Is Minimum Subarrays in a Valid Split easy or hard?

Minimum Subarrays in a Valid Split is rated Medium difficulty. The recursion and DP structure are straightforward, but recognizing that the condition only depends on gcd of the first and last elements requires some number theory insight.

Minimum Subarrays in a Valid Split Python/Java solution

The memoized DFS approach translates cleanly to Python, Java, C++, and Go. Implement a recursive function dfs(i) that returns the minimum number of segments starting from index i. Store results in a DP array or hash map to ensure each index is computed once.

How to solve Minimum Subarrays in a Valid Split in O(n)?

Near‑linear solutions rely on number theory. By tracking prime factors of each number and connecting indices that share a factor, you can jump directly to valid endpoints instead of scanning the entire suffix. With efficient factorization and bookkeeping, the complexity approaches O(n logA).

What is the best approach for Minimum Subarrays in a Valid Split?

The most practical solution uses memoized depth‑first search (top‑down dynamic programming). For each starting index, try extending the subarray and check if gcd(nums[i], nums[j]) > 1. Cache results for each index to avoid recomputation. This reduces the complexity to O(n^2 logA) time with O(n) space.

Is Minimum Subarrays in a Valid Split asked at Google/Amazon/Meta?

Problems combining dynamic programming with number theory constraints appear frequently in interviews at companies like Google, Amazon, and Meta. Variants involving GCD conditions, prime factors, and optimal partitioning are common in high‑level algorithm rounds.

What data structure is used in Minimum Subarrays in a Valid Split?

The core solution uses an array for memoization combined with recursion (DFS). Each state represents the minimum splits needed from a given index. The algorithm also relies on the gcd operation from number theory to validate subarray boundaries.

What is the time complexity of Minimum Subarrays in a Valid Split?

The common dynamic programming approach runs in O(n^2 logA) time. There are n DP states, and each state scans up to n elements while computing gcd values that take O(logA) time. Space complexity is O(n) for the memoization table.

Description Hints 5 Solution Video 15:07

2464. Minimum Subarrays in a Valid Split

Medium64.7% acceptancePremium elsewhere, free here

You are given an integer array nums.

Splitting of an integer array nums into subarrays is valid if:

the greatest common divisor of the first and last elements of each subarray is greater than 1, and
each element of nums belongs to exactly one subarray.

Return the minimum number of subarrays in a valid subarray splitting of nums. If a valid subarray splitting is not possible, return -1.

Note that:

The greatest common divisor of two numbers is the largest positive integer that evenly divides both numbers.
A subarray is a contiguous non-empty part of an array.

Example 1:

Input: nums = [2,6,3,4,3]
Output: 2
Explanation: We can create a valid split in the following way: [2,6] | [3,4,3].
- The starting element of the 1^st subarray is 2 and the ending is 6. Their greatest common divisor is 2, which is greater than 1.
- The starting element of the 2^nd subarray is 3 and the ending is 3. Their greatest common divisor is 3, which is greater than 1.
It can be proved that 2 is the minimum number of subarrays that we can obtain in a valid split.

Example 2:

Input: nums = [3,5]
Output: 2
Explanation: We can create a valid split in the following way: [3] | [5].
- The starting element of the 1^st subarray is 3 and the ending is 3. Their greatest common divisor is 3, which is greater than 1.
- The starting element of the 2^nd subarray is 5 and the ending is 5. Their greatest common divisor is 5, which is greater than 1.
It can be proved that 2 is the minimum number of subarrays that we can obtain in a valid split.

Example 3:

Input: nums = [1,2,1]
Output: -1
Explanation: It is impossible to create valid split.

Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁵

Topics

Hints open one at a time

Hint 1

Find the minimum number of subarrays needed to validly split each prefix of the input array a.

Hint 2

Denote dp[i] as the minimum number of subarrays needed to validly split [a[0], a[1], … , a[i - 1]], where dp[0] = 0.

Hint 3

Think about the dynamic programming transitions.

Hint 4

If we split the first i elements of the array, the last subarray in this splitting will end with a[i - 1] and start with some a[j], where gcd(a[j], a[i - 1]) ≠ 1. Then, we need to validly split the first j elements of the array, or [a[0]…a[j - 1]].

Hint 5

Iterate over all possible j < i such that gcd(a[j], a[i - 1]) ≠ 1 and let dp[i] = min(dp[i], dp[j] + 1).

15:07

Still stuck?Read the written solution, or watch a walkthrough.

Open solution

2464. Minimum Subarrays in a Valid Split

Topics

Hints open one at a time

Similar problems