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Text Generation
Modalities:
Text
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json
Languages:
English
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< 1K
ArXiv:
Tags:
competitive-programming
code-generation
specification-generation
proof-generation
verification
rust
License:
File size: 2,973 Bytes
b1eb0dd | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 | 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 ==> #[trigger] 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
}
}
}
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