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Problem solution · Python

Maximize the Number of Partitions After Operations

Maximize the Number of Partitions After Operations: 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
29 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 Maximize the Number of Partitions After Operations, 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

  • 29 lines of Python from the credited upstream file 3003.py.
  • The implementation visibly relies on 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 codeMaximize the Number of Partitions After Operations · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def maxPartitionsAfterOperations(self, s: str, k: int) -> int:    @functools.lru_cache(None)    def dp(i: int, canChange: bool, mask: int) -> int:      """      Returns the maximum number of partitions of s[i..n), where `canChange` is      True if we can still change a letter, and `mask` is the bitmask of the      letters we've seen.      """      if i == len(s):        return 0       def getRes(newBit: int, nextCanChange: bool) -> int:        newMask = mask | newBit        if newMask.bit_count() > k:          return 1 + dp(i + 1, nextCanChange, newBit)        return dp(i + 1, nextCanChange, newMask)       # Initialize the result based on the current letter.      res = getRes(1 << (ord(s[i]) - ord('a')), canChange)       # If allowed, explore the option to change the current letter.      if canChange:        for j in range(26):          res = max(res, getRes(1 << j, False))      return res     return dp(0, True, 0) + 1

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