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 ceil_div(x: int, d: int) -> int { | |
| (x + d - 1) / d | |
| } | |
| pub open spec fn sum_prefix(nums: Seq<i32>, d: int, n: int) -> int | |
| decreases n | |
| { | |
| if n <= 0 { | |
| 0 | |
| } else { | |
| Self::sum_prefix(nums, d, n - 1) + Self::ceil_div(nums[n - 1] as int, d) | |
| } | |
| } | |
| pub open spec fn sum_by_divisor(nums: Seq<i32>, d: int) -> int { | |
| Self::sum_prefix(nums, d, nums.len() as int) | |
| } | |
| fn sum_with_divisor(nums: &Vec<i32>, divisor: i32) -> (sum: i64) | |
| requires | |
| 1 <= nums.len() <= 50_000, | |
| forall |i: int| 0 <= i < nums.len() ==> 1 <= nums[i] <= 1_000_000, | |
| 1 <= divisor <= 1_000_000, | |
| ensures | |
| sum as int == Self::sum_by_divisor(nums@, divisor as int), | |
| 0 <= sum <= 50_000 * 1_000_000, | |
| { | |
| let mut sum: i64 = 0; | |
| let mut i: usize = 0; | |
| while i < nums.len() | |
| { | |
| let n = nums[i]; | |
| let term: i64 = (n as i64 + divisor as i64 - 1) / divisor as i64; | |
| sum += term; | |
| i += 1; | |
| } | |
| sum | |
| } | |
| pub fn smallest_divisor(nums: Vec<i32>, threshold: i32) -> (res: i32) | |
| requires | |
| 1 <= nums.len() <= 50_000, | |
| forall |i: int| 0 <= i < nums.len() ==> 1 <= nums[i] <= 1_000_000, | |
| nums.len() <= threshold <= 1_000_000, | |
| ensures | |
| 1 <= res <= 1_000_000, | |
| Self::sum_by_divisor(nums@, res as int) <= threshold as int, | |
| forall |d: int| 1 <= d < res ==> Self::sum_by_divisor(nums@, d) > threshold as int, | |
| { | |
| let mut left: i32 = 1; | |
| let mut right: i32 = 1_000_000; | |
| while left < right | |
| { | |
| let mid = left + (right - left) / 2; | |
| let sum = Self::sum_with_divisor(&nums, mid); | |
| if sum <= threshold as i64 { | |
| right = mid; | |
| } else { | |
| left = mid + 1; | |
| } | |
| } | |
| left | |
| } | |
| } | |
| } | |