50-1. 乘积最大子数组

思路1:找到状态转移方程:

maxf[i]:表示在i处最大连乘数
minf[i]:表示在i处最小连乘数
maxf[i] = max(nums[i],nums[i]*minf[i-1],nums[i]*maxf[i-1])
minf[i] = min(nums[i],nums[i]*minf[i-1],nums[i]*maxf[i-1])

#maxf[i]:表示在i处最大连乘数
#minf[i]:表示在i处最小连乘数
#maxf[i] = max(nums[i],nums[i]*minf[i-1],nums[i]*maxf[i-1])
#minf[i] = min(nums[i],nums[i]*minf[i-1],nums[i]*maxf[i-1])
class Solution:def maxProduct(self, nums):n = len(nums)maxf,minf = [0]*n,[0] * nmaxf[0],minf[0] = nums[0],nums[0]for i in range(1,n):maxf[i] = max(nums[i], nums[i] * minf[i - 1], nums[i] * maxf[i-1])minf[i] = min(nums[i], nums[i] * minf[i - 1], nums[i] * maxf[i-1])print('==maxf:', maxf)return max(maxf)nums = [2,3,-2,4]
sol = Solution()
sol.maxProduct(nums)

思路2:优化版 由于第 i 个状态只和第 i - 1个状态相关，可以只用两个变量来维护 i - 1时刻的状态，一个维护 max,　一个维护 min

class Solution:def maxProduct(self, nums):min_value = nums[0]max_value = nums[0]res = nums[0]for i in range(1, len(nums)):mx = max_valuemn = min_valuemax_value = max(nums[i], nums[i]*mx, nums[i]*mn)min_value = min(nums[i], nums[i]*mx, nums[i]*mn)print('==max_value:', max_value)print('==min_value:', min_value)res = max(max_value, res)print('==res:', res)
nums = [2,3,-2,4]
sol = Solution()
sol.maxProduct(nums)

50-2.三个数的最大乘积

思路:从小到大排序，如果都是正数则结果是最后三个相乘，如有正有负，结果有可能就是前两个相乘在乘以最后一个正数

class Solution:def maximumProduct(self, nums):nums = sorted(nums)return max(nums[-1]*nums[-2]*nums[-3], nums[0]*nums[1]*nums[-1])# nums = [1, 2, 3, 4]
nums = [-1, -2, 1, 2, 3]
sol = Solution()
sol.maximumProduct(nums)

51. 最小栈

class MinStack:def __init__(self):"""initialize your data structure here."""self.stack = []def push(self, x: int) -> None:self.stack.append(x)def pop(self) -> None:self.stack.pop()def top(self) -> int:return self.stack[-1]def min(self) -> int:return min(self.stack)# Your MinStack object will be instantiated and called as such:
# obj = MinStack()
# obj.push(x)
# obj.pop()
# param_3 = obj.top()
# param_4 = obj.min()

c++实现:

class MinStack {
public:stack<int> stack_A;stack<int> min_stack;/** initialize your data structure here. */MinStack() {}void push(int x) {stack_A.push(x);if(min_stack.empty() || min_stack.top()>=x){min_stack.push(x);}}void pop() {if(stack_A.top() == min_stack.top()){min_stack.pop();}stack_A.pop();}int top() {return stack_A.top();}int min() {return min_stack.top();}
};/*** Your MinStack object will be instantiated and called as such:* MinStack* obj = new MinStack();* obj->push(x);* obj->pop();* int param_3 = obj->top();* int param_4 = obj->min();*/

52.多数元素

排序:

class Solution:def majorityElement(self, nums: List[int]) -> int:return sorted(nums)[len(nums)//2]

投票法(最优解):

class Solution:def majorityElement(self, nums: List[int]) -> int:votes = 0for num in nums:if votes == 0:x = numif num == x:votes += 1else:votes -= 1# print('==x:', x)# print('==votes:', votes)return x

53-1.打家劫舍

class Solution(object):def rob(self, nums):""":type nums: List[int]:rtype: int"""if len(nums)==0:return 0if len(nums)<2:return max(nums)opt = [0]*len(nums)opt[0] = nums[0]opt[1] = max(nums[0],nums[1])for i in range(2, len(nums)):opt[i] = max(opt[i-2]+nums[i],opt[i-1])print('=opt:', opt)return max(opt)nums = [2,7,9,3,1]
sol = Solution()
sol.rob(nums)

53-2. 打家劫舍 II

class Solution(object):def rob(self, nums):""":type nums: List[int]:rtype: int"""if len(nums)==0:return 0if len(nums)<=2:return max(nums)opt1 = [0] * len(nums)opt2 = [0] * len(nums)#不抢第一家opt1[0] = 0opt1[1] = nums[1]#不抢最后一家opt2[0] = nums[0]opt2[1] = max(nums[:2])for i in range(2,len(nums)):opt1[i]=max(opt1[i-2]+nums[i], opt1[i-1])print(opt1)for i in range(2, len(nums)-1):opt2[i] = max(opt2[i - 2] + nums[i], opt2[i - 1])print(opt2)return max(opt1[-1],opt2[-2])
nums=[1,2,3,1]
sol = Solution()
res = sol.rob(nums)
print('res:')
print(res)

53-3. 打家劫舍 III

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def helper(self,node):if node is None:return 0, 0choose_l_value,no_choose_l_value = self.helper(node.left)choose_r_value,no_choose_r_value = self.helper(node.right)return node.val+no_choose_l_value+no_choose_r_value, max(choose_l_value,no_choose_l_value)+max(choose_r_value,no_choose_r_value)def rob(self, root: TreeNode) -> int:return max(self.helper(root))

54.岛屿数量

思路：递归　也就是求1的连通域个数,从１开始进行遍历,将遍历过得1依次置位0,遍历的次数就是连通域个数

# 求1的连通域个数,从１开始进行遍历,将遍历过得1依次置位0,遍历的次数就是连通域个数
class Solution:def helper(self, i, j, h, w):if i < 0 or i >= h or j < 0 or j >= w or self.grid[i][j] == "0":returnself.grid[i][j] = "0"self.helper(i - 1, j, h, w)self.helper(i + 1, j, h, w)self.helper(i, j-1, h, w)self.helper(i, j+1, h, w)def numIslands(self, grid):if len(grid) == 0:return []self.grid = gridh, w = len(grid), len(grid[0])nums = 0for i in range(h):for j in range(w):if self.grid[i][j] == "1":nums += 1self.helper(i, j, h, w)print('==self.grid:', self.grid)print('==nums:', nums)return numsgrid = [["1", "1", "1", "1", "0"],["1", "1", "0", "1", "0"],["1", "1", "0", "0", "0"],["0", "0", "0", "0", "0"]
]sol = Solution()
sol.numIslands(grid)

c++实现:

class Solution {
public:vector<vector<char>> grid;int h;int w;void help(int i, int j){if(i < 0 || i > this->h - 1 || j < 0 || j > this->w - 1 || this->grid[i][j] == '0'){return ;}this->grid[i][j] = '0';help(i - 1, j);help(i + 1, j);help(i, j - 1);help(i, j + 1);}int numIslands(vector<vector<char>>& grid) {this->grid = grid;this->h = grid.size();this->w = grid[0].size();int res = 0;for(int i = 0; i < this->h; i++){for(int j = 0; j < this->w; j++){if(this->grid[i][j] == '1'){res += 1;}help(i, j);}}return res;}
};

