What is the time complexity of LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition?

The Python solution on this page runs in O(n \times \log n).

What is the space complexity of LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition?

The Python solution on this page uses O(n), where n is the length of the array \textit{nums} auxiliary space.

Number of Subsequences That Satisfy the Given Sum Condition — LeetCode 1498 Python Solution

MediumArrayTwo PointersBinary SearchSorting

Problem: #1498
Pattern: Two Pointers
Reading time: 3 min
Source: leetcode.com

The problem

You are given an array of integers 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.

Example

Input: nums = [3,5,6,7], target = 9
Output: 4
Explanation: There are 4 subsequences that satisfy the condition.

Python solution

Python

class Solution:
    def numSubseq(self, nums: List[int], target: int) -> int:
        mod = 10**9 + 7
        nums.sort()
        n = len(nums)
        f = [1] + [0] * n
        for i in range(1, n + 1):
            f[i] = f[i - 1] * 2 % mod
        ans = 0
        for i, x in enumerate(nums):
            if x * 2 > target:
                break
            j = bisect_right(nums, target - x, i + 1) - 1
            ans = (ans + f[j - i]) % mod
        return ans

Complexity

Measure	Complexity
Time	O(n \times \log n)
Space	O(n), where n is the length of the array \textit{nums} auxiliary

Pattern: Two Pointers

Use the order already in the input to discard half the search space at every step. LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Two Pointers.

The two pointers guide has the Python template for the pattern and the 201 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition?: LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition is rated Medium on LeetCode.
What is the time complexity of LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition?: The Python solution on this page runs in O(n \times \log n).
What is the space complexity of LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition?: The Python solution on this page uses O(n), where n is the length of the array \textit{nums} auxiliary space.
What topics does LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition cover?: LeetCode 1498. Number of Subsequences That Satisfy the Given Sum Condition is tagged Array, Two Pointers, Binary Search and Sorting on LeetCode.