动态规划_leetcode416

# coding=utf8


# 递归
class Solution1(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """

        if not nums  or target <= 0:
            return 0

        return self.tryCombination(nums,target)


    #组合遍历
    def tryCombination(self,nums,target):

        if target == 0:
            return 1

        res = 0
        for item in nums:
            if target - item >= 0:
                res += self.tryCombination(nums,target-item)


        return res



# s = Solution1()
#
# nums = [1,2,3]
# target = 4
#
#
# print s.combinationSum4(nums,target)


# 记忆化递归
class Solution2(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """

        if not nums  or target <= 0:
            return 0



        self.memo = [-1 for i in range(target+1)]

        return self.tryCombination(nums,target)



    def tryCombination(self,nums,target):


        if self.memo[target] != -1:
            return self.memo[target]

        # self.memo[0] -1
        if target == 0:
            return 1

        res = 0
        for item in nums:
            if target - item >= 0:
                res += self.tryCombination(nums,target-item)

        self.memo[target] = res

        return res


# s = Solution2()
#
# nums = [1,2,3]
# target = 4
#
#
# print s.combinationSum4(nums,target)


# 动态规划
class Solution3(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """

        if not nums  or target <= 0:
            return 0

        memo = [-1 for i in range(target+1)]

        memo[0] = 1

        for i in range(1,target+1):
            memo[i] = 0
            for item in nums:
                if i - item >= 0:
                    memo[i] += memo[i-item]


        return memo[target]


s = Solution3()

nums = [1,2,3]
target = 4


print s.combinationSum4(nums,target)