动态规划_leetcode300(LIS)

#coding=utf-8

# 递归1### 选与不选 经典的组合问题

class Solution1(object):    def lengthOfLIS(self, nums):        """        :type nums: List[int]        :rtype: int        """        self.res = 0

        if not nums :            return 0

        ans = []        self.getLIS(nums,0,ans)

        return self.res

    def  getLIS(self,nums,index,ans):

        if index == len(nums):            if self.isLIS(ans):                self.res = max(self.res,len(ans))            return

        ans.append(nums[index])        self.getLIS(nums,index+1,ans)        ans.pop()        self.getLIS(nums,index+1,ans)

    def isLIS(self,ans):        if not ans:            return False

        if len(ans) == 1:            return True

        pre = 0        next = 1

        while next < len(ans):            if ans[pre] > ans[next]:                return False            else:                pre += 1                next += 1

        return True

# s = Solution1()# nums1 = [10, 9, 2, 5, 3, 7, 101, 18]# print  s.lengthOfLIS(nums1)

# 递归2 生成所有的组合class Solution2(object):    def lengthOfLIS(self, nums):        """        :type nums: List[int]        :rtype: int        """

        self.res = 0        self.getCombination(nums,0,[])

        return self.res

    def isLIS(self,ans):        if not ans:            return False

        if len(ans) == 1:            return True

        pre = 0        next = 1

        while next < len(ans):            if ans[pre] > ans[next]:                return False            else:                pre += 1                next += 1

        return True

    def getCombination(self,nums,index,ans):

        if self.isLIS(ans):            self.res = max(self.res,len(ans))        for i in range(index,len(nums)):            ans.append(nums[i])            self.getCombination(nums,i+1,ans)            ans.pop()

# s = Solution2()# nums1 = [10, 9, 2, 5, 3, 7, 101, 18]# nums2 = [1,2,3]# print s.lengthOfLIS(nums1)

# 动态规划class Solution3(object):    def lengthOfLIS(self, nums):        """        :type nums: List[int]        :rtype: int        """

        memo = [1 for i in range(len(nums)) ]

        for i in range(len(nums)):            for j in range(i):                if nums[i] > nums[j]:                    memo[i] = max(memo[i],memo[j]+1)        res = 0        for i in range(len(nums)):            res = max(res,memo[i])        return ress = Solution3()nums1 = [10, 9, 2, 5, 3, 7, 101, 18]nums2 = [1,2,3]print s.lengthOfLIS(nums1)

原文地址：https://www.cnblogs.com/lux-ace/p/10546562.html