55.反转链表

思路１：双指针

class Solution(object):def reverseList(self, head):""":type head: ListNode:rtype: ListNode"""# 申请两个节点，pre和 cur，pre指向Nonepre = Nonecur = head# 遍历链表，while循环里面的内容其实可以写成一行while cur:# 记录当前节点的下一个节点tmp = cur.next# 然后将当前节点指向precur.next = pre# pre和cur节点都前进一位pre = curcur = tmpreturn pre   

c++实现:

/*** Definition for singly-linked list.* struct ListNode {*     int val;*     ListNode *next;*     ListNode() : val(0), next(nullptr) {}*     ListNode(int x) : val(x), next(nullptr) {}*     ListNode(int x, ListNode *next) : val(x), next(next) {}* };*/
class Solution {
public:ListNode* reverseList(ListNode* head) {ListNode* pre = nullptr;ListNode* temp = head;while(head){temp = head->next;head->next = pre;pre = head;head = temp;}return pre;}
};

思路2.递归法

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, x):
#         self.val = x
#         self.next = Noneclass Solution:def reverseList(self, head: ListNode) -> ListNode:# pre = None# cur = head# while cur:#     node = cur.next#     cur.next = pre#     pre = cur#     cur = node# return preif head is None or head.next is None:return headnew_node = self.reverseList(head.next)print('head.val',head.val)head.next.next = headhead.next = Nonereturn new_node

56-1. 课程表

思路:对于这种从图找拓扑排序 ,只有有向无环图能够找到,将入度为0的节点先进入队列,在利用bfs进行出队处理,此时将出队的节点的下一个节点的度进行减一计数,同时遍历的节点数进行加一,最终节点都进行了遍历,则说明找到了拓扑排序.

思路1:用邻接列表

class Solution:def canFinish(self, numCourses, prerequisites):indegrees = [0] * numCourses  # 入度列表print('==indegrees:', indegrees)adjacency = [[] for i in range(numCourses)]  # 邻接列表 存储节点的下一个节点print('=adjacency:', adjacency)#得到入度和每个课程的邻接列表for cur, pre in prerequisites:indegrees[cur] += 1adjacency[pre].append(cur)print('====indegrees:', indegrees)print('====adjacency:', adjacency)quene = []# 如果度为0　就进入队列for i in range(len(indegrees)):if indegrees[i] == 0:quene.append(i)print('==quene:', quene)num_nodes = 0while quene:node = quene.pop(0)num_nodes += 1for next_node in adjacency[node]:indegrees[next_node] -= 1  # 找出下一个点相应的度-1if indegrees[next_node] == 0:  # 入度为0quene.append(next_node)print('==num_nodes:', num_nodes)return num_nodes == numCourses# numCourses, prerequisites = 2, [[1, 0]]
# numCourses, prerequisites = 2, [[1, 0], [0, 1]]
numCourses, prerequisites = 6, [[3, 0], [3, 1], [4, 1], [4, 2], [5, 3], [5, 4]]
sol = Solution()
res = sol.canFinish(numCourses, prerequisites)
print('res:', res)

思路2:用邻接矩阵的bfs

class Solution:def canFinish(self, numCourses, prerequisites):indegrees = [0] * numCourses  # 度列表adjacency = [[0 for i in range(numCourses)] for i in range(numCourses)]  # 邻接矩阵　表示节点之间关系print('==init adjacency:', adjacency)for cur, pre in prerequisites:indegrees[cur] += 1adjacency[pre][cur] = 1print('==init adjacency complete:', adjacency)print('==init indegrees complete:', indegrees)quene = []for i in range(len(indegrees)):if indegrees[i] == 0:quene.append(i)print('==quene:', quene)num_nodes = 0while quene:node = quene.pop()num_nodes += 1for j in range(numCourses):if adjacency[node][j] == 1:next_node = jadjacency[node][j] -= 1indegrees[next_node] -= 1if indegrees[next_node] == 0:quene.append(next_node)print('==num_nodes:', num_nodes)return num_nodes == numCourses# numCourses = 2
# prerequisites = [[0, 1]]
numCourses = 4
prerequisites = [[1, 0], [2, 0], [3,1],[3,2]]
sol = Solution()
sol.canFinish(numCourses, prerequisites)

56-2:课程表 II

思路：有向无环图，ＢＦＳ遍历

class Solution:def canFinish(self, numCourses, prerequisites):indegrees = [0] * numCourses  # 入度列表print('==indegrees:', indegrees)adjacency = [[] for i in range(numCourses)]  # 邻接列表print('=adjacency:', adjacency)#得到入度和每个课程的邻接列表for cur, pre in prerequisites:indegrees[cur] += 1adjacency[pre].append(cur)print('====indegrees:', indegrees)print('====adjacency:', adjacency)quene = []# 如果度为0　就进入队列for i in range(len(indegrees)):if indegrees[i] == 0:quene.append(i)print('==quene:', quene)num_nodes = 0learn_node = []while quene:node = quene.pop(0)print('=======node', node)learn_node.append(node)num_nodes += 1for next_node in adjacency[node]:indegrees[next_node] -= 1  # 找出下一个点相应的度-1if indegrees[next_node] == 0:  # 入度为0quene.append(next_node)print('==num_nodes:', num_nodes)return learn_node if num_nodes == numCourses else []# numCourses, prerequisites = 2, [[1, 0]]
# numCourses, prerequisites = 2, [[1, 0], [0, 1]]
numCourses, prerequisites = 6, [[3, 0], [3, 1], [4, 1], [4, 2], [5, 3], [5, 4]]
sol = Solution()
res = sol.canFinish(numCourses, prerequisites)
print('res:', res)

思路2:用邻接矩阵的bfs

class Solution:def canFinish(self, numCourses, prerequisites):indegrees = [0] * numCourses  # 度列表adjacency = [[0 for i in range(numCourses)] for i in range(numCourses)]  # 邻接矩阵　表示节点之间关系print('==init adjacency:', adjacency)for cur, pre in prerequisites:indegrees[cur] += 1adjacency[pre][cur] = 1print('==init adjacency complete:', adjacency)print('==init indegrees complete:', indegrees)quene = []for i in range(len(indegrees)):if indegrees[i] == 0:quene.append(i)print('==quene:', quene)num_nodes = 0learn_nodes = []while quene:node = quene.pop()learn_nodes.append(node)num_nodes += 1for j in range(numCourses):if adjacency[node][j] == 1:next_node = jadjacency[node][j] -= 1indegrees[next_node] -= 1if indegrees[next_node] == 0:quene.append(next_node)print('==num_nodes:', num_nodes)print('=learn_nodes:', learn_nodes)return learn_nodes if num_nodes == numCourses else []# numCourses = 2
# prerequisites = [[0, 1]]
numCourses = 4
prerequisites = [[1, 0], [2, 0], [3,1],[3,2]]
sol = Solution()
sol.canFinish(numCourses, prerequisites)

57.实现 Trie (前缀树)

