总时长可被 60 整除的歌曲对

Pairs of Songs With Total Durations Divisible by 60

专题: Algorithmic Programming / 算法编程
难度: L3
来源: Citadel

题目详情

问题：总时长可被 60 整除的歌曲对

考察：数组

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/pairs-of-songs-with-total-durations-divisible-by-60/

You are given a list of songs where the i^th song has a duration of time[i] seconds.

Return the number of pairs of songs for which their total duration in seconds is divisible by 60. Formally, we want the number of indices i, j such that i < j with (time[i] + time[j]) % 60 == 0.

Example 1:

Input: time = [30,20,150,100,40]
Output: 3
Explanation: Three pairs have a total duration divisible by 60:
(time[0] = 30, time[2] = 150): total duration 180
(time[1] = 20, time[3] = 100): total duration 120
(time[1] = 20, time[4] = 40): total duration 60

Example 2:

Input: time = [60,60,60]
Output: 3
Explanation: All three pairs have a total duration of 120, which is divisible by 60.

Constraints:

1 <= time.length <= 6 * 10⁴
1 <= time[i] <= 500

解析

思路：只关心每首歌时长模 60 的余数。遍历时当前余数 r 需要匹配 (60-r)%60，先累加已有匹配数量，再记录当前余数。

复杂度：时间 O(n)，空间 O(60)。