动态规划_leetcode494

#coding=utf-8

# 递归1 递归到底

# 序列选与不选的模板题 o(2**n) 20190307 找工作期间
class Solution1(object):
    def findTargetSumWays(self, nums, S):
        """
        :type nums: List[int]
        :type S: int
        :rtype: int
        """
        self.res = 0

        if not nums or not S:
            return self.res

        self.trySum(nums,S,0)

        print self.res

        return self.res


    def trySum(self,nums,target,index):

        if index == len(nums)-1:
            if nums[index] == target or -nums[index] == target:
                self.res += 1
            return

        self.trySum(nums,target-nums[index],index+1)
        self.trySum(nums,target+nums[index],index+1)




# s = Solution1()
#
# nums1 = [1, 1, 1, 1, 1]
# ts1 = 3
#
#
# s.findTargetSumWays(nums1,ts1)


# 递归2
# 层次递归 :不使用全局变量
class Solution2(object):
    def findTargetSumWays(self, nums, S):
        """
        :type nums: List[int]
        :type S: int
        :rtype: int
        """


        if not nums or not S:
            return 0


        return self.trySum(nums,S,0)



    def trySum(self,nums,target,index):


        res = 0

        if index == len(nums)-1:
            if nums[index] == target or -nums[index] == target:
                res += 1
            return res

        res += self.trySum(nums,target-nums[index],index+1)
        res += self.trySum(nums,target+nums[index],index+1)

        return res


# s = Solution2()
#
# nums1 = [1, 1, 1, 1, 1]
# ts1 = 3
#
#
# print  s.findTargetSumWays(nums1,ts1)


#https://blog.csdn.net/qq_17550379/article/details/82939713

# 记忆化递归


class Solution3(object):
    def findTargetSumWays(self, nums, S):
        """
        :type nums: List[int]
        :type S: int
        :rtype: int
        """


        if not nums :
            return 0


        self.memo = {}

        return self.trySum(nums,S,0)



    def trySum(self,nums,target,index):


        pair = (index,target)

        if  pair in self.memo:
            return self.memo[pair]

        res = 0

        if index == len(nums):
            if target == 0:
                res += 1

            return res

        res += self.trySum(nums,target-nums[index],index+1)
        res += self.trySum(nums,target+nums[index],index+1)

        self.memo[pair] = res
        return res


# s = Solution3()
#
# nums1 = [1, 1, 1, 1, 1]
# ts1 = 3
#
#
# print  s.findTargetSumWays(nums1,ts1)


# 动态规划
# https://blog.csdn.net/qq_17550379/article/details/82939713
# https://www.cnblogs.com/onlyac/p/6986139.html
class Solution4(object):
    def findTargetSumWays(self, nums, S):
        """
        :type nums: List[int]
        :type S: int
        :rtype: int        """        total = sum(nums)        memo = [[0] * (2*total+1) for i in range(len(nums) + 1)]        memo[0][total] = 1        for i in range(1,len(nums)+1):            for j in range(2*total+1):                if j+nums[i-1] < 2*total+1:                    memo[i][j] += memo[i-1][j+nums[i-1]]                if j-nums[i-1] >=0:                    memo[i][j] += memo[i-1][j-nums[i-1]]        return memo[len(nums)][total+S]