Leetcode 416 - Partition Equal Subset Sum

题目：

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.
Example1：

Input: [1, 5, 11, 5]
Output: true
Explanation: The array can be partitioned as [1, 5, 5] and [11].

Example2：

Input: [1, 2, 3, 5]
Output: false
Explanation: The array cannot be partitioned into equal sum subsets.

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思路：

该题采用动态规划的思路来做。

• dp[i][n] : 代表i个物品在体积为n的情况下的最大值。
• 状态转移方程:

dp[i][j] = Math.max(dp[i-1][j], dp[i-1][j - nums[i]] + nums[]i);

注意：
数组中所有数的和必须为偶数。如果为奇数则返回false。是偶数则和sum除以2。求出n个物品在体积为sum/2的情况下的最大值。

如果dp[n][sum/2] == sum/2返回True，否则返回False。

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代码：

public boolean canPartition(int[] nums) {
        boolean flag = false;
        if(nums == null || nums.length == 0)
            return flag;
        int sum = 0;
        for(int num:nums){
            sum += num;
        }
        if(sum % 2 == 1)
            return false;
        sum /= 2;
        int [][] dp = new int [nums.length][sum + 1];
        for(int i=nums[0];i