Partition to K Equal Sum Subsets

Medium

Arrays Dynamic Programming Recursion Backtracking

Problem

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.

Constraints

1 <= k <= nums.length <= 16
1 <= nums[i] <= 10^4
The frequency of each element is in the range [1, 4]

Examples

Input: nums = [4,3,2,3,5,2,1], k = 4

Output: true

It is possible to divide it into 4 subsets (5), (1,4), (2,3), (2,3) with equal sums of 5 each.

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

Output: false

The total sum is 10, which is not divisible by 3, so equal partition is impossible.

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