Count Pairs That Form a Complete Day II

Problem Description

Given an integer array hours representing times in hours, return an integer denoting the number of pairs i, j where i < j and hours[i] + hours[j] forms a complete day. A complete day is defined as a time duration that is an exact multiple of 24 hours.

Key Insights

• A complete day can be represented by the condition hours[i] + hours[j] % 24 == 0.
• To form pairs efficiently, we can leverage the properties of modulo operation.
• We can count occurrences of each remainder when divided by 24.
• For each hour, we can determine the required complement (24 - current remainder) to form a complete day.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1) (constant space for counting remainders since there are only 24 possible remainders)

Solution

To solve the problem, we will:

1. Create an array to count the frequency of each remainder when the hours are divided by 24.
2. Iterate through the hours array and calculate the remainder for each hour.
3. For each hour's remainder, determine the complementary remainder needed to reach a multiple of 24.
4. Count valid pairs using the frequency of the complementary remainders.
5. Return the total count of pairs.

This approach efficiently counts pairs in linear time while using a fixed amount of extra space.

Code Solutions