2176. Count Equal and Divisible Pairs in an Array
Description
Given a 0-indexed integer array nums
of length n
and an integer k
, return the number of pairs (i, j)
where 0 <= i < j < n
, such that nums[i] == nums[j]
and (i * j)
is divisible by k
.
Example 1:
Input: nums = [3,1,2,2,2,1,3], k = 2 Output: 4 Explanation: There are 4 pairs that meet all the requirements: - nums[0] == nums[6], and 0 * 6 == 0, which is divisible by 2. - nums[2] == nums[3], and 2 * 3 == 6, which is divisible by 2. - nums[2] == nums[4], and 2 * 4 == 8, which is divisible by 2. - nums[3] == nums[4], and 3 * 4 == 12, which is divisible by 2.
Example 2:
Input: nums = [1,2,3,4], k = 1 Output: 0 Explanation: Since no value in nums is repeated, there are no pairs (i,j) that meet all the requirements.
Constraints:
1 <= nums.length <= 100
1 <= nums[i], k <= 100
Solutions
Solution 1: Enumeration
We first enumerate the index $j$ in the range $[0, n)$, and then enumerate the index $i$ in the range $[0, j)$. We count the number of pairs that satisfy $\textit{nums}[i] = \textit{nums}[j]$ and $(i \times j) \bmod k = 0$.
The time complexity is $O(n^2)$, where $n$ is the length of the array $\textit{nums}$. The space complexity is $O(1)$.
1 2 3 4 5 6 7 |
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1 2 3 4 5 6 7 8 9 10 11 |
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1 2 3 4 5 6 7 8 9 10 11 12 |
|
1 2 3 4 5 6 7 8 9 10 |
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1 2 3 4 5 6 7 8 9 10 11 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 |
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