思路:利用字典存储每个单词，同时用特殊字符结尾。

class Trie:def __init__(self):"""Initialize your data structure here."""self.root = {}self.word_end = -1def insert(self, word):"""Inserts a word into the trie."""curNode = self.rootfor c in word:if c not in curNode:curNode[c] = {}curNode = curNode[c]curNode[self.word_end] = True# print('==curNode:', curNode)def search(self, word):"""Returns if the word is in the trie."""curNode = self.rootfor c in word:if c not in curNode:return FalsecurNode = curNode[c]if self.word_end not in curNode:return Falsereturn Truedef startsWith(self, prefix):"""Returns if there is any word in the trie that starts with the given prefix."""curNode = self.rootfor c in prefix:if c not in curNode:return FalsecurNode = curNode[c]return Trueword = 'apple'
prefix = 'ad'
obj = Trie()
obj.insert(word='apple')
obj.insert(word='add')
# obj.insert(word='app')
print('tree:', obj.root)
param_2 = obj.search(word)
print('search res:', param_2)
param_3 = obj.startsWith(prefix)
print('==param_3:', param_3)

58.数组中的第K个最大元素

思路：排序　取第ｋ个值就可

class Solution:def quicksort(self, arr):if len(arr) <= 1:return arrprivot = arr[len(arr) // 2]left = [i for i in arr if i < privot]middle = [i for i in arr if i == privot]right = [i for i in arr if i > privot]# left = [arr[i] for i in range(len(arr)) if arr[i] < privot]# middle = [arr[i] for i in range(len(arr)) if arr[i] == privot]# right = [arr[i] for i in range(len(arr)) if arr[i] > privot]return self.quicksort(left) + middle + self.quicksort(right)def findKthLargest(self, nums, k):return self.quicksort(nums)[::-1][k-1]# nums = [3, 2, 1, 5, 6, 4]
# k = 2
nums = [3,2,3,1,2,4,5,5,6]
k = 4
sol = Solution()
res = sol.findKthLargest(nums, k)
print('res:', res)

思路2:topk问题用最小堆

class Solution:def findKthLargest(self, nums, k):arr = []heapq.heapify(arr)for i in range(k):heapq.heappush(arr, nums[i])for i in range(k, len(nums)):heapq.heappush(arr, nums[i])heapq.heappop(arr)print('==arr:', arr)return arr[0]arr = [3,2,1,5,6,4]
k = 2
sol = Solution()
sol.findKthLargest(arr, k)

59.最大正方形

思路:题目既然求最大正方形面积，那就先由2*2正方形拓展更大即可，也就是可以用动态规划来存储左上角，左边，上边的最小值，也是正方形边长

１．转移方程为 dp[i][j] = min(dp[i-1][j],dp[i][j-1].dp[i-1][j-1])+1

２．初始化边界条件为: dp[:][0] = matrix[:][0] dp[0][:] = matrix[0][:]

class Solution:def maximalSquare(self, matrix):max_side = 0h,w = len(matrix),len(matrix[0])dp = [[0 for i in range(w)] for i in range(h)]print('初始化dp',np.array(dp))for i in range(h):dp[i][0] = int(matrix[i][0])max_side = max(max_side, dp[i][0])for i in range(w):dp[0][i] = int(matrix[0][i])max_side = max(max_side, dp[0][i])print('初始化边界dp',np.array(dp))for i in range(1,h):for j in range(1,w):if matrix[i][j]=='1':dp[i][j] = min(dp[i-1][j-1], dp[i-1][j], dp[i][j-1])+1max_side = max(max_side, dp[i][j])print('转移好dp',np.array(dp))return max_side**2matrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
# matrix = [["0","1"],["1","0"]]
sol = Solution()
res=  sol.maximalSquare(matrix)
print(res)

60.翻转二叉树

思路:递归遍历左右子树进行交换即可

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def invertTree(self, root: TreeNode) -> TreeNode:if root is None:return Noneleft = self.invertTree(root.left)right = self.invertTree(root.right)root.left = rightroot.right = leftreturn root

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:TreeNode* invertTree(TreeNode* root) {if(root == nullptr){return nullptr;}TreeNode* left = invertTree(root->left);TreeNode* right = invertTree(root->right);root->left = right;root->right = left;return root;}
};

61.请判断一个链表是否为回文链表

利用列表将列表值进行拷贝，在判断是否是回文字符串

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, x):
#         self.val = x
#         self.next = Noneclass Solution:def isPalindrome(self, head: ListNode) -> bool:stack= []while head:stack.append(head.val)head = head.nextreturn stack==stack[::-1]

c++实现:

/*** Definition for singly-linked list.* struct ListNode {*     int val;*     ListNode *next;*     ListNode() : val(0), next(nullptr) {}*     ListNode(int x) : val(x), next(nullptr) {}*     ListNode(int x, ListNode *next) : val(x), next(next) {}* };*/
class Solution {
public:bool isPalindrome(ListNode* head) {vector<int> res;while(head){res.push_back(head->val);head = head->next;}int left=0;int right=res.size()-1;while(left<right){if(res[left]==res[right]){left+=1;right-=1;}else{return false;}}return true;}
};

62:二叉树的最近公共祖先

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':if root is None or root==p or root==q:#递归终止条件　节点为空　或者节点等于p,q其中之一return rootleft = self.lowestCommonAncestor(root.left, p, q)#遍历左子树right = self.lowestCommonAncestor(root.right, p, q)#遍历右子树if left is None:#左子树为空　就去右子树　return rightif right is None:#右子树为空　就去左子树　return leftreturn root#左右子树都不为空　说明找到了节点　

c++实现:

代码段 小部件

63.除自身以外数组的乘积

思路１：超时

#超时时间复杂度O(N)
class Solution:def productExceptSelf(self, nums):output = len(nums)*[0]for i in range(len(nums)):temp = 1for j in nums[:i]:temp*=jfor j in nums[i+1:]:temp*=joutput[i] = temp# print('==output:', output)return outputnums = [1, 2, 3, 4]
sol = Solution()
sol.productExceptSelf(nums)

思路２：利用空间换时间

1.借用左右数组来存储值，L[i]代表i左边的乘积值,R[i]代表i右边的乘积值

2.最终i处的值为L[i]*R[i]

class Solution:def productExceptSelf(self, nums):length = len(nums)L,R,output = [0]*length,[0]*length,[0]*lengthL[0] = 1for i in range(1, length):L[i] = L[i-1]*nums[i-1]print('==L:', L)R[length-1] = 1for i in range(length-2, -1, -1):print('==i:', i)R[i] = R[i + 1] * nums[i + 1]print('==R:', R)for i in range(length):output[i] = L[i]*R[i]return outputnums = [1, 2, 3, 4]
sol = Solution()
sol.productExceptSelf(nums)

64.滑动窗口最大值

思路1.超时O(n*k)

class Solution:def maxSlidingWindow(self, nums, k):#时间复杂度O(Nk)超时了res = []for i in range(len(nums)-k+1):res.append(max(nums[i:i+k]))return res

思路2:

