## 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:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

## Rust Solution

``````struct NumMatrix {
matrix: Vec<Vec<i32>>,
sum: Vec<Vec<i32>>,
n: usize,
m: usize,
}

impl NumMatrix {
fn new(matrix: Vec<Vec<i32>>) -> Self {
let n = matrix.len();
if n == 0 {
return NumMatrix {
matrix,
sum: vec![],
n: 0,
m: 0,
};
}
let m = matrix[0].len();
let mut sum = vec![vec![0; m + 1]; n + 1];
for i in 0..n {
for j in 0..m {
sum[i + 1][j + 1] = matrix[i][j];
sum[i + 1][j + 1] += sum[i + 1][j];
sum[i + 1][j + 1] += sum[i][j + 1];
sum[i + 1][j + 1] -= sum[i][j];
}
}
NumMatrix { matrix, sum, n, m }
}

fn sum_region(&self, row1: i32, col1: i32, row2: i32, col2: i32) -> i32 {
let r1 = row1 as usize;
let c1 = col1 as usize;
let r2 = row2 as usize + 1;
let c2 = col2 as usize + 1;
let mut res = 0;
res += self.sum[r2][c2];
res -= self.sum[r1][c2];
res -= self.sum[r2][c1];
res += self.sum[r1][c1];
res
}
}

#[test]
fn test() {
let matrix = vec_vec_i32![
[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]
];
let nm = NumMatrix::new(matrix);
assert_eq!(nm.sum_region(2, 1, 4, 3), 8);
}
``````

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