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:
| use vstd::prelude::*; | |
| fn main() {} | |
| verus! { | |
| pub open spec fn subarray_all_leq(a: Seq<i64>, q: i64, l: int, r: int) -> bool { | |
| forall|i: int| l <= i && i <= r ==> a[i] <= q | |
| } | |
| pub open spec fn valid_interval(n: int, k: int, q: i64, a: Seq<i64>, l: int, r: int) -> bool { | |
| 0 <= l && l <= r && r < n && r - l + 1 >= k && subarray_all_leq(a, q, l, r) | |
| } | |
| pub open spec fn pair_contrib(n: int, k: int, q: i64, a: Seq<i64>, l: int, r: int) -> int { | |
| if valid_interval(n, k, q, a, l, r) { | |
| 1 | |
| } else { | |
| 0 | |
| } | |
| } | |
| pub open spec fn sum_r(n: int, k: int, q: i64, a: Seq<i64>, l: int, r: int) -> int | |
| decreases n - r | |
| { | |
| if r >= n { | |
| 0 | |
| } else { | |
| pair_contrib(n, k, q, a, l, r) + sum_r(n, k, q, a, l, r + 1) | |
| } | |
| } | |
| pub open spec fn sum_l(n: int, k: int, q: i64, a: Seq<i64>, l: int) -> int | |
| decreases n - l | |
| { | |
| if l >= n { | |
| 0 | |
| } else { | |
| sum_r(n, k, q, a, l, l) + sum_l(n, k, q, a, l + 1) | |
| } | |
| } | |
| pub open spec fn vacation_count(n: int, k: int, q: i64, a: Seq<i64>) -> int { | |
| if n <= 0 { | |
| 0 | |
| } else { | |
| sum_l(n, k, q, a, 0) | |
| } | |
| } | |
| pub open spec fn extend_good_end(q: i64, a: Seq<i64>, pos: int) -> int | |
| recommends | |
| 0 <= pos <= a.len(), | |
| decreases a.len() as int - pos | |
| { | |
| let n = a.len() as int; | |
| if pos >= n { | |
| n | |
| } else if a[pos] > q { | |
| pos | |
| } else { | |
| extend_good_end(q, a, pos + 1) | |
| } | |
| } | |
| pub open spec fn triangle_contrib(L: int, k: int) -> int { | |
| if L >= k { | |
| (L - k + 1) * (L - k + 2) / 2 | |
| } else { | |
| 0 | |
| } | |
| } | |
| pub open spec fn scan_total(k: int, q: i64, a: Seq<i64>, pos: int) -> int | |
| recommends | |
| 0 <= pos <= a.len(), | |
| decreases a.len() as int - pos | |
| { | |
| let n = a.len() as int; | |
| if pos >= n { | |
| 0 | |
| } else if a[pos] > q { | |
| scan_total(k, q, a, pos + 1) | |
| } else { | |
| let end = extend_good_end(q, a, pos); | |
| triangle_contrib(end - pos, k) + scan_total(k, q, a, end) | |
| } | |
| } | |
| pub struct Solution; | |
| impl Solution { | |
| pub fn count_vacations(n: usize, k: usize, q: i64, a: Vec<i64>) -> (res: i64) | |
| requires | |
| 1 <= n && n <= 200000, | |
| 1 <= k && k <= n, | |
| a.len() == n, | |
| forall|i: int| 0 <= i && i < n ==> -1000000000 <= a@[i] && a@[i] <= 1000000000, | |
| -1000000000 <= q && q <= 1000000000, | |
| ensures | |
| res as int == scan_total(k as int, q, a@, 0), | |
| { | |
| let mut pos: usize = 0; | |
| let mut total: i64 = 0; | |
| while pos < n { | |
| if a[pos] > q { | |
| pos += 1; | |
| } else { | |
| let start = pos; | |
| while pos < n && a[pos] <= q { | |
| pos += 1; | |
| } | |
| let seg_len = pos - start; | |
| if seg_len >= k { | |
| let x = (seg_len - k) as i64 + 1; | |
| total += x * (x + 1) / 2; | |
| } | |
| } | |
| } | |
| total | |
| } | |
| } | |
| } | |