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4053. Minimum Operations to Make Every Element Palindromic

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4053. Minimum Operations to Make Every Element Palindromic

Medium12.5% 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
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[10,12,14,16]