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Tested Python solution for LeetCode 1498 with 22 pytest cases. Generate a practice environment with lcpy.
lcpy gen -n 1498 # by problem number
lcpy gen -s number_of_subsequences_that_satisfy_the_given_sum_condition # by problem name
nums and an integer target.
Return the number of non-empty subsequences of nums such that the sum of the minimum and maximum element on it is less or equal to target. Since the answer may be too large, return it modulo 10^9 + 7.
Input: nums = [3,5,6,7], target = 9
Output: 4
Explanation: There are 4 subsequences that satisfy the condition.
[3] -> Min value + max value <= target (3 + 3 <= 9)
[3,5] -> (3 + 5 <= 9)
[3,5,6] -> (3 + 6 <= 9)
[3,6] -> (3 + 6 <= 9)
Input: nums = [3,3,6,8], target = 10
Output: 6
Explanation: There are 6 subsequences that satisfy the condition. (nums can have repeated numbers).
[3] , [3] , [3,3], [3,6] , [3,6] , [3,3,6]
Input: nums = [2,3,3,4,6,7], target = 12
Output: 61
Explanation: There are 63 non-empty subsequences, two of them do not satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).
class Solution:
# Time: O(n log n)
# Space: O(1) auxiliary (sorting aside)
def num_subseq(self, nums: list[int], target: int) -> int:
nums = sorted(nums)
mod = 1_000_000_007
n = len(nums)
pows = [1] * n
for i in range(1, n):
pows[i] = pows[i - 1] * 2 % mod
result = 0
left, right = 0, n - 1
while left <= right:
if nums[left] + nums[right] <= target:
result = (result + pows[right - left]) % mod
left += 1
else:
right -= 1
return result
| Time | Space |
|---|---|
| O(n log n) | O(1) auxiliary (sorting aside) |