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Problem solution · Python

Find the Maximum Length of Valid Subsequence I

Find the Maximum Length of Valid Subsequence I: a Python solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Dynamic programming
Source
walkccc LeetCode Solutions
Length
13 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Dynamic programming

For Find the Maximum Length of Valid Subsequence I, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 13 lines of Python from the credited upstream file 3201.py.
  • The implementation visibly relies on sequence storage, ordered lookup, cached states.
  • No explicit loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeFind the Maximum Length of Valid Subsequence I · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def maximumLength(self, nums: list[int]) -> int:    # dp[i][j] := the maximum length of a valid subsequence, where the last    # number mod k equal to i and the next desired number mod k equal to j    dp = [[0] * 2 for _ in range(2)]     # Extend the pattern xyxyxy...xy.    for x in nums:      for y in range(2):        dp[x % 2][y] = dp[y][x % 2] + 1     return max(map(max, dp))

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