416. Partition Equal Subset Sum

416. Partition Equal Subset Sum

• 題目描述：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.

• 題目大意：給定一個數組，問數組能否分爲兩個相同的部分

• 思路：dp，dp[i]表示數字i是否是原數組中任意個子集合的和，只需找到dp[target]是否爲真,target等於數組中所有元素和除以2，如果數組中所有元素和不能整除2則返回false。

  狀態轉移方程：dp[j] = dp[j] || dp[j - nums[i]] (nums[i] <= j <= target)

• 代碼：

  package DP;
  
  /**
  * @author OovEver
  * 2018/1/6 16:43
  */
  public class LeetCode416 {
    public boolean canPartition(int[] nums) {
        if (nums == null || nums.length == 0) {
            return true;
        }
        int sum = 0;
        for (int i=0;i<nums.length;i++) {
            sum += nums[i];
        }
        if (sum % 2 != 0) {
            return false;
        }
        int target = sum / 2;
        boolean[] dp = new boolean[target + 1];
        dp[0] = true;
        for(int i=0;i<nums.length;i++) {
            for(int j=target;j>=nums[i];j--) {
                dp[j] = dp[j] || dp[j - nums[i]];
            }
        }
        return dp[target];
    }
  }