416. Partition Equal Subset Sum

Given a non-empty array containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.

Note:

1. Each of the array element will not exceed 100.
2. The array size will not exceed 200.

 

Example 1:

Input: [1, 5, 11, 5]

Output: true

Explanation: The array can be partitioned as [1, 5, 5] and [11].

 

Example 2:

Input: [1, 2, 3, 5]

Output: false

Explanation: The array cannot be partitioned into equal sum subsets.

这道题可以说非常好，我想到两种方法，第一种是dfs，current sum==target sum就return True,否则for i in range(len(nums)),每次选一个num[i]加到current sum里，然后nums变为nums[:i]+nums[i+1:]，进行递归。

可惜啊，这方法超时了。

于是乎，咱们直接上dp。说到dp这题是subset sum的变种题。

图表：

横坐标是amount也就是target sum，纵坐标是nums,dp规则见代码。就这样~

class Solution(object):
    def canPartition(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        totalsum=sum(nums)
        if totalsum%2:
            return False
        targetsum=totalsum/2
        
        mem=[[False for _ in range(targetsum+1)] for _ in range(len(nums))]
        for r in range(len(nums)):
            mem[r][0]=True
        
        for r in range(len(nums)):
            for c in range(1,targetsum+1):
                if nums[r]>c:
                    mem[r][c]=mem[r-1][c]
                else:
                    if mem[r-1][c]:
                        mem[r][c]=True
                    else:
                        mem[r][c]=mem[r-1][c-nums[r]]
        
        return mem[-1][-1]