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Solution: Pairs of Songs With Total Durations Divisible by 60

Explore how to identify pairs of songs where the total duration is divisible by 60 by using a remainder tracking approach. Understand the process of counting valid pairs through modular arithmetic and how to implement this efficiently with linear time and constant space complexity.

Statement

You are given a list of songs, where the duration of each song is represented by an integer array time, where time[i] indicates the length of the ithi^{th} song in seconds.

Your task is to find and return the number of pairs of songs (i, j) such that:

  • i < j (i.e., the pair should consist of two distinct songs)

  • The sum of their durations is divisible by 60, i.e., (time[i] + time[j]) % 60 == 0.

Constraints:

  • ...