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.

class Solution(object):
    def canPartition(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        # 方法一

        s = sum(nums)
        if s%2 == 1:return False
        s = s//2
        n = len(nums)
        
        dp = [[False for _ in range(s+1)] for _ in range(n+1)]
        
        dp[0][0] = True
        
        for i in range(1,n+1):
            dp[i][0] = True
            
        for j in range(1,s+1):
            dp[0][j] = False
            
        for i in range(1,n+1):
            for j in range(1,s+1):
                dp[i][j] = dp[i-1][j]
                if j >= nums[i-1]:
                    dp[i][j] = dp[i][j] or dp[i-1][j-nums[i-1]]
                    
        return dp[n][s]
    
        #方法二

        s = sum(nums)
        if s%2 == 1: return False
        s = s//2
        n = len(nums)
        dp = [False for _ in range(s+1)]
        dp[0] = True
        for num in nums:
            for j in reverse(range(1,s+1)):
                if j >= num:
                    dp[j] = dp[j] or dp[j-num]
                    
        return dp[s]