How do you solve Minimum Cost to Make Array Equalindromic on LeetCode?

Minimum Cost to Make Array Equalindromic (LeetCode #2967) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: The median of the array helps minimize the total cost when converting to a palindromic number.

What is the time complexity of Minimum Cost to Make Array Equalindromic?

The optimal solution for Minimum Cost to Make Array Equalindromic runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the array, and O(n) for calculating the cost for each candidate palindromic number.

What is the brute force solution for Minimum Cost to Make Array Equalindromic?

The brute force approach for Minimum Cost to Make Array Equalindromic is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every palindromic number less than 10^9 and calculating the cost to convert all elements of the array to that number. This is simple but inefficient as it checks all possibilities. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Cost to Make Array Equalindromic?

Minimum Cost to Make Array Equalindromic uses the following concepts: Array, Math, Binary Search, Greedy, Sorting. The recommended patterns to study are: Sorting, Greedy Algorithms.

What are the interview tips for Minimum Cost to Make Array Equalindromic?

Always clarify the problem and constraints before jumping into coding. Think about edge cases, such as arrays with all identical numbers or very large numbers. Explain your thought process clearly while coding; it shows your understanding.

What are common mistakes when solving Minimum Cost to Make Array Equalindromic?

Forgetting to sort the array before finding the median. Not considering the range of palindromic numbers around the median.

#2967

Minimum Cost to Make Array Equalindromic

Medium

ArrayMathBinary SearchGreedySortingSortingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal solution leverages the properties of palindromic numbers and the median of the array. By focusing on the median, we can minimize the total cost effectively.

⚙️

Algorithm

4 steps

1Step 1: Sort the array to find the median.
2Step 2: Identify the closest palindromic numbers around the median.
3Step 3: Calculate the cost to convert all elements to these palindromic candidates.
4Step 4: Return the minimum cost.

solution.py19 lines

1def is_palindrome(x): return str(x) == str(x)[::-1]
2
3def closest_palindromic(m):
4    candidates = []
5    for i in range(m - 10, m + 10):
6        if is_palindrome(i): candidates.append(i)
7    return candidates
8
9
10def min_cost_to_palindromic(nums):
11    nums.sort()
12    n = len(nums)
13    median = nums[n // 2] if n % 2 != 0 else nums[n // 2 - 1]
14    palindromic_candidates = closest_palindromic(median)
15    min_cost = float('inf')
16    for p in palindromic_candidates:
17        cost = sum(abs(num - p) for num in nums)
18        min_cost = min(min_cost, cost)
19    return min_cost

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the array, and O(n) for calculating the cost for each candidate palindromic number.

1The median of the array helps minimize the total cost when converting to a palindromic number.
2Palindromic numbers are symmetric, which allows us to focus on a limited range around the median.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.