308. Range Sum Query 2D - Mutable

Problem:

Given a 2D matrix 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

Analysis:
换成2D，一开始是想把二维转换成一维，结果是错的。其余的基本上是依葫芦画瓢，求sum有点儿难度。大区间减去上面的和左边的区间，然后加上左上角的区间，因为减2了次。

Solution:

from https://raw.githubusercontent.com/hot13399/leetcode-graphic-answer/master/308.%20Range%20Sum%20Query%202D%20-%20Mutable.jpg