# 0308. Range Sum Query 2D - Mutable

<https://leetcode.com/problems/range-sum-query-2d-mutable>

## Description

Given a 2D matrix `matrix`, handle multiple queries of the following types:

1. **Update** the value of a cell in `matrix`.
2. Calculate the **sum** of the elements of `matrix` inside the rectangle defined by its **upper left corner** `(row1, col1)` and **lower right corner** `(row2, col2)`.

Implement the NumMatrix class:

* `NumMatrix(int[][] matrix)` Initializes the object with the integer matrix `matrix`.
* `void update(int row, int col, int val)` **Updates** the value of `matrix[row][col]` to be `val`.
* `int sumRegion(int row1, int col1, int row2, int col2)` Returns the **sum** of the elements of `matrix` inside the rectangle defined by its **upper left corner** `(row1, col1)` and **lower right corner** `(row2, col2)`.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/03/14/summut-grid.jpg)

```
**Input**
["NumMatrix", "sumRegion", "update", "sumRegion"]
[[[[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]]], [2, 1, 4, 3], [3, 2, 2], [2, 1, 4, 3]]
**Output**
[null, 8, null, 10]
**Explanation**
NumMatrix numMatrix = new NumMatrix([[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]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e. sum of the left red rectangle)
numMatrix.update(3, 2, 2);       // matrix changes from left image to right image
numMatrix.sumRegion(2, 1, 4, 3); // return 10 (i.e. sum of the right red rectangle)
```

**Constraints:**

* `m == matrix.length`
* `n == matrix[i].length`
* `1 <= m, n <= 200`
* `-105 <= matrix[i][j] <= 105`
* `0 <= row < m`
* `0 <= col < n`
* `-105 <= val <= 105`
* `0 <= row1 <= row2 < m`
* `0 <= col1 <= col2 < n`
* At most `104` calls will be made to `sumRegion` and `update`.

## ac1: plain pre-sum

Notice:

* matrix cannot use `clone()`, the array is Object, so it's shallow copy
* be careful handling first row, out of boundary exception.

```java
class NumMatrix {
    int[][] matrix, sumMatrix;

    public NumMatrix(int[][] matrix) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return;

        this.matrix = matrix;
        int row = matrix.length;
        int col = matrix[0].length;

        this.sumMatrix = new int[row][col];
        for(int c = 0; c < col; c++) {
            sumMatrix[0][c] = matrix[0][c];
        }
        for (int r = 1; r < row; r++) {
            for (int c = 0; c < col; c++) {
                sumMatrix[r][c] = sumMatrix[r-1][c] + matrix[r][c];
            }
        }
    }

    public void update(int row, int col, int val) {
        int diff = val - matrix[row][col];
        matrix[row][col] = val;
        for (int r = row; r < sumMatrix.length; r++) {
            sumMatrix[r][col] += diff;
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        int sum = 0;

        for (int c = col1; c <= col2; c++) {
            if (row1 == 0) {
                sum += sumMatrix[row2][c];
            } else {
                sum += sumMatrix[row2][c] - sumMatrix[row1-1][c];
            }
        }
        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);
 */
```

## ac2: Binary Indexed Tree

```java
class NumMatrix {
    int[][] matrix, bit;

    public NumMatrix(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return;
        this.matrix = matrix;
        int row = matrix.length;
        int col = matrix[0].length;

        bit = new int[row+1][col+1];
        for (int r = 0; r < row; r++) {
            for (int c = 0; c < col; c++) {
                int val = matrix[r][c];
                matrix[r][c] = 0;
                update(r, c, val);
            }
        }
    }

    public void update(int row, int col, int val) {
        int diff = val - matrix[row][col];
        matrix[row][col] = val;
        for (int r = row+1; r < bit.length; r += r & -r) {
            for (int c = col+1; c < bit[0].length; c += c & -c) {
                bit[r][c] += diff;
            }
        }
    }

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

    }
    private int getSum(int row, int col) {
        int sum = 0;
        for (int r = row+1; r > 0; r -= r & -r) {
            for (int c = col+1; c > 0; c -= c & -c) {
                sum += bit[r][c];
            }
        }
        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);
 */
```

![](https://raw.githubusercontent.com/hot13399/leetcode-graphic-answer/master/308.%20Range%20Sum%20Query%202D%20-%20Mutable.jpg)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/0308-range-sum-query-2d-mutable.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.