698. Partition to K Equal Sum Subsets

Given an array of integers nums and a positive integer k, find whether it’s possible to divide this array into k non-empty subsets whose sums are all equal.

Example 1:

Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
Output: True
Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.

Note:

1 <= k <= len(nums) <= 16.

0 < nums[i] < 10000.

class Solution {
public boolean canPartitionKSubsets(int[] nums, int k) {
int N = nums.length;
Arrays.sort(nums);
int sum = Arrays.stream(nums).sum();
int target = sum / k;
if (sum % k > 0 || nums[N - 1] > target)
return false;

boolean[] dp = new boolean[1 << N];
dp[0] = true;
int[] total = new int[1 << N];

for (int state = 0; state < (1 << N); state++) {
if (!dp[state])
continue;
for (int i = 0; i < N; i++) {
int future = state | (1 << i);
if (state != future && !dp[future]) {
if (nums[i] <= target - (total[state] % target)) {
dp[future] = true;
total[future] = total[state] + nums[i];
} else {
break;
}
}
}
}
return dp[(1 << N) - 1];
}
}