Range Sum Query 2D Mutable Problem LeetCode

Problem:
Given a 2D matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:
Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

Note:

• The matrix is only modifiable by the update function.
• You may assume the number of calls to update and sumRegion function is distributed evenly.
• You may assume that row1 ≤ row2 and col1 ≤ col2.

 HINTS:

•  create a 2d matrix to hold the sum of each column till particular row, e.g., colsum[i][j] stores the sum of the columns in the ith row till jth column, its like accumulating the column sum
• when an update operation is called on a cell, for each cell below this cell, deduct the value on that cell from the original matrix and add this new value
• when finding the sum, deduct from the column cells for the given set of coordinates and accumulate the value

Solution: