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: 2,083 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 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
impl Solution {
pub open spec fn spec_floor_sqrt_rec(lo: int, hi: int, n: int) -> int
recommends
0 <= lo < hi,
lo * lo <= n,
n < hi * hi,
decreases hi - lo,
{
if lo + 1 >= hi {
lo
} else {
let mid = lo + (hi - lo) / 2;
if mid * mid <= n {
Self::spec_floor_sqrt_rec(mid, hi, n)
} else {
Self::spec_floor_sqrt_rec(lo, mid, n)
}
}
}
pub open spec fn spec_floor_sqrt(n: int) -> int {
if n <= 0 {
0int
} else {
Self::spec_floor_sqrt_rec(0, n + 1, n)
}
}
pub open spec fn spec_bulbs_on(n: int) -> int {
n - Self::spec_floor_sqrt(n)
}
pub fn floor_sqrt_u64(x: u64) -> (r: u64)
requires
1 <= x <= 1_000_000_002_000_001_000u64,
ensures
r as int == Self::spec_floor_sqrt(x as int),
r <= 2_000_000_000u64,
{
let mut lo = 1u64;
let mut hi = 2_000_000_001u64;
while lo < hi {
let mid = lo + (hi - lo) / 2;
if mid * mid <= x {
lo = mid + 1;
} else {
hi = mid;
}
}
let r = lo - 1;
r
}
pub fn min_bulbs_n(k: u64) -> (n: u64)
requires
1 <= k <= 1_000_000_000_000_000_000u64,
ensures
Self::spec_bulbs_on(n as int) == k as int,
forall|m: int|
1 <= m < (n as int) ==> #[trigger] Self::spec_bulbs_on(m) < k as int,
{
let ub = k + 2_000_000_000u64 + 1000u64;
let mut lo = 1u64;
let mut hi = ub;
while lo < hi {
let mid = lo + (hi - lo) / 2;
let s = Self::floor_sqrt_u64(mid);
let cnt = mid - s;
if cnt >= k {
hi = mid;
} else {
lo = mid + 1;
}
}
lo
}
}
}
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