【leetcode】1497. Check If Array Pairs Are Divisible by k

题目如下：

Given an array of integers arr of even length n and an integer k.

We want to divide the array into exactly n / 2 pairs such that the sum of each pair is divisible by k.

Return True If you can find a way to do that or False otherwise. 

Example 1:

Input: arr = [1,2,3,4,5,10,6,7,8,9], k = 5
Output: true
Explanation: Pairs are (1,9),(2,8),(3,7),(4,6) and (5,10).

Example 2:

Input: arr = [1,2,3,4,5,6], k = 7
Output: true
Explanation: Pairs are (1,6),(2,5) and(3,4).

Example 3:

Input: arr = [1,2,3,4,5,6], k = 10
Output: false
Explanation: You can try all possible pairs to see that there is no way to divide arr into 3 pairs each with sum divisible by 10.

Example 4:

Input: arr = [-10,10], k = 2
Output: true

Example 5:

Input: arr = [-1,1,-2,2,-3,3,-4,4], k = 3
Output: true

Constraints:

• arr.length == n
• 1 <= n <= 10^5
• n is even.
• -10^9 <= arr[i] <= 10^9
• 1 <= k <= 10^5

解题思路：统计arr中每个元素除k后的余数出现的次数，接下来只要判断余数i出现的次数是否和余数k-i出现的次数相等即可。对于余数为0的情况，只要满足出现的次数为偶数即可。

代码如下：

class Solution(object):
    def canArrange(self, arr, k):
        """
        :type arr: List[int]
        :type k: int
        :rtype: bool
        """
        dic = {}
        for i in arr:
            remainder = i % k
            dic[remainder] =  dic.setdefault(remainder,0) + 1
        for key,val in dic.iteritems():
            if val == 0:continue
            elif key == 0 and val % 2 != 0:
                return False
            elif key == 0 and val % 2 == 0:
                continue
            elif k - key not in dic or dic[k-key] != val:
                return False
        return True