Leetcode: Range Sum Query 2D - Mutable

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).

Range Sum Query 2D
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.

 1 public class NumMatrix {
 2   int m, n;
 3   int[][] arr;    // stores matrix[][]
 4   int[][] BITree; // 2-D binary indexed tree
 5 
 6   public NumMatrix(int[][] matrix) {
 7     if (matrix.length == 0 || matrix[0].length == 0) {
 8         return;
 9     }
10 
11     m = matrix.length;
12     n = matrix[0].length;
13 
14     arr = new int[m][n];
15     BITree = new int[m + 1][n + 1];
16 
17     for (int i = 0; i < m; i++) {
18       for (int j = 0; j < n; j++) {
19         update(i, j, matrix[i][j]); // init BITree[][]
20         arr[i][j] = matrix[i][j];   // init arr[][]
21       }
22     }
23   }
24 
25   public void update(int i, int j, int val) {
26     int diff = val - arr[i][j];  // get the diff
27     arr[i][j] = val;             // update arr[][]
28 
29     i++; j++;
30     while (i <= m) {
31       int k = j;
32       while (k <= n) {
33         BITree[i][k] += diff; // update BITree[][]
34         k += k & (-k); // update column index to that of parent
35       }
36       i += i & (-i);   // update row index to that of parent
37     }
38   }
39 
40   int getSum(int i, int j) {
41     int sum = 0;
42 
43     i++; j++;
44     while (i > 0) {
45       int k = j;
46       while (k > 0) {
47         sum += BITree[i][k]; // accumulate the sum
48         k -= k & (-k); // move column index to parent node
49       }
50       i -= i & (-i);   // move row index to parent node
51     }
52     return sum;
53   }
54 
55   public int sumRegion(int i1, int j1, int i2, int j2) {
56     return getSum(i2, j2) - getSum(i1-1, j2) - getSum(i2, j1-1) + getSum(i1-1, j1-1);
57   }
58 }
59 
60 
61 // Your NumMatrix object will be instantiated and called as such:
62 // NumMatrix numMatrix = new NumMatrix(matrix);
63 // numMatrix.sumRegion(0, 1, 2, 3);
64 // numMatrix.update(1, 1, 10);
65 // numMatrix.sumRegion(1, 2, 3, 4);