How do you solve Find the Sum of Subsequence Powers on LeetCode?

Find the Sum of Subsequence Powers (LeetCode #3098) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting the array helps in easily finding the minimum differences between adjacent elements.

What is the time complexity of Find the Sum of Subsequence Powers?

The optimal solution for Find the Sum of Subsequence Powers runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to sorting the array, and O(1) for space since we are using a constant amount of extra space.

What is the brute force solution for Find the Sum of Subsequence Powers?

The brute force approach for Find the Sum of Subsequence Powers is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible subsequences of length k and calculating their powers. This is straightforward but inefficient due to the exponential number of subsequences. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Find the Sum of Subsequence Powers?

Find the Sum of Subsequence Powers uses the following concepts: Array, Dynamic Programming, Sorting. The recommended patterns to study are: Combinatorial Counting, Sorting.

What are the interview tips for Find the Sum of Subsequence Powers?

Always discuss your thought process and potential optimizations with the interviewer. Practice combinatorial problems to get comfortable with counting techniques. Be prepared to explain why sorting or other preprocessing steps are beneficial.

What are common mistakes when solving Find the Sum of Subsequence Powers?

Failing to consider the modulo operation when summing large numbers. Not optimizing the subsequence generation process, leading to excessive time complexity.

#3098

Find the Sum of Subsequence Powers

Hard

ArrayDynamic ProgrammingSortingCombinatorial CountingSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

By sorting the array first, we can efficiently calculate the minimum absolute difference between adjacent elements, which simplifies the process of finding powers for subsequences of length k.

⚙️

Algorithm

4 steps

1Step 1: Sort the array 'nums'.
2Step 2: Initialize a variable to hold the total sum of powers.
3Step 3: For each adjacent pair in the sorted array, calculate the contribution to the sum based on how many subsequences can be formed using that pair.
4Step 4: Return the total sum modulo 10^9 + 7.

solution.py13 lines

1# Full working Python code
2def sum_of_subsequence_powers(nums, k):
3    MOD = 10**9 + 7
4    nums.sort()
5    total_sum = 0
6    n = len(nums)
7    for i in range(n - 1):
8        # Calculate the number of ways to choose k-2 elements from the remaining n-2 elements
9        count = (comb(n - i - 1, k - 2)) % MOD
10        total_sum = (total_sum + count * abs(nums[i] - nums[i + 1])) % MOD
11    return total_sum
12
13from math import comb

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the array, and O(1) for space since we are using a constant amount of extra space.

1Sorting the array helps in easily finding the minimum differences between adjacent elements.
2Using combinatorial counting allows us to efficiently calculate how many subsequences can be formed with a given pair.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.