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: 3,234 Bytes
033007a | 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 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
pub open spec fn value_occurs(permutation: Seq<i32>, value: int) -> bool {
exists|pos: int| 0 <= pos < permutation.len() && permutation[pos] == value
}
pub open spec fn all_values_occur(permutation: Seq<i32>) -> bool {
forall|value: int| 1 <= value <= permutation.len() ==> #[trigger] value_occurs(permutation, value)
}
pub open spec fn is_valid_permutation(permutation: Seq<i32>) -> bool {
1 <= permutation.len() <= 100_000
&& forall|i: int| 0 <= i < permutation.len() ==> 1 <= #[trigger] permutation[i] <= permutation.len()
&& forall|i: int, j: int| 0 <= i < j < permutation.len() ==> permutation[i] != permutation[j]
&& all_values_occur(permutation)
}
pub open spec fn are_valid_queries(queries: Seq<i32>, n: int) -> bool {
1 <= queries.len() <= 100_000
&& forall|i: int| 0 <= i < queries.len() ==> 1 <= #[trigger] queries[i] <= n
}
pub open spec fn position_of(permutation: Seq<i32>, value: int) -> int
recommends
is_valid_permutation(permutation),
1 <= value <= permutation.len(),
{
choose|pos: int| 0 <= pos < permutation.len() && permutation[pos] == value
}
pub open spec fn total_vasya(permutation: Seq<i32>, queries: Seq<i32>, k: int) -> int
recommends
is_valid_permutation(permutation),
are_valid_queries(queries, permutation.len() as int),
0 <= k <= queries.len(),
decreases k,
{
if k <= 0 {
0
} else {
total_vasya(permutation, queries, k - 1) + position_of(permutation, queries[k - 1] as int) + 1
}
}
pub open spec fn total_petya(permutation: Seq<i32>, queries: Seq<i32>, k: int) -> int
recommends
is_valid_permutation(permutation),
are_valid_queries(queries, permutation.len() as int),
0 <= k <= queries.len(),
decreases k,
{
if k <= 0 {
0
} else {
total_petya(permutation, queries, k - 1) + permutation.len() - position_of(permutation, queries[k - 1] as int)
}
}
impl Solution {
pub fn effective_approach(permutation: Vec<i32>, queries: Vec<i32>) -> (result: (i64, i64))
requires
is_valid_permutation(permutation@),
all_values_occur(permutation@),
are_valid_queries(queries@, permutation.len() as int),
ensures
result.0 as int == total_vasya(permutation@, queries@, queries.len() as int),
result.1 as int == total_petya(permutation@, queries@, queries.len() as int),
{
let n = permutation.len();
let mut positions = Vec::new();
let mut t = 0usize;
while t <= n {
positions.push(0i64);
t += 1;
}
let mut i = 0usize;
while i < n {
let value = permutation[i] as usize;
positions.set(value, i as i64 + 1);
i += 1;
}
let mut vasya = 0i64;
let mut petya = 0i64;
let mut j = 0usize;
while j < queries.len() {
let value = queries[j] as usize;
let p = positions[value];
vasya += p;
petya += n as i64 - p + 1;
j += 1;
}
(vasya, petya)
}
}
}
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