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Tasks:
Text Generation
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Text
Formats:
json
Languages:
English
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< 1K
ArXiv:
Tags:
competitive-programming
code-generation
specification-generation
proof-generation
verification
rust
License:
File size: 2,828 Bytes
75cb225 | 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 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
impl Solution {
pub open spec fn ceil_div_pos(a: int, b: int) -> int
recommends
a >= 0,
b > 0,
{
if a % b == 0 {
a / b
} else {
a / b + 1
}
}
pub open spec fn max_rest_days_spec(n: int, p: int, l: int, t: int) -> int
recommends
n >= 1,
p >= 1,
l >= 1,
t >= 1,
{
let tasks = (n + 6) / 7;
let pairs = tasks / 2;
let odd = tasks % 2;
let pair_pts = l + 2 * t;
let pair_total = pairs * pair_pts;
let study_days = if p <= pair_total {
Self::ceil_div_pos(p, pair_pts)
} else {
let rem = p - pair_total;
if odd == 1 {
let one_day_pts = l + t;
if rem <= one_day_pts {
pairs + 1
} else {
pairs + 1 + Self::ceil_div_pos(rem - one_day_pts, l)
}
} else {
pairs + Self::ceil_div_pos(rem, l)
}
};
n - study_days
}
pub fn max_rest_days(n: i64, p: i64, l: i64, t: i64) -> (res: i64)
requires
1 <= n <= 1_000_000_000,
1 <= p <= 1_000_000_000_000_000_000,
1 <= l <= 1_000_000_000,
1 <= t <= 1_000_000_000,
((n + 6) / 7 / 2) * (l + 2 * t) <= 9_000_000_000_000_000_000,
p <= n * l + ((n + 6) / 7) * t,
ensures
res as int == Self::max_rest_days_spec(n as int, p as int, l as int, t as int),
{
let tasks: i64 = (n + 6) / 7;
let pairs: i64 = tasks / 2;
let odd: i64 = tasks % 2;
let pair_pts: i64 = l + 2 * t;
let pair_total: i64 = pairs * pair_pts;
let mut study_days: i64;
if p <= pair_total {
if p % pair_pts == 0 {
study_days = p / pair_pts;
} else {
study_days = p / pair_pts + 1;
}
} else {
study_days = pairs;
let mut rem: i64 = if p >= pair_total { p - pair_total } else { 0 };
if odd == 1 {
let one_day_pts: i64 = l + t;
if rem <= one_day_pts {
study_days = study_days + 1;
rem = 0;
} else {
study_days = study_days + 1;
rem = rem - one_day_pts;
}
}
if rem > 0 {
if rem % l == 0 {
study_days = study_days + rem / l;
} else {
study_days = study_days + rem / l + 1;
}
}
}
n - study_days
}
}
}
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