LeetCode #377: Combination Sum IV

junchen1992

于 2016-09-20 16:10:07 发布

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分类专栏：算法 LeetCode 文章标签： leetcode

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本文探讨了给定正整数数组求和至目标值的所有可能组合数量的问题，并提供了一个使用动态规划解决该问题的Python实现。同时讨论了允许负数的情况及如何限制问题以容纳负数。

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Problem Statement

(Source) 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?

Solution

class Solution(object):

    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        nums.sort()
        dp = [0] * (target + 1)
        dp[0] = 1
        for i in xrange(1, target + 1):
            for x in nums:
                if x > i:
                    break
                else:
                    dp[i] += dp[i - x]
        return dp[-1]