#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)