动态规划：时间复杂度O(N)
1.将数组分成k+1个，剩下的一个可能不足; 
2.left数组存储每个拆分的从左到右的值,对于left来说每个块最右边元素最大;
3.right数组存储每个拆分的从右到左的值,对于right来说每个块最左边元素最大;
4.最后在利用left和right求最大值,max(left[i],right(j)) i每个块最右边元素索引,j每个块最左边元素索引

class Solution:def maxSlidingWindow(self, nums, k):n = len(nums)if n * k == 0:return []if k == 1:return numsleft = [0] * nleft[0] = nums[0]right = [0] * nright[n - 1] = nums[n - 1]for i in range(1, n):#从左往右if i%k==0:#分块的第一个元素left[i] = nums[i]else:left[i] = max(left[i-1],nums[i])# 从右往左j = n-i-1# 分块的最右边元素if (j+1) % k == 0:right[j] = nums[j]else:right[j] = max(right[j + 1], nums[j])print('===left:', left)print('===right:', right)#最后在利用left和right求最大值output = []for i in range(n - k + 1):output.append(max(left[i + k - 1], right[i]))return outputnums = [1,3,-1,-3,5,3,6,7]
k = 3
sol = Solution()
res = sol.maxSlidingWindow(nums, k)
print('res:', res)

思路3:双端队列:用一个队列一直存储更新最大值

# 双端队列:用一个队列一直存储更新最大值
class Solution:def maxSlidingWindow(self, nums, k):length = len(nums)if length == 0:return []res = []quene = []for j in range(length):i = j-k+1if i > 0 and quene[0] == nums[i-1]:#当要左移掉的元素等于quene头部元素,那么quene就移除头部元素quene.pop(0)while quene and quene[-1] < nums[j]:#保持quene里面都是单调递减的,且头部元素最大quene.pop()quene.append(nums[j])print('==quene:', quene)if i >= 0:res.append(quene[0])return resnums = [1, 3, -1, -3, 5, 3, 6, 7]
k = 3
sol = Solution()
res = sol.maxSlidingWindow(nums, k)
print(res)

c++代码:

class Solution {
public:vector<int> maxSlidingWindow(vector<int>& nums, int k) {vector<int> res;deque<int> queue_A;for(int i=0;i<nums.size();i++){int j=i-k+1;if(j>0 && nums[j-1]==queue_A.front()){queue_A.pop_front();}while (queue_A.size() && queue_A.back()<nums[i]){queue_A.pop_back();}queue_A.push_back(nums[i]);if(j>=0){res.push_back(queue_A.front());}     }return res;}
};

65.搜索二维矩阵 II

class Solution:def find(self,number,matrix):rows=len(matrix)#行数cols=len(matrix[0])#列数if rows<0 and cols<0:return Falsecol=0row=rows-1while row>=0 and col<cols:if matrix[row][col]<number:col+=1elif matrix[row][col]>number:row-=1else:return True#找到return False#没找到
if __name__ == '__main__':matrix = [[1, 3, 5, 6],[2, 5, 8, 12],[4, 9, 10, 17],[6, 11, 11, 18]]sol=Solution()print(sol.find(17,matrix))

66. 完全平方数

思路:可看成M(n) = M(n-1k)+1,这里就可以用回溯当成求子集问题,但是容易超出时间限制．

1.回溯

#公式为　M(n) = M(n - k) + 1
import math
class Solution(object):def numSquares(self, n):square_nums = [i**2 for i in range(1, int(math.sqrt(n))+1)]print('==square_nums:', square_nums)res = []track = []def minNumSquares(k,track):""" recursive solution """# bottom cases: find a square numberif k in square_nums:track.append(k)res.append(track)#满足选择条件return 1min_num = float('inf')# Find the minimal value among all possible solutionsfor square in square_nums:if k < square:break# 满足选择列表store = track.copy()track.append(square)#做选择new_num = minNumSquares(k-square, track) + 1#回溯track = store#撤消选择min_num = min(min_num, new_num)return min_numreturn minNumSquares(n, track), res
n = 3
sol = Solution()
numbers, res = sol.numSquares(n)
print('个数:', numbers, res)

2.对于递归这种,其实都是可以用dp来减少计算量

#公式为　M(n) = M(n - k) + 1
class Solution(object):def numSquares(self, n):""":type n: int:rtype: int"""square_nums = [i ** 2 for i in range(0, int(math.sqrt(n)) + 1)]print('square_nums==:', square_nums)dp = [float('inf')] * (n + 1)# bottom casedp[0] = 0for i in range(1, n + 1):for square in square_nums:if i < square:#小于平方的数 就breakbreakprint('==square:', square)dp[i] = min(dp[i], dp[i - square] + 1)print('==dp:', dp)return dp[-1]
n = 4
sol = Solution()
numbers = sol.numSquares(n)
print('个数:', numbers)

c++实现:

class Solution {
public:int numSquares(int n) {vector<int> dp(n+1, INT_MAX);vector<int> nums;for(int i=1; i < int(sqrt(n)) + 1; i++){nums.push_back(pow(i, 2));}dp[0] = 0;for(int i = 1; i < n+1; i++){for(int j=0; j < nums.size(); j++){if(i < nums[j]){break;}dp[i] = min(dp[i], dp[i - nums[j]] + 1);}}return dp[n];}
};

67.移动零

思路1:移０法

class Solution:def moveZeroes(self, nums: List[int]) -> None:"""Do not return anything, modify nums in-place instead."""n = len(nums)i=0while 0 in nums:nums.remove(0)i+=1nums.extend([0]*i)return nums

思路２:指针记录非0索引

class Solution:def moveZeroes(self, nums: List[int]) -> None:"""Do not return anything, modify nums in-place instead."""idx = 0 n = len(nums)for i in range(len(nums)):if nums[i]!=0:nums[idx] = nums[i]idx+=1nums[idx:] = (n - idx )*[0]return nums

思路3:指针　交换数字

class Solution:def moveZeroes(self, nums: List[int]) -> None:"""Do not return anything, modify nums in-place instead."""idx = 0n = len(nums)for i in range(len(nums)):if nums[i]!=0:nums[idx], nums[i] = nums[i], nums[idx]idx+=1# print(idx)# print(nums)# nums[idx:] = (n - idx )*[0]return nums

思路4:优化特殊非０元素

class Solution:def moveZeroes(self, nums: List[int]) -> None:"""Do not return anything, modify nums in-place instead."""idx = 0n = len(nums)for i in range(len(nums)):if nums[i]!=0:if i!=idx:nums[idx], nums[i] = nums[i], nums[idx]idx+=1else:idx +=1# print(idx)# print(nums)# nums[idx:] = (n - idx )*[0]return nums

68.寻找重复数

思路:对于上述题目示例１，将数组值作为索引，会发现陷入无穷循环，而无穷循环的起始点就是重复出现的数，故构成一个环，所以就想到用快慢指针进行解决，如下图所示,A是起点，Ｂ是环开始点，Ｃ是相遇点，快指针是慢指针速度的两倍。

在Ｃ点相遇以后，在从起始点和Ｃ点用相同速度奔跑，就在Ｂ点相遇了，即可以得到重复的数字。

class Solution:def findDuplicate(self, nums: List[int]) -> int:fast = 0slow = 0while True:# print('==fast:', fast)# print('==slow:', slow)fast = nums[nums[fast]]slow = nums[slow]if fast == slow:breakstart = 0while True:start = nums[start]fast = nums[fast]if start ==fast:break# print(start)return start

