Count Almost Equal Pairs I

Problem Description

You are given an array nums consisting of positive integers. We call two integers x and y in this problem almost equal if both integers can become equal after performing the following operation at most once: Choose either x or y and swap any two digits within the chosen number. Return the number of indices i and j in nums where i < j such that nums[i] and nums[j] are almost equal.

Key Insights

• Two numbers are almost equal if their sorted digits can match after at most one swap in either number.
• A digit swap in one of the numbers can create a new arrangement of digits.
• Use a sorted representation of the digits to easily compare the potential equality of the two numbers.
• Count pairs of numbers that can be transformed into the same sequence of digits.

Space and Time Complexity

Time Complexity: O(n^2 * k log k), where n is the number of elements in nums and k is the maximum number of digits in any number. Space Complexity: O(n), for storing the sorted digit representations.

Solution

To solve this problem, we can use the following approach:

1. Create a helper function that takes a number, converts it to a string, and returns a sorted string of its digits.
2. Use a dictionary to track how many times each sorted digit representation appears.
3. For each number in the array, retrieve its sorted digit representation and count how many times it has been seen before.
4. Use the counts to calculate the number of almost equal pairs.

Code Solutions