[LeetCode416]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:

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.

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使用动态规划的方法来解决这个问题，用布尔数组dp[i]表示能否用给定数组中的项求和得到i，能则为true，否则为false，得到状态转移方程为dp[j]=dp[j]||dp[j-nums[i]]，代码如下：
class Solution {
public:
bool canPartition(vector<int>& nums) {
int n=nums.size();
int sum=0;
for(int i=0;i<n;i++)
{
sum+=nums[i];
}
if(sum%2!=0)
return false;
bool dp[sum/2+1]={false};
dp[0]=true;
for(int i=0;i<n;i++)
{
for(int j=sum/2;j>=nums[i];j--)
{
dp[j]=dp[j]||dp[j-nums[i]];
}
}
return dp[sum/2];
}
};