Is Minimum Operations to Make the Array Beautiful easy or hard?

Minimum Operations to Make the Array Beautiful is usually categorized as a Medium difficulty problem. The main challenge is recognizing the correct state transition or greedy rule that allows you to convert a naive simulation into a linear dynamic programming solution.

Minimum Operations to Make the Array Beautiful Python/Java solution

The solution is typically implemented with a single loop that tracks violations and updates an operation counter. FleetCode provides implementations in Python, Java, C++, Go, TypeScript, and Rust using the same O(n) dynamic programming logic.

How to solve Minimum Operations to Make the Array Beautiful in O(n)?

Iterate through the array while maintaining a state that represents whether the current prefix is already valid. When the current element breaks the beauty condition with the previous element, increment the operation counter and logically adjust the state to reflect the performed modification. This avoids revisiting earlier elements and guarantees O(n) processing time.

What is the best approach for Minimum Operations to Make the Array Beautiful?

The most efficient approach uses a linear dynamic programming or greedy state transition. You process the array once and track whether the current element violates the beauty constraint relative to the previous element. When a violation occurs, perform one operation and update the state so the rest of the array remains valid. This produces an O(n) time and O(1) space solution.

Is Minimum Operations to Make the Array Beautiful asked at Google/Amazon/Meta?

Problems involving array transformations with minimal operations and dynamic programming patterns frequently appear in interviews at companies like Google, Amazon, and Meta. Variants that require enforcing adjacency rules or pair constraints are especially common in coding rounds.

What data structure is used in Minimum Operations to Make the Array Beautiful?

The core structure is a simple array traversal combined with dynamic programming states. Instead of complex data structures, the algorithm typically maintains a few variables that track the previous element’s condition and the current operation count.

What is the time complexity of Minimum Operations to Make the Array Beautiful?

The optimal solution runs in O(n) time because the array is scanned once while maintaining a small state describing the previous element’s validity. Space complexity can be reduced to O(1) by storing only the last state instead of a full DP array.

Description Hints 3 Solution

3717. Minimum Operations to Make the Array Beautiful

Medium36.9% acceptancePremium elsewhere, free here

You are given an integer array nums.

An array is called beautiful if for every index i > 0, the value at nums[i] is divisible by nums[i - 1].

In one operation, you may increment any element nums[i] (with i > 0) by 1.

Return the minimum number of operations required to make the array beautiful.

Example 1:

Input: nums = [3,7,9]

Output: 2

Explanation:

Applying the operation twice on nums[1] makes the array beautiful: [3,9,9]

Example 2:

Input: nums = [1,1,1]

Output: 0

Explanation:

The given array is already beautiful.

Example 3:

Input: nums = [4]

Output: 0

Explanation:

The array has only one element, so it's already beautiful.

Constraints:

1 <= nums.length <= 100
1 <= nums[i] <= 50

Topics

Array Dynamic Programming

Hints open one at a time

Hint 1

Use dynamic programming.

Hint 2

For each index i, compute dp[i][val] where dp[i][val] is the minimum number of increments needed to make position i equal to val.

Hint 3

Carefully combine DP states for index i with those for index i - 1.

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[3,7,9]

Input

[1,1,1]

Input

[4]

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