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:

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.

思路：这是一道典型的背包问题，问题可以抽象成是否存在一个组合使该组合的和为sum/2，令dp[i , j]表示选了第i个数后是否能使和达到j，那么dp[0, 0] = 1

对于每个数i来说，可以选择i，也可以不选择i，不选择的话dp[i, j] = dp[i - 1, j]，选择的话dp[i, j] = dp[i - 1, j - i]，则dp[i, j]=dp[i - 1, j] || dp[i - 1, j - i]

最后返回dp[nums.size(), sum/2]

但是一般来说，这种题还可以优化空间，即用一个数组来计算。具体看http://love-oriented.com/pack/P01.html

代码：

class Solution {
public:
bool canPartition(vector<int>& nums) {
int sum = accumulate(nums.begin(), nums.end(), 0), target = sum >> 1;
if(sum & 1) return false;
vector<int> dp(target + 1, 0);
dp[0] = 1;
for(auto num : nums)
for(int i = target; i >= num; -- i)
dp[i] = dp[i] || dp[i - num];

return dp[target];
}
};