2006. Count Number of Pairs With Absolute Difference K
Description
Given an integer array nums
and an integer k
, return the number of pairs (i, j)
where i < j
such that |nums[i] - nums[j]| == k
.
The value of |x|
is defined as:
x
ifx >= 0
.-x
ifx < 0
.
Example 1:
Input: nums = [1,2,2,1], k = 1 Output: 4 Explanation: The pairs with an absolute difference of 1 are: - [1,2,2,1] - [1,2,2,1] - [1,2,2,1] - [1,2,2,1]
Example 2:
Input: nums = [1,3], k = 3 Output: 0 Explanation: There are no pairs with an absolute difference of 3.
Example 3:
Input: nums = [3,2,1,5,4], k = 2 Output: 3 Explanation: The pairs with an absolute difference of 2 are: - [3,2,1,5,4] - [3,2,1,5,4] - [3,2,1,5,4]
Constraints:
1 <= nums.length <= 200
1 <= nums[i] <= 100
1 <= k <= 99
Solutions
Solution 1: Brute Force Enumeration
We notice that the length of the array $nums$ does not exceed $200$, so we can enumerate all pairs $(i, j)$, where $i < j$, and check if $|nums[i] - nums[j]|$ equals $k$. If it does, we increment the answer by one.
Finally, we return the answer.
The time complexity is $O(n^2)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.
1 2 3 4 5 6 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 |
|
1 2 3 4 5 6 7 8 9 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
|
Solution 2: Hash Table or Array
We can use a hash table or array to record the occurrence count of each number in the array $nums$. Then, we enumerate each number $x$ in the array $nums$, and check if $x + k$ and $x - k$ are in the array $nums$. If they are, we increment the answer by the sum of the occurrence counts of $x + k$ and $x - k$.
Finally, we return the answer.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $nums$.
1 2 3 4 5 6 7 8 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |
|