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: 2,586 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 99 100 101 102 103 104 105 106 107 108 109 110 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
pub open spec fn pref_sum(a: Seq<i64>, idx: int) -> int
recommends
0 <= idx <= a.len(),
decreases idx,
{
if idx <= 0 {
0int
} else {
pref_sum(a, idx - 1) + a[idx - 1] as int
}
}
pub open spec fn leftmost_l(s: Seq<u8>, lo: int, hi: int) -> int
recommends
0 <= lo <= hi <= s.len(),
decreases if hi > lo { hi - lo } else { 0int },
{
if lo >= hi {
-1int
} else if s[lo] == 1u8 {
lo
} else {
leftmost_l(s, lo + 1, hi)
}
}
pub open spec fn rightmost_r(s: Seq<u8>, lo: int, hi: int) -> int
recommends
0 <= lo <= hi <= s.len(),
decreases if hi > lo { hi - lo } else { 0int },
{
if lo >= hi {
-1int
} else if s[hi - 1] == 2u8 {
hi - 1
} else {
rightmost_r(s, lo, hi - 1)
}
}
pub open spec fn greedy(a: Seq<i64>, s: Seq<u8>, lo: int, hi: int) -> int
recommends
a.len() == s.len(),
0 <= lo <= hi <= a.len(),
decreases if hi > lo { hi - lo } else { 0int },
{
let l = leftmost_l(s, lo, hi);
let r = rightmost_r(s, lo, hi);
if l < 0 || r < 0 || l >= r {
0int
} else {
(pref_sum(a, r + 1) - pref_sum(a, l)) + greedy(a, s, l + 1, r)
}
}
impl Solution {
pub fn max_score(a: Vec<i64>, s: Vec<u8>) -> (result: i64)
requires
2 <= a.len() <= 200_000,
a.len() == s.len(),
forall|i: int| 0 <= i < a.len() ==> 1 <= #[trigger] a[i] <= 100_000,
forall|i: int| 0 <= i < s.len() ==> #[trigger] s[i] == 1u8 || s[i] == 2u8,
ensures
result as int == greedy(a@, s@, 0, a.len() as int),
{
let n = a.len();
let mut prefix: Vec<i64> = Vec::with_capacity(n + 1);
prefix.push(0);
let mut i: usize = 0;
while i < n {
let next = prefix[i] + a[i];
prefix.push(next);
i = i + 1;
}
let mut total: i64 = 0;
let mut lo: usize = 0;
let mut hi: usize = n;
let mut keep_going: bool = true;
while keep_going {
while lo < hi && s[lo] != 1 {
lo = lo + 1;
}
while lo < hi && s[hi - 1] != 2 {
hi = hi - 1;
}
if lo + 1 < hi {
total = total + prefix[hi] - prefix[lo];
lo = lo + 1;
hi = hi - 1;
} else {
keep_going = false;
}
}
total
}
}
}
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