69.最长递增子序列的个数

思路:利用dp,一个数组存储向上递增的长度,一个数组存储相同长度序列的个数

class Solution:def findNumberOfLIS(self, nums):if nums ==[]:return(0)n = len(nums)opt_length = [1]*nopt_counter = [1]*nfor i in range(1, n):for j in range(i):if nums[j] < nums[i]:if opt_length[j]+1 > opt_length[i]:# 代表第一次遇到最长子序列opt_length[i] = 1+opt_length[j]opt_counter[i] = opt_counter[j]elif opt_length[j]+1 == opt_length[i]:# 代表已经遇到过最长子序列opt_counter[i] = opt_counter[i]+opt_counter[j]# print('====opt_length:', opt_length)# print('====opt_counter:', opt_counter)tmp = max(opt_length)res = sum([opt_counter[i] for i in range(n) if opt_length[i] == tmp])return (res)sol = Solution()
nums = [1, 3, 5, 4, 7]
res = sol.findNumberOfLIS(nums)
print('===res:', res)

70. 删除无效的括号

思路:回溯

class Solution:def removeInvalidParentheses(self, s: str) -> List[str]:if not s:return [""]if s[0] not in "()":return [s[0]+i for i in self.removeInvalidParentheses(s[1:])]if len(s) < 2:return [""]if s[0] == ")":return self.removeInvalidParentheses(s[1:])res = set(self.removeInvalidParentheses(s[1:]))for i in range(1, len(s)):if s[i] == ")":a, b = set(self.removeInvalidParentheses(s[1:i])), set(self.removeInvalidParentheses(s[i+1:]))res |= {f"({i}){j}" for i in a for j in b}p = len(max(res, key=len))return [i for i in res if len(i) == p]

71-1.零钱兑换

思路：找准状态状转移方程,f代表选择银币的函数，则f(11)=f(11-1)+1或f(11)=f(11-2)+1或f(11)=f(11-5)+1,则一般方程为:

f(money) = min(f(money), f(money-coin)+1)

class Solution:def coinChange(self, coins: List[int], amount: int) -> int:#状态转移方程f(money) = min(f(money),f(money-coin)+1)f = [float('inf')] * (amount + 1)f[0] = 0# print('==f:', f)for i in range(1, amount + 1):for coin in coins:if i - coin >= 0:f[i] = min(f[i], f[i - coin] + 1)# print('==f:', f)return f[-1] if f[-1]!=float('inf') else -1

71-2:零钱兑换 II

思路1:回溯　会超时

# 组合问题 回溯　超时
class Solution:def backtrace(self, amount, start, coins, track):if amount == 0:  # 终止条件# self.res.append(track)self.res+=1returnfor i in range(start, len(coins)):  # 选择条件if coins[i] > amount:continue# store = track.copy()# track.append(coins[i])self.backtrace(amount - coins[i], i, coins, track)# track = storedef change(self, amount, coins):self.res = 0#[]coins = sorted(coins)self.backtrace(amount, 0, coins, [])return self.res# amount = 5
# coins = [2]
amount = 5
coins = [1, 2, 5]
# amount = 500
# coins = [3,5,7,8,9,10,11]
sol = Solution()
res = sol.change(amount, coins)
print('==res:', res)

思路２:当成完全背包问题，用dp

#dp[i][j] 硬币为i　金额为j的组合数
import numpy as np
class Solution:def change(self, amount, coins):if len(coins) == 0:if amount == 0:return 1else:return 0dp = [[0 for i in range(amount+1)] for j in range(len(coins))]print('==np.array(dp):', np.array(dp))dp[0][0] = 1for j in range(coins[0], amount+1, coins[0]):dp[0][j] = 1print('==np.array(dp):', np.array(dp))for i in range(1, len(coins)):print('==coins[i]:', coins[i])for j in range(amount+1):dp[i][j] = dp[i - 1][j]#不选if j >= coins[i]:#选 注意与0 1背包有一点不同dp[i][j] += dp[i][j - coins[i]]print('==np.array(dp):', np.array(dp))return dp[-1][-1]amount = 5
coins = [1, 2, 5]
sol = Solution()
sol.change(amount, coins)

72.比特位计数

思路：

#思路:计算n的时候n-1计算过了
#n&n-1 就是抹掉二进制n最右边的1
class Solution:def countBits(self, num):#动态规划res = [0]*(num+1)for i in range(1, num+1):res[i] = res[i & i-1] + 1return resnum = 5
sol = Solution()
res = sol.countBits(num)
print('==res:', res)

73.前 K 个高频元素

思路:hash字典

class Solution:def topKFrequent(self, nums, k):dict_ = {}for num in nums:dict_[num] = dict_.get(num, 0)+1print('==dict_:', dict_)sort_dict = sorted(dict_.items(), key=lambda x:(x[-1], x[0]), reverse=True)return [sort_dict[j][0] for j in range(k)]# nums = [1,1,1,2,2,3]
# k = 2
nums = [-1, -1]
k = 1
# nums = [1, 2]
# k = 2sol = Solution()
res = sol.topKFrequent(nums, k)
print('==res:', res)

74.字符串解码

思路:栈

class Solution:def decodeString(self, s):stack = []  # (str, int) 记录之前的字符串和括号外的上一个数字num = 0res = ""  # 实时记录当前可以提取出来的字符串for c in s:if c.isdigit():num = num * 10 + int(c)elif c == "[":stack.append((res, num))res, num = "", 0elif c == "]":top = stack.pop()print('===top:', top)res = top[0] + res * top[1]print('==res:', res)else:res += creturn res# s = "3[a]2[bc]"
s = "3[a2[c]]"
sol = Solution()
res = sol.decodeString(s)
print('res:', res)

75.除法求值

思路:并查集

# 并查集
class Solution:def __init__(self):self.f = {}  # 每个节点的依次关系self.d = {}  # 每个节点的值　将根节点值置为1def find(self, x):  # 查找与你连通的最上面一位self.f.setdefault(x, x)self.d.setdefault(x, 1)if self.f[x] == x:return xelse:t = self.f[x]self.f[x] = self.find(t)self.d[x] *= self.d[t]return self.f[x]def union(self, A, B, value):  # 合并集a, b = self.find(A), self.find(B)if a != b:self.f[a] = bself.d[a] = self.d[B] / self.d[A] * value# print('===f===:', f)# print('===d===:', d)def check(self, x, y):if x not in self.f or y not in self.f:return -1.0a, b = self.find(x), self.find(y)# print('==a, b:', a, b)if a != b:  # 如果不在同一条线上就返回-1return -1.0return self.d[x] / self.d[y]def calcEquation(self, equations, values, queries):for i, nums in enumerate(equations):self.union(nums[0], nums[1], values[i])print('===f:', self.f)print('===d:', self.d)res = []for x, y in queries:res.append(self.check(x, y))return resequations = [["a", "b"], ["b", "c"]]
values = [2.0, 3.0]
queries = [["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"]]# equations = [["a","b"]]
# values = [2.0]
# queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
sol = Solution()
res = sol.calcEquation(equations, values, queries)
print('==res:', res)

