2367. Number of Arithmetic Triplets
Description
You are given a 0-indexed, strictly increasing integer array nums
and a positive integer diff
. A triplet (i, j, k)
is an arithmetic triplet if the following conditions are met:
i < j < k
,nums[j] - nums[i] == diff
, andnums[k] - nums[j] == diff
.
Return the number of unique arithmetic triplets.
Example 1:
Input: nums = [0,1,4,6,7,10], diff = 3 Output: 2 Explanation: (1, 2, 4) is an arithmetic triplet because both 7 - 4 == 3 and 4 - 1 == 3. (2, 4, 5) is an arithmetic triplet because both 10 - 7 == 3 and 7 - 4 == 3.
Example 2:
Input: nums = [4,5,6,7,8,9], diff = 2 Output: 2 Explanation: (0, 2, 4) is an arithmetic triplet because both 8 - 6 == 2 and 6 - 4 == 2. (1, 3, 5) is an arithmetic triplet because both 9 - 7 == 2 and 7 - 5 == 2.
Constraints:
3 <= nums.length <= 200
0 <= nums[i] <= 200
1 <= diff <= 50
nums
is strictly increasing.
Solutions
Solution 1: Brute Force
We notice that the length of the array $nums$ is no more than $200$. Therefore, we can directly enumerate $i$, $j$, $k$, and check whether they meet the conditions. If they do, we increment the count of the triplet.
The time complexity is $O(n^3)$, where $n$ is the length of the array $nums$. The space complexity is $O(1)$.
1 2 3 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
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