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Problem solution · Python

Range Sum Query 2D - Mutable

Range Sum Query 2D - Mutable: 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
46 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 Range Sum Query 2D - Mutable, 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

  • 46 lines of Python from the credited upstream file 308.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 codeRange Sum Query 2D - Mutable · PythonPython
Use this to learn the idea, then write your own version.
class FenwickTree:  def __init__(self, m: int, n: int):    self.sums = [[0] * (n + 1) for _ in range(m + 1)]   def add(self, row: int, col: int, delta: int) -> None:    i = row    while i < len(self.sums):      j = col      while j < len(self.sums[0]):        self.sums[i][j] += delta        j += FenwickTree.lowbit(j)      i += FenwickTree.lowbit(i)   def get(self, row: int, col: int) -> int:    summ = 0    i = row    while i > 0:      j = col      while j > 0:        summ += self.sums[i][j]        j -= FenwickTree.lowbit(j)      i -= FenwickTree.lowbit(i)    return summ   @staticmethod  def lowbit(i: int) -> int:    return i & -i  class NumMatrix:  def __init__(self, matrix: list[list[int]]):    self.matrix = matrix    self.tree = FenwickTree(len(matrix), len(matrix[0]))     for i in range(len(matrix)):      for j, val in enumerate(matrix[i]):        self.tree.add(i + 1, j + 1, val)   def update(self, row: int, col: int, val: int) -> None:    self.tree.add(row + 1, col + 1, val - self.matrix[row][col])    self.matrix[row][col] = val   def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:    return (self.tree.get(row2 + 1, col2 + 1) - self.tree.get(row1, col2 + 1) -            self.tree.get(row2 + 1, col1) + self.tree.get(row1, col1))

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