Datasets:
Tasks:
Text Generation
Modalities:
Text
Formats:
json
Languages:
English
Size:
< 1K
ArXiv:
Tags:
competitive-programming
code-generation
specification-generation
proof-generation
verification
rust
License:
File size: 3,675 Bytes
4c0e24e | 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 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
impl Solution {
pub open spec fn row_sum_in(mat: Seq<Vec<i32>>, r: int, c1: int, c2: int) -> int
decreases c2 - c1
{
if c1 >= c2 {
0
} else {
mat[r][c1] as int + Self::row_sum_in(mat, r, c1 + 1, c2)
}
}
pub open spec fn rect_sum(mat: Seq<Vec<i32>>, r1: int, r2: int, c1: int, c2: int) -> int
decreases r2 - r1
{
if r1 >= r2 {
0
} else {
Self::row_sum_in(mat, r1, c1, c2) + Self::rect_sum(mat, r1 + 1, r2, c1, c2)
}
}
pub open spec fn spec_max(a: int, b: int) -> int {
if a > b { a } else { b }
}
pub open spec fn spec_min(a: int, b: int) -> int {
if a < b { a } else { b }
}
pub open spec fn block_sum(mat: Seq<Vec<i32>>, i: int, j: int, k: int, m: int, n: int) -> int {
Self::rect_sum(
mat,
Self::spec_max(0, i - k),
Self::spec_min(m, i + k + 1),
Self::spec_max(0, j - k),
Self::spec_min(n, j + k + 1),
)
}
pub fn matrix_block_sum(mat: Vec<Vec<i32>>, k: i32) -> (answer: Vec<Vec<i32>>)
requires
1 <= mat.len() <= 100,
1 <= mat[0].len() <= 100,
forall |i: int| 0 <= i < mat.len() ==> #[trigger] mat[i].len() == mat[0].len(),
forall |i: int, j: int| 0 <= i < mat.len() && 0 <= j < mat[0].len() ==>
1 <= #[trigger] mat[i][j] <= 100,
1 <= k <= 100,
ensures
answer.len() == mat.len(),
forall |i: int| 0 <= i < answer.len() ==> #[trigger] answer[i].len() == mat[0].len(),
forall |i: int, j: int| 0 <= i < answer.len() && 0 <= j < mat[0].len() ==>
(#[trigger] answer[i][j]) as int == Self::block_sum(
mat@, i, j, k as int, mat.len() as int, mat[0].len() as int,
),
{
let m = mat.len();
let n = mat[0].len();
let ku = k as usize;
let mut prefix: Vec<Vec<i32>> = Vec::new();
let mut i: usize = 0;
while i < m {
let mut row: Vec<i32> = Vec::new();
let mut j: usize = 0;
while j < n {
let above: i32 = if i > 0 { prefix[i - 1][j] } else { 0 };
let left: i32 = if j > 0 { row[j - 1] } else { 0 };
let diag: i32 = if i > 0 && j > 0 { prefix[i - 1][j - 1] } else { 0 };
let val: i32 = mat[i][j] + above + left - diag;
row.push(val);
j += 1;
}
prefix.push(row);
i += 1;
}
let mut answer: Vec<Vec<i32>> = Vec::new();
i = 0;
while i < m {
let mut row: Vec<i32> = Vec::new();
let mut j: usize = 0;
while j < n {
let r1: usize = if i >= ku { i - ku } else { 0 };
let r2: usize = if i + ku < m { i + ku } else { m - 1 };
let c1: usize = if j >= ku { j - ku } else { 0 };
let c2: usize = if j + ku < n { j + ku } else { n - 1 };
let top_right: i32 = if r1 > 0 { prefix[r1 - 1][c2] } else { 0 };
let bottom_left: i32 = if c1 > 0 { prefix[r2][c1 - 1] } else { 0 };
let top_left: i32 = if r1 > 0 && c1 > 0 { prefix[r1 - 1][c1 - 1] } else { 0 };
let val: i32 = prefix[r2][c2] - top_right - bottom_left + top_left;
row.push(val);
j += 1;
}
answer.push(row);
i += 1;
}
answer
}
}
}
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