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: 5,223 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
impl Solution {
pub open spec fn spec_overlaps_window(start: int, d: int, l: int, r: int) -> bool {
start <= r && l <= start + d - 1
}
pub open spec fn spec_overlap_count_prefix(start: int, d: int, left: Seq<i32>, right: Seq<i32>, upto: int) -> int
recommends
0 <= upto <= left.len(),
left.len() == right.len(),
decreases upto,
{
if upto <= 0 {
0
} else {
Self::spec_overlap_count_prefix(start, d, left, right, upto - 1)
+ if Self::spec_overlaps_window(start, d, left[upto - 1] as int, right[upto - 1] as int) {
1int
} else {
0int
}
}
}
pub open spec fn spec_overlap_count(start: int, d: int, left: Seq<i32>, right: Seq<i32>) -> int
recommends
left.len() == right.len(),
{
Self::spec_overlap_count_prefix(start, d, left, right, left.len() as int)
}
pub fn overlaps_window(start: i32, d: i32, l: i32, r: i32) -> (res: bool)
requires
1 <= d,
ensures
res == Self::spec_overlaps_window(start as int, d as int, l as int, r as int),
{
(start as i64) <= (r as i64) && (l as i64) <= (start as i64) + (d as i64) - 1
}
pub fn overlap_count(start: i32, d: i32, left: &Vec<i32>, right: &Vec<i32>) -> (res: i32)
requires
1 <= d,
left.len() == right.len(),
left.len() <= i32::MAX,
forall|j: int| 0 <= j < left.len() as int ==> 1 <= #[trigger] left[j] <= right[j],
ensures
res as int == Self::spec_overlap_count(start as int, d as int, left@, right@),
0 <= res <= left.len() as i32,
{
let mut cnt: i32 = 0;
let mut j: usize = 0;
while j < left.len()
{
if Self::overlaps_window(start, d, left[j], right[j]) {
cnt = cnt + 1;
}
j = j + 1;
}
cnt
}
pub fn best_start_days(n: i32, d: i32, left: Vec<i32>, right: Vec<i32>) -> (res: (i32, i32))
requires
1 <= n,
n <= 100000,
1 <= d <= n,
1 <= left.len() <= n as nat,
left.len() == right.len(),
forall|j: int| 0 <= j < left.len() as int ==> 1 <= #[trigger] left[j] <= right[j] <= n,
ensures
1 <= res.0 <= n - d + 1,
1 <= res.1 <= n - d + 1,
forall|s: int|
1 <= s <= n as int - d as int + 1
==> Self::spec_overlap_count(res.0 as int, d as int, left@, right@)
>= #[trigger] Self::spec_overlap_count(s, d as int, left@, right@),
forall|s: int|
1 <= s <= n as int - d as int + 1
==> Self::spec_overlap_count(res.1 as int, d as int, left@, right@)
<= #[trigger] Self::spec_overlap_count(s, d as int, left@, right@),
forall|s: int|
1 <= s <= n as int - d as int + 1
&& #[trigger] Self::spec_overlap_count(s, d as int, left@, right@)
== Self::spec_overlap_count(res.0 as int, d as int, left@, right@)
==> res.0 as int <= s,
forall|s: int|
1 <= s <= n as int - d as int + 1
&& #[trigger] Self::spec_overlap_count(s, d as int, left@, right@)
== Self::spec_overlap_count(res.1 as int, d as int, left@, right@)
==> res.1 as int <= s,
{
let m = n - d + 1;
let mm = m as usize;
let mut diff: Vec<i32> = Vec::with_capacity(mm + 2);
let mut p: usize = 0;
while p < mm + 2
{
diff.push(0);
p += 1;
}
let mut j: usize = 0;
while j < left.len()
{
let l = left[j];
let r = right[j];
let lo = if l - d + 1 > 1 { l - d + 1 } else { 1 };
let hi = if r < m { r } else { m };
if lo <= hi {
let li = lo as usize;
let hi1 = (hi + 1) as usize;
diff[li] = diff[li] + 1;
diff[hi1] = diff[hi1] - 1;
}
j += 1;
}
let mut best_bro: i32 = 1;
let mut best_mom: i32 = 1;
let mut best_bro_count: i32 = i32::MIN;
let mut best_mom_count: i32 = i32::MAX;
let mut cur: i32 = 0;
let mut start: usize = 1;
while start <= mm
{
cur += diff[start];
let old_best_bro = best_bro;
let old_best_mom = best_mom;
let old_best_bro_count = best_bro_count;
let old_best_mom_count = best_mom_count;
if cur > best_bro_count {
best_bro_count = cur;
best_bro = start as i32;
}
if cur < best_mom_count {
best_mom_count = cur;
best_mom = start as i32;
}
start += 1;
}
(best_bro, best_mom)
}
}
}
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