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:

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.

这道题让分成两个部分，那么就是找一些数字加起来==sum/2

就是说对于num[i]可以加也可以不加（0或1）

模型成把一个容量为（sum/2）的背包装满，背包问题，就像geeks for geeks写的，这个backtracking 过程中存在大量重复操作O(2^n)

DP子问题：n个物品（n层），goal容量0-v

“将前i件物品放入容量为v的背包中”
dp[i][v] = dp[i-1][v] || dp[i-1][v-nums[i]];

   public boolean canPartition(int[] nums) {  
     int sum = 0;  
     for(int i = 0; i < nums.length; i++)  
       sum += nums[i];  
     if(sum%2 == 1) return false;  
     int n = sum/2;  
     boolean[] dp = new boolean[n+1];  
     dp[0] = true;  
     for(int i = 0; i <nums.length; i++){  
       for(int j = n; j >= nums[i]; j--){  
         dp[j] = dp[j] || dp[j-nums[i]];  
       }  
     }  
     System.out.println(Arrays.toString(dp));  
     return dp[n];  
   }