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:
| 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) ==> 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 | |
| } | |
| } | |
| } | |