。所以采用两端一起走的方式，不断比较，那一头走的少就走那一头，如果有交集最后肯定会相遇。
"""
class Solution:
def ladderLength(self, beginWord: str, endWord: str, wordList) -> int:
if endWord not in wordList:
return 0
head = {beginWord}
tail = {endWord}
wordSet = set(wordList)
wordSet.remove(endWord)
res = 0
while head and tail:
res += 1
if len(head) > len(tail):
head, tail = tail, head
nextLevel = set()
for i in head:
for j in range(len(i)):
for letter in range(97, 97+26):
# 利用二十六个字母在每一个位置进行替换
newWord = i[:j] + chr(letter) + i[j+1:]
if newWord in tail:
return res + 1
if newWord not in wordSet:
continue
wordSet.remove(newWord)
nextLevel.add(newWord)
head = nextLevel
return 0
"""
BFS双向的模板：适用于从某个初始状态到某个终止状态求最短路径
head = {初始状态}
tail = {终止状态}
while head and tail:
# 每次都从短的开始
if len(head) > len(tail):
head, tail = tail, head
nextLeval = set()
for i in head:
# 扩展下一层
if 扩展的下一层的某个元素 in tail：
# 表示已经找到了
return
head = nextLevel
# 每次的head和tail都在更新为某层的状态
"""
433. 最小基因变化 - 套用上面的双向BFS模板
"""
和上面的单词结论几乎一致，都是每次给定一个初始状态、一个终止状态，改变一个字母，找到最小的变化（其实也就是找到最小路径）
"""
class Solution:
def minMutation(self, start: str, end: str, bank) -> int:
change = ["A", "C", "G", "T"]
if end not in bank or len(bank) == 0:
return -1
head = {start}
tail = {end}
bank.remove(end)
res = 0
while head and tail:
res += 1
if len(head) > len(tail):
head, tail = tail, head
nextLevel = set()
# 拓展下一层
for i in head:
for j in range(len(i)):
for cha in change:
newGene = i[:j]+cha+i[j+1:]
if newGene in tail:
return res
if newGene not in bank:
continue
nextLevel.add(newGene)
# 已经走过的就不用再走了
bank.remove(newGene)
head = nextLevel
return -1