Pairs of Songs With Total Durations Divisible by 60 - Solution & Explanation

This approach uses the idea of complementary remainders. If the sum of the remainders of two numbers when divided by 60 equals 60, then their sum is divisible by 60. For example, if the remainder of a number A is 10, you would need a number B whose remainder is 50 to ensure their sum is divisible by 60 (since 10 + 50 = 60).

We can leverage this by keeping a count of all remainders encountered so far and for each number, check for its complement remainder that, when added, will result in a number divisible by 60.

The C solution uses an array 'remainder' to store counts of remainders of each number in the input divided by 60. For each element, it checks how many elements with a complementary remainder have been seen so far and adds that count to the total.

In this approach, we use a brute force double loop to compare each pair of songs. For each song, pair it with every other song that comes after it and check if their total duration is divisible by 60. This is a straightforward method but inefficient for large inputs.

Although simple, this method is not optimal for large datasets but can work if constraints are smaller.

The brute force C solution uses nested loops to compute every possible pair of songs and checks if their combined duration is divisible by 60. This results in a simple, albeit inefficient solution.