How do you solve Find the Sum of the Power of All Subsequences on LeetCode?

Find the Sum of the Power of All Subsequences (LeetCode #3082) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * k) time complexity and O(k) space complexity. Key insight: Subsequences can be counted using dynamic programming to avoid exponential time complexity.

What is the brute force solution for Find the Sum of the Power of All Subsequences?

The brute force approach for Find the Sum of the Power of All Subsequences is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible subsequences of the array and checking if their sums equal to k. This method is straightforward but inefficient for larger arrays due to its exponential time complexity. The optimal Optimal Solution approach improves this to O(n * k).

What algorithm or data structure is used to solve Find the Sum of the Power of All Subsequences?

Find the Sum of the Power of All Subsequences uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Subset Sum Problem.

What are the interview tips for Find the Sum of the Power of All Subsequences?

Always clarify the problem statement and constraints before diving into coding. Think about edge cases, such as empty arrays or sums that cannot be formed. Explain your thought process as you code to demonstrate your understanding.

What are common mistakes when solving Find the Sum of the Power of All Subsequences?

Failing to account for the empty subsequence when initializing the DP array. Not updating the DP array in reverse order, leading to incorrect counts.

#3082

Find the Sum of the Power of All Subsequences

Hard

ArrayDynamic ProgrammingDynamic ProgrammingSubset Sum Problem

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n * k)Space O(k)

The optimal solution uses dynamic programming to count the number of subsequences that sum to k. This approach is efficient because it avoids generating all subsequences and instead builds up the solution using previously computed results.

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Algorithm

3 steps

1Step 1: Initialize a DP array of size k+1 to store counts of subsequences that sum to each index.
2Step 2: For each number in nums, update the DP array from back to front to avoid overwriting results from the current iteration.
3Step 3: The value at DP[k] will give the total count of subsequences that sum to k.

solution.py8 lines

1def sum_of_power(nums, k):
2    MOD = 10**9 + 7
3    dp = [0] * (k + 1)
4    dp[0] = 1  # Base case: one way to make sum 0 (empty subsequence)
5    for num in nums:
6        for j in range(k, num - 1, -1):
7            dp[j] = (dp[j] + dp[j - num]) % MOD
8    return dp[k]

ℹ

Complexity note: The time complexity is O(n * k) because we iterate through each number and update the DP array for each possible sum up to k. The space complexity is O(k) due to the DP array.

1Subsequences can be counted using dynamic programming to avoid exponential time complexity.
2The number of ways to form a sum can be built incrementally using previously computed results.

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