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 is represented by the condition that the sum of two hours is a multiple of 24.
- We can utilize a hash table (or dictionary) to count occurrences of each remainder when hours are divided by 24.
- For each hour, calculate its remainder when divided by 24 and find the complement remainder that would sum to 24.
- The number of valid pairs can be counted based on the occurrences of these remainders.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1) (since the hash table size is fixed at 24)
Solution
To solve the problem, we can use a hash table to count the frequency of each remainder (from 0 to 23) when hours are divided by 24. For each hour, we calculate its remainder and find its complement remainder that would sum to 24. The total pairs are derived based on the frequency of these remainders. The algorithm involves iterating through the array once, making it efficient.