Partition Array into Two Equal Product Subsets

Partition Array into Two Equal Product Subsets

What is this problem about?

The Partition Array into Two Equal Product Subsets problem asks whether an array can be partitioned into two non-empty subsets with equal product. This coding problem uses bit manipulation to enumerate subsets and check if any subset and its complement have equal products. The array, recursion, enumeration, and bit manipulation interview pattern is demonstrated.

Why is this asked in interviews?

Meta asks this to test bitmask subset enumeration with product equality. With small array sizes, enumerating all 2^n subsets is feasible. The key insight: if total product P is a perfect square (P = S²), some subset might have product S.

Algorithmic pattern used

Bitmask subset enumeration. Compute total product P. For each non-empty proper subset (bitmask from 1 to 2^n-2): compute subset product. If subset_product == P / subset_product (i.e., subset_product² == P), return true. Handle zeros carefully (product involving zero requires special treatment).

Example explanation

arr=[2,4,2,4]. Total product=64=8². Subsets of product 8: {2,4}→8. Complement {2,4}→8. Return true.

arr=[1,2,3,4]. Total=24. Need subset with product √24 (not integer). Return false.

Common mistakes candidates make

• Not handling zeros (a subset with a 0 makes product 0).
• Not checking that both subsets are non-empty.
• Integer overflow when computing products of many elements.
• Forgetting that subset_product * complement_product = total_product (use this as check).

Interview preparation tip

Subset enumeration with bitmasks is feasible for n ≤ 20. For product equality, check if (product^2 == total_product) using the square root test for exact integer square roots. Bitmask enumeration is the brute-force approach; always discuss it first, then mention optimizations like early termination or memoized recursion for larger inputs.