如何将此递归解决方案转换为 DP 解决方案？

Posted 2023-02-22

【中文标题】如何将此递归解决方案转换为 DP 解决方案？

【英文标题】：How do I turn this recursive solution to a DP solution?

【发布时间】：2020-03-19 08:07:21

【问题描述】：

您好，我已经为 LeetCode 上的分区相等子集问题 (https://leetcode.com/problems/partition-equal-subset-sum/) 起草了一个递归解决方案，该解决方案已被接受：

class Solution(object):
    def canPartition(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        if not nums or len(nums) < 2:
            return False
        if sum(nums) % 2 != 0:
            return False
        target = sum(nums) // 2
        # if the maximum number in nums goes larger than target, 
        # then this maximum number cannot be partitioned into any subarray
        # hence there's no solution in this case, return False early
        if max(nums) > target:   
            return False
        nums.sort(reverse = True)
        return self.helper(nums, 0, target, 0)

    def helper(self, nums, index, target, curr):
        # since "target" value is derived from dividing total sum, 
        # we only need to search for one sum that makes target value in the array
        # the rest is guaranteed to sum up to "target" 
        if curr == target:
            return True
        for i in range(index, len(nums)):
            if curr + nums[i] > target:
                continue
            if self.helper(nums, i + 1, target, curr + nums[i]):
                return True
        return False

但是，作为后续行动，真正返回两个子集而不仅仅是 True/False 的最佳方法是什么。如果我必须更新上述现有代码，保存的子集的代码会是什么样子？我是那些开始使用 DP 的人之一。提前致谢。

【参考方案1】：

想出了解决办法：

class Solution(object):
    def canPartition(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        if not nums or len(nums) < 2:
            return []
        if sum(nums) % 2 != 0:
            return []
        target = sum(nums) // 2
        if max(nums) > target:   
            return []
        nums.sort(reverse = True)
        res = []
        self.helper(nums, 0, target, [], res)
        return res

    def helper(self, nums, index, target, curr, res):
        if sum(curr) == target:
            res.append(list(curr))
            return
        for i in range(index, len(nums)):
            if sum(curr) + nums[i] > target:
                continue
            self.helper(nums, i + 1, target, curr + [nums[i]], res)