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)