1.分割等和子集
1 class Solution(object): 2 def canPartition(self, nums): 3 if(sum(nums)&1): 4 return False 5 6 target=sum(nums)//2 7 8 # dp[i]表示是否能从 nums中取出一些数字，其和为i 9 dp=[False]*(target+1) 10 11 dp[0]=True 12 13 for num in nums: 14 for i in range(target,num-1,-1): 15 dp[i]=dp[i] or dp[i-num] 16 17 return dp[target]
2.coins change i
组成amount的最少硬币数
1 class Solution(object): 2 def coinChange(self, coins, amount): 3 # dp[i]表示凑成金额i所需的最少硬币数 4 # dp[i]=min(dp[i],dp[i-coins[j]] if i-coins[j]>=0) 5 # dp[0]=0 6 7 dp=[float('inf') for j in range(amount+1)] 8 dp[0]=0 9 10 for j in range(1,amount+1): 11 for i in range(len(coins)): 12 if(j>=coins[i] and dp[j-coins[i]]!=float('inf')): 13 dp[j]=min(dp[j],dp[j-coins[i]]+1) 14 15 return dp[amount] if dp[amount]!=float('inf') else -1 16
3.1 coins change ii
组成amounts的所有可能数
1 class Solution(object): 2 def change(self, amount, coins): 3 m=len(coins) 4 n=amount 5 6 dp=[[0]*(n+1)]*(m+1) 7 dp[0][0]=1 8 9 # 下面写法错误，没有任何硬币，所以无法组成 10 # for j in range(n+1): 11 # if j %coins[0]==0: 12 # dp[0][j]=1 13 14 for i in range(1,m+1): 15 dp[i][0]=1 16 17 for i in range(1,m+1): 18 for j in range(1,n+1): 19 dp[i][j]=dp[i-1][j]+(dp[i][j-coins[i-1]] if j-coins[i-1]>=0 else 0) 20 21 return dp[m][n]
def change(self, amount, coins): m=len(coins) n=amount # dp[i]表示组成i的组合数 dp=[0]*(n+1) dp[0]=1 for i in range(m): for j in range(coins[i],n+1): dp[j]=dp[j]+dp[j-coins[i]] return dp[amount]
3.2 coins change i
组成amount所需的最少硬币数
1 class Solution(object): 2 def coinChange(self, coins, amount): 3 """ 4 :type coins: List[int] 5 :type amount: int 6 :rtype: int 7 """ 8 9 m=len(coins) 10 n=amount 11 12 # dp[j]表示组成amount j所需的最少硬币数 13 dp=[float('inf') for j in range(n+1)] 14 15 dp[0]=0 16 for j in range(1,n+1): 17 for i in range(m): 18 if(j>=coins[i]): 19 dp[j]=min(dp[j],dp[j-coins[i]]+1) 20 21 return dp[n] if dp[n]!=float('inf') else -1
4. 打家劫舍
1 class Solution(object): 2 def helper(self,nums): 3 # dp[i]表示偷 前i个房子时 最高的金额数 4 dp=[0]*len(nums) 5 dp[0]=nums[0] 6 7 for i in range(1,len(nums)): 8 dp[i]=max(dp[i-1],nums[i]+(dp[i-2] if i-2>=0 else 0)) 9 10 return dp[-1] 11 12 def rob(self, nums): 13 if(len(nums)==0): 14 return 0 15 16 if(len(nums)==1): 17 return nums[0] 18 19 if(len(nums)==2): 20 return max(nums[0],nums[1]) 21 22 nums1=nums[:-1] 23 nums2=nums[1:] 24 25 return max(self.helper(nums1),self.helper(nums2))
5.LIS
1 class Solution(object): 2 def lengthOfLIS(self, nums): 3 n=len(nums) 4 if(n==0 or n==1): 5 return n 6 7 dp=[1]*n 8 9 for i in range(1,n): 10 for j in range(i): 11 if(nums[j]<nums[i]): 12 dp[i]=max(dp[j]+1,dp[i]) 13 14 return max(dp)
6.最大和连续子数组
1 class Solution(object): 2 def maxSubArray(self, nums): 3 n=len(nums) 4 if(n==0): 5 return 0 6 7 curSum=0 8 maxSum=float('-inf') 9 10 for i in range(n): 11 curSum+=nums[i] 12 maxSum=max(curSum,maxSum) 13 14 if(curSum<0): 15 curSum=0 16 17 18 return maxSum
7.众数
1 class Solution(object): 2 def majorityElement(self, nums): 3 n=len(nums) 4 if(n==0): 5 return [] 6 7 if(n==1): 8 return nums 9 10 res=[] 11 12 num1=float('inf') 13 num2=float('inf') 14 cnt1=0 15 cnt2=0 16 17 for i in range(n): 18 if(nums[i]==num1): 19 cnt1+=1 20 elif(nums[i]==num2): 21 cnt2+=1 22 elif(cnt1==0): 23 num1=nums[i] 24 cnt1=1 25 elif(cnt2==0): 26 num2=nums[i] 27 cnt2=1 28 else: 29 cnt1-=1 30 cnt2-=1 31 32 cnt1,cnt2=0,0 33 for num in nums: 34 if(num==num1): 35 cnt1+=1 36 elif(num==num2): 37 cnt2+=1 38 39 if(cnt1>n//3): 40 res.append(num1) 41 if(cnt2>n//3): 42 res.append(num2) 43 44 return res
误区1：
num1和num2初始化为nums[0]。再执行循环。
假设数组中只有两个不相同的元素，那么结束循环时，num1和num2仍指向同一个元素