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.

需要分成和相等的两部分，数组所有元素的和为sum，那么两部分的和就分别是sum/2
只要在数组中抽出一些元素出来使得和达到sum/2就可以了，dfs解决，为了提高搜索效率和方便剪枝可以先排序

public class Solution {
public boolean canPartition(int[] nums)
{
int sum=0;
for(int num :nums)
sum+=num;
if(sum%2!=0)
return false;
sum/=2;
Arrays.sort(nums);
for(int i=0,j=nums.length-1;i<j;i++,j--)
{
int temp=nums[i];
nums[i]=nums[j];
nums[j]=temp;
}
return dfs(0, sum, 0, nums, -1);
}

public boolean dfs(int index,int target,int sum_now,int[] nums,int last_index)
{
if(last_index>=nums.length-1||sum_now>target)
return false;
if(sum_now==target)
return true;
for(int i=last_index+1;i<nums.length;i++)
if(dfs(i, target, sum_now+nums[i], nums, i))
return true;
return false;
}
}