76.根据身高重建队列

思路：按身高由高到低进行排序,身高相等时按索引从小排序

#新建一个队列按照索引进行插入

#思路:按身高由高到低进行排序,身高相等时按索引从小排序
#新建一个队列按照索引进行插入
class Solution:def reconstructQueue(self, people):people = sorted(people, key=lambda x: (-x[0], x[1]))print('===people:', people)output = []for p in people:print('===p:', p)output.insert(p[1], p)print('==output:', output)return output
people = [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]
sol = Solution()
sol.reconstructQueue(people)

77-1.目标和

思路2：动态规划 dp[i][j]表示到i为止，数字和为j的方案数，下面以两个例子为例

# dp[i][j] = dp[i-1][j-nums[i]]+dp[i-1][j+nums[i]]
class Solution:def findTargetSumWays(self, nums, S):sum_ = sum(nums)if abs(S) > sum_:return 0opt = [[0 for i in range(2 * sum_ + 1)] for i in range(len(nums))]print(np.array(opt))##nums = [0,0,0,0,0,0,0,0,1]# S = 1if nums[0] == 0:  # 边界条件opt[0][sum_] = 2else:opt[0][sum_ - nums[0]] = 1opt[0][sum_ + nums[0]] = 1print(np.array(opt))for i in range(1, len(nums)):for j in range(2 * sum_ + 1):l = j - nums[i] if j - nums[i] > 0 else 0r = j + nums[i] if j + nums[i] < 2 * sum_ + 1 else 0opt[i][j] = opt[i - 1][l] + opt[i - 1][r]# print('===print(np.array(opt)):', np.array(opt))return opt[-1][sum_ + S]# nums = [1, 1, 1, 1, 1]
# S = 3
# nums = [1000]
# S = 1000
nums = [0, 0, 0, 0, 0, 0, 0, 0, 1]
S = 1
sol = Solution()
res = sol.findTargetSumWays(nums, S)
print('==res:', res)

77-2.分割等和子集

思路１:

（１）转换成0 1背包问题，找到数组和的一半的子集

（２）dp[i][j]表示到i为止和为j是否存在

（３）dp[i][j] = dp[i-1][j]　不选择nums[i]

（４）dp[i][j] = dp[i-1][j-nums]　选择nums[i]

（５）如果 j<nums[i] dp[i][j] = dp[i-1][j]

以[1,2,3,6]为例

#转换成0 1背包问题 找到数组和的一半的子集
#到i为止和为j是否存在
#dp[i][j] = dp[i-1][j]#不选择nums[i]
#dp[i][j] = dp[i-1][j-nums]#选择nums[i]
#如果 j<nums[i] dp[i][j] = dp[i-1][j]
class Solution:def canPartition(self, nums):# nums = sorted(nums)# print('==nums:', nums)n = len(nums)if n<2:#数组长度无法划分return Falsesum_ = sum(nums)max_value = max(nums)if sum_ % 2==1:#奇数的话没法拆分return Falsetarget = sum_//2if max_value>target:#最大值大于一半了　不满足条件return Falsedp = [[False for i in range(target+1)] for i in range(n)]print('===np.array(dp):', np.array(dp))for i in range(n):#不选取任何正整数，则被选取的正整数等于 00dp[i][0] = Truedp[0][nums[0]] = True#i==0 只有一个正整数 nums[0] 可以被选取for i in range(1,n):for j in range(1, target+1):if j<nums[i]:#j<nums[i]dp[i][j] = dp[i-1][j]else:#不选择nums[i]与选择nums[i]dp[i][j] = dp[i - 1][j] or dp[i - 1][j-nums[i]]print('===np.array(dp):', np.array(dp))return dp[-1][target]
# nums = [1, 5, 11, 5]
nums = [1, 2, 3, 6]
sol = Solution()
res = sol.canPartition(nums)
print('==res:', res)

思路２：优化版　用一维数组替代，只不过采用逆序

其中dp[j] = dp[j] || dp[j - nums[i]] 可以理解为 dp[j] （新）= dp[j] （旧） || dp[j - nums[i]] （旧），如果采用正序的话 dp[j - nums[i]]会被之前的操作更新为新值

import numpy as np
#转换成0 1背包问题 找到数组和的一半的子集
#优化版
#dp[j] = [j]#不选择nums[i]
#dp[j] = dp[j-nums]#选择nums[i]
# #如果 j<nums[i] dp[i][j] = dp[i-1][j]
class Solution:def canPartition(self, nums):# nums = sorted(nums)# print('==nums:', nums)n = len(nums)if n<2:#数组长度无法划分return Falsesum_ = sum(nums)max_value = max(nums)if sum_ % 2==1:#奇数的话没法拆分return Falsetarget = sum_//2if max_value>target:#最大值大于一半了　不满足条件return Falsedp = [False for i in range(target+1)]print('===np.array(dp):', np.array(dp))#不选取任何正整数dp[0] = Truedp[nums[0]] = True#i==0 只有一个正整数 nums[0] 可以被选取for i in range(1, n):for j in range(target, 0, -1):if j<nums[i]:#j<nums[i]dp[j] = dp[j]else:#不选择nums[i]与选择nums[i]dp[j] = dp[j] or dp[j-nums[i]]print('===np.array(dp):', np.array(dp))return dp[-1]
# nums = [1, 5, 11, 5]
nums = [1, 2, 3, 6]
sol = Solution()
res = sol.canPartition(nums)
print('==res:', res)

78-1.路径总和

1.递归法

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution(object):def hasPathSum(self, root, sum):""":type root: TreeNode:type sum: int:rtype: bool"""if not root:return Falseif not root.left and not root.right and root.val==sum:return Truesum -=root.valreturn self.hasPathSum(root.left,sum) or self.hasPathSum(root.right,sum)

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:bool hasPathSum(TreeNode* root, int targetSum) {if(root == nullptr){return false;}if (root->left == nullptr && root->right == nullptr && targetSum==root->val){return true;}targetSum -=root->val;return hasPathSum(root->left,targetSum) || hasPathSum(root->right,targetSum);}
};

2.利用栈--DFS

class Solution(object):def hasPathSum(self, root, sum):""":type root: TreeNode:type sum: int:rtype: bool"""# # #递归终止条件 # if root is None:#     return False# if root.left is None and root.right is None and root.val == sum:#     return True# sum = sum - root.val# # print('===sum:', sum)# return self.hasPathSum(root.left, sum) or self.hasPathSum(root.right, sum) if not root:return Falsequene = [(root, root.val)]while quene:node,value = quene.pop()if node.left is None and node.right is None and value==sum:return Trueif node.left is not None:quene.append((node.left,value+node.left.val))if node.right is not None:quene.append((node.right,value+node.right.val))   # print('==quene:',quene)return False

3.利用队列--BFS

class Solution(object):def hasPathSum(self, root, sum):""":type root: TreeNode:type sum: int:rtype: bool"""# # #递归终止条件 # if root is None:#     return False# if root.left is None and root.right is None and root.val == sum:#     return True# sum = sum - root.val# # print('===sum:', sum)# return self.hasPathSum(root.left, sum) or self.hasPathSum(root.right, sum) if not root:return Falsequene = [(root, root.val)]while quene:node,value = quene.pop(0)if node.left is None and node.right is None and value==sum:return Trueif node.left is not None:quene.append((node.left,value+node.left.val))if node.right is not None:quene.append((node.right,value+node.right.val))   # print('==quene:',quene)return False

