Minimum Division Operations to Make Array Non Decreasing Python/Java solution

Most implementations follow the same greedy idea. Traverse the array from right to left, compare each value with the next allowed value, and perform divisions when needed. This approach can be implemented in Python, JavaScript, Java, or C++ with roughly O(n log V) complexity.

What is the best approach for Minimum Division Operations to Make Array Non Decreasing?

The greedy right‑to‑left reduction approach is the most efficient. Iterate from the end of the array and ensure each element is less than or equal to the next valid value. If it is larger, repeatedly divide it using valid divisors until the constraint holds. This method minimizes operations locally and runs in about O(n log V) time.

Is Minimum Division Operations to Make Array Non Decreasing asked at Google/Amazon/Meta?

Problems combining greedy logic with number‑theory style reductions appear in interviews at companies like Google, Amazon, and Meta. Variants often test the ability to enforce ordering constraints in arrays while minimizing operations.

What data structure is used in Minimum Division Operations to Make Array Non Decreasing?

The common implementation uses a stack or a running bound variable while iterating from right to left. The stack stores validated elements and helps maintain the maximum allowed value for the previous index. The core logic relies on array traversal and divisor calculations.

What is the time complexity of Minimum Division Operations to Make Array Non Decreasing?

The optimal greedy solution runs in O(n log V) time where n is the array length and V is the maximum element value. Each element may be reduced multiple times, but division quickly shrinks numbers. Space complexity is O(n) if a stack is used, or O(1) if only a running bound is tracked.

Description Hints 2 Solution Video 15:35

3326. Minimum Division Operations to Make Array Non Decreasing

Q: Is Minimum Division Operations to Make Array Non Decreasing easy or hard?

The problem is rated Medium on LeetCode with an acceptance rate around 29%. The difficulty comes from recognizing the greedy invariant and understanding how divisor reductions interact with the non‑decreasing constraint.

Q: How to solve Minimum Division Operations to Make Array Non Decreasing in O(n)?

A near‑linear strategy processes the array from right to left and keeps the maximum allowed value for the current position. When an element exceeds this bound, divide it by appropriate divisors until it becomes valid. Because each operation significantly reduces the number, the practical complexity behaves close to O(n) for typical constraints.

Medium29.1% acceptance2 companies

You are given an integer array nums.

Any positive divisor of a natural number x that is strictly less than x is called a proper divisor of x. For example, 2 is a proper divisor of 4, while 6 is not a proper divisor of 6.

You are allowed to perform an operation any number of times on nums, where in each operation you select any one element from nums and divide it by its greatest proper divisor.

Return the minimum number of operations required to make the array non-decreasing.

If it is not possible to make the array non-decreasing using any number of operations, return -1.

Example 1:

Input: nums = [25,7]

Output: 1

Explanation:

Using a single operation, 25 gets divided by 5 and nums becomes [5, 7].

Example 2:

Input: nums = [7,7,6]

Output: -1

Example 3:

Input: nums = [1,1,1,1]

Output: 0

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁶

Asked at 2 companies

Google Amazon

Topics

Hints open one at a time

Hint 1

Iterate backward from the last index.

Hint 2

Each number can be divided by its largest proper divisor to yield its smallest prime divisor.

15:35

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