# Time:  O(nlon + n * t), t is the value of target.
# Space: O(t)

# Given an integer array with all positive numbers and no duplicates,
# find the number of possible combinations that add up to a positive integer target.
#
# Example:
#
# nums = [1, 2, 3]
# target = 4
#
# The possible combination ways are:
# (1, 1, 1, 1)
# (1, 1, 2)
# (1, 2, 1)
# (1, 3)
# (2, 1, 1)
# (2, 2)
# (3, 1)
#
# Note that different sequences are counted as different combinations.
#
# Therefore the output is 7.
# Follow up:
# What if negative numbers are allowed in the given array?
# How does it change the problem?
# What limitation we need to add to the question to allow negative numbers?

class Solution(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        dp = [0] * (target+1)
        dp[0] = 1
        nums.sort()

        for i in xrange(1, target+1):
            for j in xrange(len(nums)):
                if nums[j] <= i:
                    dp[i] += dp[i - nums[j]]
                else:
                    break

        return dp[target]