Is Partition to K Equal Sum Subsets easy or hard?

Partition to K Equal Sum Subsets is considered Medium on LeetCode but often feels closer to Hard for beginners. The difficulty comes from pruning the exponential search space and recognizing patterns like bucket filling or bitmask DP.

Partition to K Equal Sum Subsets Python or Java solution?

Python and Java implementations usually follow the same pattern: compute the target subset sum, sort the array descending, and use recursive backtracking to place numbers into k buckets. Bitmask DP versions are also common in Java and C++ because bit operations are efficient.

How to solve Partition to K Equal Sum Subsets in O(n * 2^n)?

Use dynamic programming with bitmask state compression. Each mask represents which elements are already used. The DP state stores the current subset sum modulo the target value. Transition by adding unused elements while keeping the partial sum ≤ target. Reaching the full mask means all numbers were partitioned successfully.

What is the best approach for Partition to K Equal Sum Subsets?

Backtracking with target subset sums is the most common approach. Sort the array in descending order and recursively assign numbers to k buckets while keeping each bucket's sum ≤ target. With pruning and symmetry checks, the search space reduces significantly. Time complexity is roughly O(k * 2^n) with O(n) recursion space.

Is Partition to K Equal Sum Subsets asked at Google Amazon Meta?

Partition to K Equal Sum Subsets appears frequently in interviews at companies that test recursion and combinatorial search, including Google, Amazon, and Meta-style interview prep sets. The problem evaluates backtracking optimization, pruning strategies, and understanding of subset state representations.

What data structure is used in Partition to K Equal Sum Subsets?

The typical solution uses arrays to track bucket sums and recursion for backtracking. Advanced implementations also use bitmasks and hash-based memoization to store visited subset states, enabling dynamic programming with compressed state representation.

What is the time complexity of Partition to K Equal Sum Subsets?

The optimized backtracking solution runs in about O(k * 2^n) time because it explores subset combinations while pruning invalid states. The dynamic programming solution with bitmask state compression runs in O(n * 2^n) time and uses O(2^n) memory for DP states.

Description Hints 1 Solution Video 11:03

698. Partition to K Equal Sum Subsets

Medium38.6% acceptance8 companies

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 is 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].

Asked at 8 companies

LinkedIn Zeta Microsoft

Google Amazon Tiktok Meta Bloomberg

Topics

Hints open one at a time

Hint 1

We can figure out what target each subset must sum to. Then, let's recursively search, where at each call to our function, we choose which of k subsets the next value will join.

11:03

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