partition-to-k-equal-sum-subsets

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Description

Given an integer array nums and an integer k, return true if it is 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.

Example 2:

Input: nums = [1,2,3,4], k = 3
Output: false

 

Constraints:

• 1 <= k <= nums.length <= 16
• 1 <= nums[i] <= 104
• The frequency of each element is in the range [1, 4].

Solution(Python)

class Solution(object):
    def canPartitionKSubsets(self, nums, k):
        nums.sort()
        target, rem = divmod(sum(nums), k)
        if rem or nums[-1] > target:
            return False
        dp = [False] * (1 << len(nums))
        dp[0] = True
        total = [0] * (1 << len(nums))

        for state in range(1 << len(nums)):
            if not dp[state]:
                continue
            for i, num in enumerate(nums):
                future = state | (1 << i)
                if state != future and not dp[future]:
                    if num <= target - (total[state] % target):
                        dp[future] = True
                        total[future] = total[state] + num
                    else:
                        break
        return dp[-1]