78-2:路径总和 II

思路：回溯　这种里面要调用两层回溯的　　track就不要放在递归函数里面了

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def dfs(self, node, sum_):if node is None:return 0store = self.track.copy()self.track.append(node.val)# print('==self.track:', self.track)if node.left is None and node.right is None and sum_==node.val:         self.res.append(self.track)sum_ -= node.valself.dfs(node.left, sum_)self.dfs(node.right, sum_)# self.track.pop()self.track = storedef pathSum(self, root: TreeNode, sum: int) -> List[List[int]]:self.res = []self.track = []self.dfs(root, sum)return self.res

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:vector<vector<int>> res;vector<int> track;void dfs(TreeNode* root, int targetSum){if(root==nullptr){return ;}vector<int> store;store = track;track.push_back(root->val);        if(root->left==nullptr && root->right==nullptr && targetSum==root->val){res.push_back(track);}targetSum -= root->val;dfs(root->left, targetSum);dfs(root->right, targetSum);track = store;}vector<vector<int>> pathSum(TreeNode* root, int targetSum) {dfs(root, targetSum);return res;}
};

78-3:路径总和 III

思路：用一个列表存储从节点开始的数字和

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
#用列表记录从每一个节点开始的和
class Solution:def dfs(self, node, sum_list, sum):if node is None:return 0 sum_list = [num+node.val for num in sum_list]sum_list.append(node.val)for num in sum_list:if num==sum:self.res+=1self.dfs(node.left, sum_list, sum)self.dfs(node.right, sum_list, sum)def pathSum(self, root: TreeNode, sum: int) -> int:self.res = 0self.dfs(root, [], sum)return self.res

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:int res;void dfs(TreeNode* node, vector<int> num_list, int sum){if(node == nullptr){return ;}for (int i=0; i<num_list.size(); i++){num_list[i] += node->val;}   num_list.push_back(node->val);for(int i=0; i<num_list.size(); i++){if(num_list[i]==sum){res++;}}dfs(node->left, num_list, sum);dfs(node->right, num_list, sum);}int pathSum(TreeNode* root, int sum) {vector<int> num_list;dfs(root, num_list, sum);return res;}
};

79.找到所有数组中消失的数字

思路1:hash

#利用hash存储出现过得数字
class Solution:def findDisappearedNumbers(self, nums):dict_ = {}for num in nums:dict_[num] = dict_.get(num, 0)+1print('==dict_:', dict_)res =[]for i in range(1, len(nums)+1):if i not in dict_:res.append(i)return res
nums = [4,3,2,7,8,2,3,1]
sol = Solution()
res = sol.findDisappearedNumbers(nums)
print('==res:', res)

思路2:原地修改

#利用list原地进行修改
class Solution:def findDisappearedNumbers(self, nums):for i in range(len(nums)):index = abs(nums[i]) - 1if nums[index] > 0:nums[index] *= -1print('==nums:', nums)res =[]for i in range(len(nums)):if nums[i]>0:res.append(i+1)return res
nums = [4,3,2,7,8,2,3,1]
# nums = [1, 3, 3, 4, 5]
sol = Solution()
res = sol.findDisappearedNumbers(nums)
print('==res:', res)

80.汉明距离

思路:通过异或取得不同数的　在向右移动　依次与1进行& 获得1的个数

#思路:通过异或取得不同数的　在向右移动　依次与1进行& 获得1的个数
class Solution:def hammingDistance(self, x, y):res = x ^ y#异或取得不同的数 异或　相同为0　不同为1# print('==res:', res)dis = 0while res:#向右移位# print('==res&1:', res&1)if res&1:dis+=1res = res>>1# print('==res:', res)return dis
x = 1
y = 4
sol = Solution()
sol.hammingDistance(x, y)

81.把二叉搜索树转换为累加树

思路：其实就是逆中序遍历，利用二叉搜索树的特点，跟节点值更新为右孩子和根节点值之和，左孩子值更新为根节点与左孩子值之和。

1.迭代法：

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def convertBST(self, root: TreeNode) -> TreeNode:stack = []node = rootvalue = 0while stack or node:while node:#把跟节点与右子树节点依次压进栈 实现逆中序遍历stack.append(node)node = node.rightprint('==stack:', stack)node = stack.pop()print('==node:',node)value += node.valnode.val = valueprint('==node.left:', node.left)node = node.leftreturn root

2.递归法：

其中res存储逆中序遍历(右根左)的值，便于查看

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def helper(self, node):if node:self.helper(node.right)# self.res.append(node.val)self.value+=node.valnode.val = self.valueself.helper(node.left)def convertBST(self, root: TreeNode) -> TreeNode:# self.res =[]self.value = 0self.helper(root)return root

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:int res = 0;void help(TreeNode* node){if(node == nullptr){return ;}help(node->right);res += node->val;node->val = res;help(node->left);}TreeNode* convertBST(TreeNode* root) {help(root);return root;}
};

82.二叉树的直径

思路:递归函数用来获取每一层深度，然后在分别对左右子树深度求和，这里要注意的是最长直径不一定过根节点，所有要用一个变量存储遍历每个节点时的最大直径．

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def get_depth(self, node):if node is None:return 0l = self.get_depth(node.left)r = self.get_depth(node.right)self.max_value = max(self.max_value, l+r)return max(l,r)+1def diameterOfBinaryTree(self, root: TreeNode) -> int:self.max_value = 0if root is None:return 0self.get_depth(root)return self.max_value

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}* };*/
class Solution {
public:int max_value=0;int help(TreeNode* node){if(!node){return 0;}int l = help(node->left);int r = help(node->right);max_value =  max(max_value, l+r);return max(l,r)+1;}int diameterOfBinaryTree(TreeNode* root) {help(root);return max_value;}
};

83.和为K的子数组

思路１：枚举（超时）　Ｏ(n2)

class Solution:def subarraySum(self, nums, k):res=0for i in range(len(nums)):tmp = 0for j in range(i,len(nums)):tmp+=nums[j]if tmp==k:res+=1print('=res:',res)return res# nums = [1,1,1]
# k = 2
nums = [1,-1,0]
k = 0
sol = Solution()
sol.subarraySum(nums, k)

思路２：hash,利用字典的key值存储累加和，value值存储出现次数

#利用字典　key存储累加的数字　value为出现的次数
class Solution:def subarraySum(self, nums, k):count_dict = {}count, sum_ = 0, 0for num in nums:sum_+=numif sum_==k:count+=1if sum_-k in count_dict:count+=count_dict[sum_-k]if sum_ in count_dict:count_dict[sum_]+=1else:count_dict[sum_]=1print('==count_dict:', count_dict)print('count:', count)return countnums = [1, 1, 1]
k = 2
# nums = [1, -1, 1]
# k = 0
sol = Solution()
sol.subarraySum(nums, k)

