[leetcode] 1010. Pairs of Songs With Total Durations Divisible by 60

Description

In a list of songs, 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: [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: [60,60,60]
Output: 3
Explanation: All three pairs have a total duration of 120, which is divisible by 60.

Note:

1. 1 <= time.length <= 60000.
2. 1 <= time[i] <= 500.

分析

题目的意思是：求出所有两个数加起来能够被60整除的对，我最开始用暴力破解了一下，果然超时了，看了结果才发现需要找规律，做法是这样，首先对所有的数用60取余数，然后进行统计，我这里用字典实现了统计的过程，接着就是从余数中统计出哪些组合能够被60整除了，余数为0或者30的数，组合形式的数目为v*(v-1)//2，不要问我为什么，我也只是验证了一下，发现是这个样子的。对于小于30的数，看字典中有没有能够加在一起构成60的，如果有组合形式就为，避免重复，大于30的就要跳过了哈：

cnt+=cnt_dict[k]*cnt_dict[60-k]

代码

class Solution:
    def numPairsDivisibleBy60(self, time: List[int]) -> int:
        n=len(time)
        cnt=0
        cnt_dict={}
        for i in range(n):
            key=time[i]%60
            if(key in cnt_dict):
                cnt_dict[key]+=1
            else:
                cnt_dict[key]=1
                
        for k,v in cnt_dict.items():
            if(k==0 or k==30):
                cnt+=v*(v-1)//2
            elif(k>30):
                continue
            elif(60-k in cnt_dict):
                cnt+=cnt_dict[k]*cnt_dict[60-k]
        return cnt

参考文献

[LeetCode] Tried this in Python