Partition Equal Subset Sum

题目地址：
https://leetcode.com/problems/partition-equal-subset-sum/description/

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:

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.

解题思路：
link: https://discuss.leetcode.com/topic/67539/0-1-knapsack-detailed-explanation

代码：

public boolean canPartition(int[] nums) {
    int sum = 0;

    for (int num : nums) {
        sum += num;
    }

    if ((sum & 1) == 1) {
        return false;
    }
    sum /= 2;

    int n = nums.length;
    boolean[][] dp = new boolean[n+1][sum+1];
    for (int i = 0; i < dp.length; i++) {
        Arrays.fill(dp[i], false);
    }

    dp[0][0] = true;

    for (int i = 1; i < n+1; i++) {
        dp[i][0] = true;
    }
    for (int j = 1; j < sum+1; j++) {
        dp[0][j] = false;
    }

    for (int i = 1; i < n+1; i++) {
        for (int j = 1; j < sum+1; j++) {
            dp[i][j] = dp[i-1][j];
            if (j >= nums[i-1]) {
                dp[i][j] = (dp[i][j] || dp[i-1][j-nums[i-1]]);
            }
        }
    }

    return dp[n][sum];
}

 优化：

public boolean canPartition(int[] nums) {
    int sum = 0;

    for (int num : nums) {
        sum += num;
    }

    if ((sum & 1) == 1) {
        return false;
    }
    sum /= 2;

    int n = nums.length;
    boolean[] dp = new boolean[sum+1];
    Arrays.fill(dp, false);
    dp[0] = true;

    for (int num : nums) {
        for (int i = sum; i > 0; i--) {
            if (i >= num) {
                dp[i] = dp[i] || dp[i-num];
            }
        }
    }

    return dp[sum];
}