84.最短无序连续子数组

思路1：单调递增栈

class Solution:def findUnsortedSubarray(self, nums):#找到递增的拐点stack = []left = len(nums)-1for i in range(len(nums)):while stack and nums[i] < nums[stack[-1]]:index = stack.pop()left = min(left, index)stack.append(i)print('==stack:', stack)print('left:', left)#找到逆序递增的拐点stack = []right = 0for i in range(len(nums)-1, -1, -1):while stack and nums[i] > nums[stack[-1]]:index = stack.pop()right = max(right, index)stack.append(i)print('==right:', right)return right-left+1 if right-left>0 else 0nums = [2, 6, 4, 8, 10, 9, 15]
# nums = [2, 1, 6]
# nums = [1, 2]
# nums = [2, 1]
# nums = [5, 4, 3, 2, 1]
sol = Solution()
res = sol.findUnsortedSubarray(nums)
print('======res:', res)

思路2:排序

class Solution:def findUnsortedSubarray(self, nums: List[int]) -> int:# print('==nums:', nums)sort_nums = sorted(nums)# print('==sort_nums:', sort_nums)left = len(nums) - 1right = 0for i in range(len(nums)):if nums[i] != sort_nums[i]:left = min(left, i)right = max(right, i)# print('==left:', left)# print('==right:', right)return right - left + 1 if right - left > 0 else 0

85.合并二叉树

思路:采用前序遍历访问二叉树，如果节点其一为none，就返回另一个

1.递归法

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def mergeTrees(self, t1: TreeNode, t2: TreeNode) -> TreeNode:if t1 is None:return t2if t2 is None:return t1t1.val+=t2.valt1.left = self.mergeTrees(t1.left,t2.left)t1.right = self.mergeTrees(t1.right,t2.right)return t1

2.迭代法

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution:def mergeTrees(self, t1: TreeNode, t2: TreeNode) -> TreeNode:if t1 is None:return t2stack= [(t1,t2)]while stack:t = stack.pop()if t[0] is None or t[1] is None:continuet[0].val +=t[1].valif t[0].left is None:t[0].left = t[1].leftelse:stack.append((t[0].left, t[1].left))if t[0].right is None:t[0].right = t[1].rightelse:stack.append((t[0].right, t[1].right))return t1

c++实现:

/*** Definition for a binary tree node.* struct TreeNode {*     int val;*     TreeNode *left;*     TreeNode *right;*     TreeNode() : val(0), left(nullptr), right(nullptr) {}*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}* };*/
class Solution {
public:TreeNode* mergeTrees(TreeNode* root1, TreeNode* root2) {if(root1 == nullptr){return root2;}if(root2 == nullptr){return root1;}root1->val += root2->val;root1->left = mergeTrees(root1->left, root2->left);root1->right = mergeTrees(root1->right, root2->right);return root1;}
};

86.任务调度器

思路： 贪心 填桶法

class Solution(object):def leastInterval(self, tasks, n):""":type tasks: List[str]:type n: int:rtype: int"""length = len(tasks)if length <= 1:return lengthprint('===length:', length)# 用于记录每个任务出现的次数task_dict = {}for task in tasks:#不存在task时　返回0task_dict[task] = task_dict.get(task,0)+1print('==task_dict:', task_dict)# 按任务出现的次数从大到小排序task_sort = sorted(task_dict.items(), key=lambda x: x[1], reverse=True)print('==task_sort:', task_sort)# # 出现最多次任务的次数max_task_count = task_sort[0][1]# 至少需要的最短时间res = (max_task_count - 1) * (n + 1)for sort in task_sort:if sort[1] == max_task_count:res += 1print('==res:', res)# # 如果结果比任务数量少，则返回总任务数return res if res >= length else lengthtasks = ["A","A","A","B","B","B"]
n = 2
# n = 0
sol = Solution()
sol.leastInterval(tasks, n)

87-1.回文子串

思路１：两层for循环遍历进行判断是否是回文字符串即可，超出时间限制

#双层for循环超出时间限制
class Solution:def judge_palindrome(self, s):l = 0r = len(s) -1while l<=r:if s[l]==s[r]:l+=1r-=1else:return Falsereturn Truedef countSubstrings(self, s):res=0for i in range(len(s)):# print('==i:', i)for j in range(i, len(s)):# print('==j', j)# print('==s[i:j+1]:', s[i:j+1])if self.judge_palindrome(s[i:j+1]):res += 1return res# s = "abc"
s = "aaa"
sol = Solution()
res = sol.countSubstrings(s)
print('==res:', res)

思路2,中心枚举，专门用self.res存储 left与righe索引方便查看，，最后求和就是会文字符串的个数。

import numpy as np
class Solution:def helper(self,left,right,s):while left>=0 and right<len(s) and s[left]==s[right]:self.res[left][right]=1self.fin_res+=1left-=1right+=1def countSubstrings(self, s):self.res = [[0 for i in range(len(s)) ] for i in range(len(s))]self.fin_res = 0for i in range(len(s)):self.helper(i,i,s)self.helper(i,i+1,s)print(np.array(self.res))return self.fin_ress = "aaa"
sol = Solution()
sol.countSubstrings(s)

87-2：回文串分割 IV

思路:中心枚举 用一个矩阵存储回文字符串左右索引的值，最后看看是不是分为三段即可

import numpy as np
class Solution:def helper(self,left,right,s):while left>=0 and right<len(s) and s[left]==s[right]:self.res[left][right] = 1left-=1right+=1def checkPartitioning(self, s):length = len(s)self.res = [[0 for _ in range(length)]for _ in range(length)]for i in range(length):self.helper(i, i, s)self.helper(i, i+1, s)print(np.array(self.res))for i in range(length):for j in range(i+1, length):if self.res[0][i] and self.res[i+1][j] and self.res[j+1][length-1]:return Truereturn False# s = "abcbdd"
s = "bcbddxy"
# s = "juchzcedhfesefhdeczhcujzzvbmoeombv"
sol = Solution()
res = sol.checkPartitioning(s)
print('==res:', res)

87-3.最长回文子串

class Solution:def helper(self,left,right,s):while left>=0 and right<len(s) and s[left]==s[right]:left-=1right+=1if len(s[left+1:right])>len(self.res):self.res = s[left+1:right]def longestPalindrome(self, s: str) -> str:self.res = ''for i in range(len(s)):self.helper(i,i,s)self.helper(i,i+1,s)return self.res

88-1.单调递增的数字

class Solution(object):def monotoneIncreasingDigits(self, N):""":type N: int:rtype: int"""digits = []A = list(map(int, str(N)))# print('==A:', A)for i in range(len(A)):for d in range(1, 10):# print('==digits + [d] * (len(A) - i):', digits + [d] * (len(A) - i))if digits + [d] * (len(A) - i) > A:digits.append(d - 1)breakelse:digits.append(9)# print('==digits:', digits)return int("".join(map(str, digits)))

88-2:每日温度

思路：单调递增栈

class Solution:def dailyTemperatures(self, T):#单调递增栈res = [0]*len(T)stack = []for i in range(len(T)):while stack and T[i] > T[stack[-1]]:res[stack[-1]] = i - stack[-1]stack.pop()print('==stack', stack)print('==res:', res)stack.append(i)return res
T = [73, 74, 75, 71, 69, 72, 76, 73]
sol = Solution()
sol.dailyTemperatures(T)

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