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[11/27] 446. Arithmetic Slices II - Subsequence
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Hard
159493Add to ListShareGiven an integer array nums
, return the number of all the arithmetic subsequences of nums
.
A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.
- For example,
[1, 3, 5, 7, 9]
,[7, 7, 7, 7]
, and[3, -1, -5, -9]
are arithmetic sequences. - For example,
[1, 1, 2, 5, 7]
is not an arithmetic sequence.
A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.
- For example,
[2,5,10]
is a subsequence of[1,2,1,2,4,1,5,10]
.
The test cases are generated so that the answer fits in 32-bit integer.
Example 1:
Input: nums = [2,4,6,8,10] Output: 7 Explanation: All arithmetic subsequence slices are: [2,4,6] [4,6,8] [6,8,10] [2,4,6,8] [4,6,8,10] [2,4,6,8,10] [2,6,10]
Example 2:
Input: nums = [7,7,7,7,7] Output: 16 Explanation: Any subsequence of this array is arithmetic.
Constraints:
1 <= nums.length <= 1000
-231 <= nums[i] <= 231 - 1
Accepted
49,066
Submissions
120,562
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Runtime: 3267 ms, faster than 24.85% of Python3 online submissions for Arithmetic Slices II - Subsequence.
Memory Usage: 185.7 MB, less than 14.20% of Python3 online submissions for Arithmetic Slices II - Subsequence.
Memory Usage: 185.7 MB, less than 14.20% of Python3 online submissions for Arithmetic Slices II - Subsequence.
from collections import defaultdict
class Solution:
def numberOfArithmeticSlices(self, nums: List[int]) -> int:
dp = defaultdict(int)
res = 0
for e in range(1, len(nums)):
for s in range(e):
diff = nums[e] - nums[s]
res += dp[(s, diff)]
dp[(e, diff)] += dp[(s,diff)] + 1
return res