1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
#[derive(Clone, Debug)]
pub struct CumSum2D {
v: Vec<Vec<i64>>,
}
impl CumSum2D {
pub fn new(source: &[Vec<i64>]) -> Self {
let h = source.len();
let w = source[0].len();
let mut v = vec![vec![0i64; w + 1]; h + 1];
for i in 0..h {
for j in 0..w {
v[i + 1][j + 1] = source[i][j] + v[i][j + 1] + v[i + 1][j] - v[i][j];
}
}
CumSum2D { v }
}
pub fn query(&self, top: usize, bottom: usize, left: usize, right: usize) -> i64 {
self.v[bottom + 1][right + 1] - self.v[bottom + 1][left] - self.v[top][right + 1]
+ self.v[top][left]
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_cumsum_2d() {
let a = CumSum2D::new(&[
vec![1, 2, 3, 4],
vec![1, 2, 3, 4],
vec![1, 2, 3, 4],
vec![1, 2, 3, 4],
]);
assert_eq!(
a.v,
vec![
vec![0, 0, 0, 0, 0],
vec![0, 1, 3, 6, 10],
vec![0, 2, 6, 12, 20],
vec![0, 3, 9, 18, 30],
vec![0, 4, 12, 24, 40]
]
);
assert_eq!(a.query(0, 0, 0, 0), 1);
assert_eq!(a.query(0, 1, 0, 1), 6);
assert_eq!(a.query(1, 2, 2, 3), 14);
assert_eq!(a.query(0, 0, 0, 3), 10);
assert_eq!(a.query(0, 3, 0, 0), 4);
assert_eq!(a.query(3, 3, 3, 3), 4);
assert_eq!(a.query(0, 3, 0, 3), 40);
}
}