What is the time complexity of Length of the Longest Subsequence That Sums to Target?

The optimal solution for Length of the Longest Subsequence That Sums to Target runs in O(n * target) time and uses O(target) space. The time complexity is O(n * target) because we iterate through each number and update the DP array for each possible sum up to the target.

What is the brute force solution for Length of the Longest Subsequence That Sums to Target?

The brute force approach for Length of the Longest Subsequence That Sums to Target 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 their sums. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n * target).

What algorithm or data structure is used to solve Length of the Longest Subsequence That Sums to Target?

Length of the Longest Subsequence That Sums to Target uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Subset Sum Problem.

What are the interview tips for Length of the Longest Subsequence That Sums to Target?

Always clarify the problem and constraints before diving into coding. Explain your thought process while coding to demonstrate your understanding. Practice writing out the DP transitions on paper before coding to solidify your understanding.

What are common mistakes when solving Length of the Longest Subsequence That Sums to Target?

Not initializing the DP array correctly, leading to incorrect results. Failing to update the DP array in the correct order, which can overwrite needed values.

#2915

Length of the Longest Subsequence That Sums to Target

Medium

ArrayDynamic ProgrammingDynamic ProgrammingSubset Sum Problem

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n * target)Space O(target)

Using dynamic programming allows us to build up solutions to subproblems, efficiently tracking the longest subsequence that sums to the target.

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Algorithm

3 steps

1Step 1: Initialize a DP array where dp[j] holds the maximum length of subsequence that sums to j.
2Step 2: Iterate through each number in nums, updating the DP array from the back to avoid overwriting results from the same iteration.
3Step 3: Return dp[target] if it's greater than 0; otherwise, return -1.

solution.py10 lines

1# Full working Python code
2
3def longest_subsequence(nums, target):
4    dp = [-1] * (target + 1)
5    dp[0] = 0
6    for num in nums:
7        for j in range(target, num - 1, -1):
8            if dp[j - num] != -1:
9                dp[j] = max(dp[j], dp[j - num] + 1)
10    return dp[target] if dp[target] != -1 else -1

ℹ

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

1Dynamic programming helps in breaking down the problem into manageable subproblems.
2Understanding how to manipulate the DP array is crucial for optimizing the solution.

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