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Problem solution · Python

Remove All Ones With Row and Column Flips II

Remove All Ones With Row and Column Flips II: 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
33 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 Remove All Ones With Row and Column Flips II, 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

  • 33 lines of Python from the credited upstream file 2174-2.py.
  • The implementation visibly relies on sequence storage, 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 codeRemove All Ones With Row and Column Flips II · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def removeOnes(self, grid: list[list[int]]) -> int:    m = len(grid)    n = len(grid[0])    maxMask = 1 << m * n    # dp[i] := the minimum number of operations to remove all 1s from the grid,    # where `i` is the bitmask of the state of the grid    dp = [math.inf] * maxMask    dp[0] = 0     for mask in range(maxMask):      for i in range(m):        for j in range(n):          if grid[i][j] == 1:            newMask = mask            # Set the cells in the same row with 0.            for k in range(n):              newMask &= ~(1 << i * n + k)            # Set the cells in the same column with 0.            for k in range(m):              newMask &= ~(1 << k * n + j)            dp[mask] = min(dp[mask], 1 + dp[newMask])     return dp[self.encode(grid, m, n)]   def encode(self, grid: list[list[int]], m: int, n: int) -> int:    encoded = 0    for i in range(m):      for j in range(n):        if grid[i][j]:          encoded |= 1 << i * n + j    return encoded

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