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:
- Each of the array element will not exceed 100.
- 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.
LeetCode:链接
给定一个数组,求能不能把数组分成两部分使得两个子数组的和相等。
先进行数学分析,设子集为A、B,则有sum(A)+sum(B)=sum(nums),sum(A)=sum(B),则有sum(A)=sum(nums)/2。故可以将题目转化为从nums中寻找是否有和为sum(nums)/2的子集,有则返回True,否则返回False。
寻找和为sum(nums)/2的子集,可以使用动态规划的思路。用dp[i]来存储和为i的组合个数,对nums里边的数字用n进行遍历,对于所有i>=n的i,有dp[i]=dp[i]+dp[i-n]。
class Solution(object):
def canPartition(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
n = len(nums)
s = sum(nums)
if s % 2 != 0:
return False
target = s // 2
dp = [0] * (target+1)
dp[0] = 1
for num in nums:
i = target
while i >= num:
dp[i] = dp[i] + dp[i-num]
i -= 1
# 组合方法必须大于等于2
if dp[target] >= 2:
return True
else:
return False