Is Minimum Operations to Make Every Element Palindromic easy or hard?

It is rated Medium on FleetCode with a 14.9% acceptance rate. The difficulty comes from recognizing that you need to precompute palindromes and apply binary search, rather than checking each number individually.

Minimum Operations to Make Every Element Palindromic Python/Java solution

In Python, precompute palindromes into a sorted list and use the bisect module for binary search. In Java, use Arrays.binarySearch on an int array of palindromes. Both approaches run in O(n log m) time and are available on FleetCode in Python, Java, C++, Go, and TypeScript.

What is the best approach for Minimum Operations to Make Every Element Palindromic?

The best approach is to precompute all palindromic numbers up to a reasonable upper bound, store them in a sorted list, and then for each element use binary search to find the closest palindrome. This gives O(n log m) time complexity, where n is the array length and m is the number of precomputed palindromes.

Is Minimum Operations to Make Every Element Palindromic asked at Google/Amazon/Meta?

This problem is tagged under Array and Binary Search on FleetCode, and similar palindrome-manipulation problems appear in interviews at top companies. The core technique of precomputing candidates and using binary search is a common interview pattern at Google, Amazon, and Meta.

What data structure is used in Minimum Operations to Make Every Element Palindromic?

A sorted array or list is used to store all precomputed palindromic numbers. Binary search is then applied on this sorted list to find the closest palindrome for each element in the input array.

What is the time complexity of Minimum Operations to Make Every Element Palindromic?

The optimal solution using precomputed palindromes and binary search runs in O(n log m) time, where n is the number of elements and m is the number of precomputed palindromes. The space complexity is O(m) to store the sorted list of palindromes.

Description Hints 3 Solution Video 21:06

4053. Minimum Operations to Make Every Element Palindromic

Q: How to solve Minimum Operations to Make Every Element Palindromic in O(n log n)?

Precompute all palindromic numbers up to the maximum possible value in the array and store them in a sorted list. Then for each element, use binary search to find the closest palindrome by checking the insertion point and the element before it. Sum the minimum absolute differences to get the answer.

Medium15.5% acceptance

You are given an integer array nums.

In one operation, you may choose an index i and either increment or decrement nums[i] by 2.

Return the minimum number of operations required to make every element in nums a positive palindrome. Different elements may be changed into different palindromic integers.

Example 1:

Input: nums = [10,12,14,16]

Output: 9

Explanation:

One optimal sequence of operations is:

Decrement nums[0] by 2 once to change it from 10 to 8.
Decrement nums[1] by 2 twice to change it from 12 to 8.
Decrement nums[2] by 2 three times to change it from 14 to 8.
Increment nums[3] by 2 three times to change it from 16 to 22.

After 1 + 2 + 3 + 3 = 9 operations, nums = [8, 8, 8, 22], and every element is a positive palindromic integer.

It can be shown that fewer than 9 operations cannot achieve this.

Example 2:

Input: nums = [9,10,11,10]

Output: 2

Explanation:

Decrement nums[1] and nums[3] by 2 once each.

After 2 operations, nums = [9, 8, 11, 8], and every element is a positive palindromic integer.

At least one operation is needed for each of these two elements, so the minimum number of operations is 2.

Example 3:

Input: nums = [125]

Output: 2

Explanation:

Decrement nums[0] by 2 twice to change it from 125 to 121, which is a positive palindromic integer.

A single operation would change it to 123 or 127, neither of which is palindromic. Thus, the minimum number of operations is 2.

Constraints:

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

Topics

Array Binary Search

Hints open one at a time

Hint 1

Each operation preserves parity. Handle each element independently by finding its nearest positive palindrome of the same parity.

Hint 2

Precompute all positive palindromes up to 2,000,000,002 by mirroring their first halves, and separate them into sorted lists by parity. Perform this precomputation only once, using global or static initialization, and reuse the lists across all test cases.

Hint 3

Binary search the appropriate list for the closest candidates on either side of each element. Changing x into p costs |x - p| / 2 operations.

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4053. Minimum Operations to Make Every Element Palindromic

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