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; | |
| pub open spec fn min_spec(a: int, b: int) -> int { | |
| if a <= b { a } else { b } | |
| } | |
| pub open spec fn mutated_sum(arr: Seq<i32>, value: int) -> int | |
| decreases arr.len() | |
| { | |
| if arr.len() == 0 { | |
| 0 | |
| } else { | |
| min_spec(arr[arr.len() - 1] as int, value) + mutated_sum(arr.drop_last(), value) | |
| } | |
| } | |
| pub open spec fn abs_diff(a: int, b: int) -> int { | |
| if a >= b { a - b } else { b - a } | |
| } | |
| fn compute_sum(arr: &Vec<i32>, value: i32) -> (result: i32) | |
| requires | |
| 1 <= arr.len() <= 10_000, | |
| forall |i: int| 0 <= i < arr.len() ==> 1 <= arr[i] <= 100_000, | |
| 0 <= value <= 100_000, | |
| ensures | |
| result as int == mutated_sum(arr@, value as int), | |
| { | |
| let n = arr.len(); | |
| let mut sum: i32 = 0; | |
| let mut j: usize = 0; | |
| while j < n { | |
| if arr[j] <= value { | |
| sum = sum + arr[j]; | |
| } else { | |
| sum = sum + value; | |
| } | |
| j = j + 1; | |
| } | |
| sum | |
| } | |
| impl Solution { | |
| pub fn find_best_value(arr: Vec<i32>, target: i32) -> (result: i32) | |
| requires | |
| 1 <= arr.len() <= 10_000, | |
| forall |i: int| 0 <= i < arr.len() ==> 1 <= arr[i] <= 100_000, | |
| 1 <= target <= 100_000, | |
| ensures | |
| result >= 0, | |
| forall |v: int| v >= 0 ==> abs_diff(mutated_sum(arr@, result as int), target as int) <= abs_diff(mutated_sum(arr@, v), target as int), | |
| forall |v: int| (v >= 0 && abs_diff(mutated_sum(arr@, v), target as int) == abs_diff(mutated_sum(arr@, result as int), target as int)) ==> result as int <= v, | |
| { | |
| let n = arr.len(); | |
| let mut max_val: i32 = arr[0]; | |
| let mut i: usize = 1; | |
| while i < n { | |
| if arr[i] > max_val { | |
| max_val = arr[i]; | |
| } | |
| i = i + 1; | |
| } | |
| let total_sum = compute_sum(&arr, max_val); | |
| if total_sum <= target { | |
| return max_val; | |
| } | |
| let mut lo: i32 = 0; | |
| let mut hi: i32 = max_val; | |
| while lo < hi { | |
| let mid = lo + (hi - lo) / 2; | |
| let sum_mid = compute_sum(&arr, mid); | |
| if sum_mid >= target { | |
| hi = mid; | |
| } else { | |
| lo = mid + 1; | |
| } | |
| } | |
| let sum_lo = compute_sum(&arr, lo); | |
| let sum_prev = compute_sum(&arr, lo - 1); | |
| if sum_lo - target < target - sum_prev { | |
| lo | |
| } else { | |
| lo - 1 | |
| } | |
| } | |
| } | |
| } | |