#2808

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Minimum Seconds to Equalize a Circular Array

Find the minimum number of seconds to equalize a circular array using array scanning and hash lookup techniques.

Problem Statement

You are given a 0-indexed array nums of length n containing integers. Your task is to determine the minimum number of seconds required to make all elements in the array equal by following a specific operation. In one second, each element in the array can be replaced simultaneously by the value at any other index of the array.

The key observation is that you can select any element as the target value for all elements in the array. You need to calculate the number of seconds required to transform all elements into that target value. The final goal is to find the minimum number of seconds required for equalizing the entire array.

Examples

Example 1

Input: nums = [1,2,1,2]

Output: 1

We can equalize the array in 1 second in the following way:

At 1st second, replace values at each index with [nums[3],nums[1],nums[3],nums[3]]. After replacement, nums = [2,2,2,2]. It can be proven that 1 second is the minimum amount of seconds needed for equalizing the array.

Example 2

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

Output: 2

We can equalize the array in 2 seconds in the following way:

At 1st second, replace values at each index with [nums[0],nums[2],nums[2],nums[2],nums[3]]. After replacement, nums = [2,3,3,3,3].
At 2nd second, replace values at each index with [nums[1],nums[1],nums[2],nums[3],nums[4]]. After replacement, nums = [3,3,3,3,3]. It can be proven that 2 seconds is the minimum amount of seconds needed for equalizing the array.

Example 3

Input: nums = [5,5,5,5]

Output: 0

We don't need to perform any operations as all elements in the initial array are the same.

Constraints

1 <= n == nums.length <= 105
1 <= nums[i] <= 109

Solution Approach

Scan the Array and Identify Frequencies

Start by calculating the frequency of each element in the array using a hash map. This will allow you to easily identify the most frequent value and determine the number of transformations needed for all elements to become that value.

Calculate Transformation Time

For each possible target value, calculate the number of seconds required to transform all elements to that value. This involves checking how many elements differ from the target and determining the minimal time by considering the largest group of elements that need transformation.

Choose the Optimal Target

Select the value that minimizes the transformation time. This involves considering each potential target and computing how quickly the entire array can be equalized based on its frequency and position.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the final approach. If the array is scanned once and each element's frequency is stored, the complexity is O(n), where n is the length of the array. The space complexity is also O(n) for storing frequencies of elements in a hash table.

What Interviewers Usually Probe

Look for understanding of hash map usage for counting frequencies.
Check for ability to identify the most frequent element and consider it as a candidate target.
Evaluate how efficiently the candidate target selection process is performed.

Common Pitfalls or Variants

Common pitfalls

Misunderstanding the problem and focusing on inefficient operations like sorting the array.
Failing to account for all possible target values in the array, which could lead to suboptimal solutions.
Neglecting to handle edge cases like arrays where all elements are already equal.

Follow-up variants

Variation 1: Include additional constraints on the range of values in the array.
Variation 2: Require that all replacements must be made in parallel within the same second.
Variation 3: Add a constraint where the number of replacements must be minimized.

FAQ

What is the primary pattern for solving 'Minimum Seconds to Equalize a Circular Array'?

The primary pattern involves array scanning and hash lookup, where you calculate the frequency of each value and determine the minimum number of seconds to make all elements equal.

How do you calculate the minimum number of seconds?

You calculate the number of seconds by checking how many elements need to change for each target value, then choosing the one with the minimal required seconds.

Is the solution for this problem based on greedy techniques?

The solution relies on identifying the optimal target value based on frequency, which could be seen as a greedy approach to minimize transformations.

How do hash tables help in solving this problem?

Hash tables help by allowing you to count the frequency of each element efficiently, enabling quick identification of the most frequent element, which is key to minimizing transformation time.

What should I do if all elements in the array are already equal?

If all elements are the same, no transformations are needed, so the minimum number of seconds is zero.

terminal

Solution

Solution 1: Enumeration

We assume that all elements eventually become $x$, and $x$ must be an element in the array.

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class Solution:
    def minimumSeconds(self, nums: List[int]) -> int:
        d = defaultdict(list)
        for i, x in enumerate(nums):
            d[x].append(i)
        ans = inf
        n = len(nums)
        for idx in d.values():
            t = idx[0] + n - idx[-1]
            for i, j in pairwise(idx):
                t = max(t, j - i)
            ans = min(ans, t // 2)
        return ans

Continue Practicing

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