# Question

Formatted question description: https://leetcode.ca/all/304.html

```
304 Range Sum Query 2D - Immutable
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
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12
Note:
You may assume that the matrix does not change.
There are many calls to sumRegion function.
You may assume that row1 ≤ row2 and col1 ≤ col2.
```

# Algorithm

Maintain a two-dimensional array dp, where `dp[i][j]`

represents the sum of all the numbers in the cumulative interval (0, 0) to (i, j).

Then if we want to quickly find `(r1 , c1)`

to `(r2, c2)`

rectangular interval, only `dp[r2][c2]-dp[r2][c1-1]-dp[r1-1][c2] + dp[r1-1 ][c1-1]`

.

# Code

Java