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# 0631. Design Excel Sum Formula

<https://leetcode.com/problems/design-excel-sum-formula>

## Description

Design the basic function of **Excel** and implement the function of the sum formula.

Implement the `Excel` class:

* `Excel(int height, char width)` Initializes the object with the `height` and the `width` of the sheet. The sheet is an integer matrix `mat` of size `height x width` with the row index in the range `[1, height]` and the column index in the range `['A', width]`. All the values should be **zero** initially.
* `void set(int row, char column, int val)` Changes the value at `mat[row][column]` to be `val`.
* `int get(int row, char column)` Returns the value at `mat[row][column]`.
* `int sum(int row, char column, List<String> numbers)` Sets the value at `mat[row][column]` to be the sum of cells represented by `numbers` and returns the value at `mat[row][column]`. This sum formula **should exist** until this cell is overlapped by another value or another sum formula. `numbers[i]` could be on the format:
  * `"ColRow"` that represents a single cell.
    * For example, `"F7"` represents the cell `mat[7]['F']`.
  * `"ColRow1:ColRow2"` that represents a range of cells. The range will always be a rectangle where `"ColRow1"` represent the position of the top-left cell, and `"ColRow2"` represents the position of the bottom-right cell.
    * For example, `"B3:F7"` represents the cells `mat[i][j]` for `3 <= i <= 7` and `'B' <= j <= 'F'`.

**Note:** You could assume that there will not be any circular sum reference.

* For example, `mat[1]['A'] == sum(1, "B")` and `mat[1]['B'] == sum(1, "A")`.

**Example 1:**

```
**Input**
["Excel", "set", "sum", "set", "get"]
[[3, "C"], [1, "A", 2], [3, "C", ["A1", "A1:B2"]], [2, "B", 2], [3, "C"]]
**Output**
[null, null, 4, null, 6]
**Explanation**
Excel excel = new Excel(3, "C");
 // construct a 3*3 2D array with all zero.
 //   A B C
 // 1 0 0 0
 // 2 0 0 0
 // 3 0 0 0
excel.set(1, "A", 2);
 // set mat[1]["A"] to be 2.
 //   A B C
 // 1 2 0 0
 // 2 0 0 0
 // 3 0 0 0
excel.sum(3, "C", ["A1", "A1:B2"]); // return 4
 // set mat[3]["C"] to be the sum of value at mat[1]["A"] and the values sum of the rectangle range whose top-left cell is mat[1]["A"] and bottom-right cell is mat[2]["B"].
 //   A B C
 // 1 2 0 0
 // 2 0 0 0
 // 3 0 0 4
excel.set(2, "B", 2);
 // set mat[2]["B"] to be 2. Note mat[3]["C"] should also be changed.
 //   A B C
 // 1 2 0 0
 // 2 0 2 0
 // 3 0 0 6
excel.get(3, "C"); // return 6
```

**Constraints:**

* `1 <= height <= 26`
* `'A' <= width <= 'Z'`
* `1 <= row <= height`
* `'A' <= column <= width`
* `-100 <= val <= 100`
* `1 <= numbers.length <= 5`
* `numbers[i]` has the format `"ColRow"` or `"ColRow1:ColRow2"`.
* At most `100` calls will be made to `set`, `get`, and `sum`.

## ac

```java
```