## 308. Range Sum Query 2D - Mutable

Given a 2D matrixmatrix, 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:

1. The matrix is only modifiable by the update function.
2. You may assume the number of calls to update and sumRegion function is distributed evenly.
3. You may assume that row 1 ≤ row 2 and col 1 ≤ col 2.

Thoughts:

Construct a 2D binary indexed tree such that each entry in the tree [i,j] corresponds the sum of its responsible children

Sum in the tree expresses the sum from matrix[i -1][j -1] to [0][0] so a solution performed using the submatrix sum: that is sum(row2 + 1, col + 1) - sum(row1, col2 + 1) - sum(row2 + 1, col1) + sum(row1, col1)

Code: T: O(log(mn)) = O(log(m) +

``````class NumMatrix {
int [][] tree, nums;
int m , n;
public NumMatrix(int[][] matrix) {
if(matrix.length == 0 || matrix[0].length == 0)
return;
m = matrix.length;
n = matrix[0].length;
tree = new int[m + 1][n + 1];
nums = new int[m][n];
for (int i = 0; i < m ; i ++){
for (int j = 0; j < n; j++){
update(i,j,matrix[i][j]);
}
}
}

public void update(int row, int col, int val) {
if(m == 0 || n == 0) return;
int delta = val - nums[row][col];
nums[row][col] = val;
for(int i = row + 1; i <= m ; i += i & (-i)){
for(int j = col + 1; j <= n ; j += j & (-j)){
tree[i][j] += delta;
}
}
}

public int sumRegion(int row1, int col1, int row2, int col2) {
return (sum(row2 + 1, col2 + 1) - sum(row1, col2 + 1) - sum(row2+ 1, col1) + sum(row1, col1));
}

public int sum(int row, int col){
int sum = 0;
for(int i = row; i > 0; i -= i & (-i) ){
for (int j = col; j > 0; j-= j & (-j)){
sum += tree[i][j];
}
}

return sum;
}
}

/**
* Your NumMatrix object will be instantiated and called as such:
* NumMatrix obj = new NumMatrix(matrix);
* obj.update(row,col,val);
* int param_2 = obj.sumRegion(row1,col1,row2,col2);
*/
``````