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Problem solution · Python

Largest Magic Square

Largest Magic Square: a Python solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
47 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

Direct simulation

For Largest Magic Square, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 47 lines of Python from the credited upstream file 1895.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 codeLargest Magic Square · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def largestMagicSquare(self, grid: list[list[int]]) -> int:    m = len(grid)    n = len(grid[0])    # prefixRow[i][j] := the sum of the first j numbers in the i-th row    prefixRow = [[0] * (n + 1) for _ in range(m)]    # prefixCol[i][j] := the sum of the first j numbers in the i-th column    prefixCol = [[0] * (m + 1) for _ in range(n)]     for i in range(m):      for j in range(n):        prefixRow[i][j + 1] = prefixRow[i][j] + grid[i][j]        prefixCol[j][i + 1] = prefixCol[j][i] + grid[i][j]     def isMagicSquare(i: int, j: int, k: int) -> bool:      """Returns True if grid[i..i + k)[j..j + k) is a magic square."""      diag, antiDiag = 0, 0      for d in range(k):        diag += grid[i + d][j + d]        antiDiag += grid[i + d][j + k - 1 - d]      if diag != antiDiag:        return False      for d in range(k):        if self._getSum(prefixRow, i + d, j, j + k - 1) != diag:          return False        if self._getSum(prefixCol, j + d, i, i + k - 1) != diag:          return False      return True     def containsMagicSquare(k: int) -> bool:      """Returns True if the grid contains any magic square of size k x k."""      for i in range(m - k + 1):        for j in range(n - k + 1):          if isMagicSquare(i, j, k):            return True      return False     for k in range(min(m, n), 1, -1):      if containsMagicSquare(k):        return k     return 1   def _getSum(self, prefix: list[list[int]], i: int, l: int, r: int) -> int:    """Returns sum(grid[i][l..r]) or sum(grid[l..r][i])."""    return prefix[i][r + 1] - prefix[i][l]

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