How do you solve Subsequence Sum After Capping Elements on LeetCode?

Subsequence Sum After Capping Elements (LeetCode #3685) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(nk) time complexity and O(k) space complexity. Key insight: Capping elements reduces the problem size.

What is the time complexity of Subsequence Sum After Capping Elements?

The optimal solution for Subsequence Sum After Capping Elements runs in O(nk) time and uses O(k) space. The DP approach iterates through nums and updates achievable sums, leading to O(nk) complexity.

What is the brute force solution for Subsequence Sum After Capping Elements?

The brute force approach for Subsequence Sum After Capping Elements is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all possible subsequences for each capped array and check if any sum to k. This is inefficient as it explores all combinations. The optimal Optimal Solution approach improves this to O(nk).

What algorithm or data structure is used to solve Subsequence Sum After Capping Elements?

Subsequence Sum After Capping Elements uses the following concepts: Array, Two Pointers, Dynamic Programming, Sorting. The recommended patterns to study are: Dynamic Programming, Knapsack Problem.

What are the interview tips for Subsequence Sum After Capping Elements?

Clarify the problem constraints. Discuss potential edge cases. Explain your thought process clearly.

What are common mistakes when solving Subsequence Sum After Capping Elements?

Not considering all capped values. Ignoring the need for subsequence sums.

#3685

Subsequence Sum After Capping Elements

Medium

ArrayTwo PointersDynamic ProgrammingSortingDynamic ProgrammingKnapsack Problem

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(nk)Space O(k)

Sort the array and use a dynamic programming approach to track achievable sums for each capped value efficiently.

⚙️

Algorithm

3 steps

1Step 1: Sort nums in descending order.
2Step 2: Initialize a boolean array dp of size k + 1 to track achievable sums.
3Step 3: For each x from 1 to n, cap nums and update dp to reflect achievable sums.

solution.py12 lines

1def canSum(nums, k):
2    nums.sort(reverse=True)
3    result = []
4    for x in range(1, len(nums) + 1):
5        dp = [False] * (k + 1)
6        dp[0] = True
7        for num in nums:
8            if num > x: continue
9            for j in range(k, num - 1, -1):
10                dp[j] = dp[j] or dp[j - num]
11        result.append(dp[k])
12    return result

ℹ

Complexity note: The DP approach iterates through nums and updates achievable sums, leading to O(nk) complexity.

1Capping elements reduces the problem size.
2Dynamic programming efficiently tracks achievable sums.

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