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 subset_sum(nums: Seq<i32>, sel: Seq<bool>, hi: int) -> int | |
| decreases hi | |
| { | |
| if hi <= 0 { 0 } | |
| else { | |
| (if sel[hi - 1] { nums[hi - 1] as int } else { 0 }) | |
| + subset_sum(nums, sel, hi - 1) | |
| } | |
| } | |
| impl Solution { | |
| pub fn max_sum_div_three(nums: Vec<i32>) -> (result: i32) | |
| requires | |
| 1 <= nums.len() <= 40000, | |
| forall |i: int| 0 <= i < nums.len() ==> 1 <= nums[i] <= 10000, | |
| ensures | |
| result >= 0, | |
| result as int % 3 == 0, | |
| exists |sel: Seq<bool>| sel.len() == nums.len() as int | |
| && subset_sum(nums@, sel, nums.len() as int) == result as int, | |
| forall |sel: Seq<bool>| sel.len() == nums.len() as int | |
| && subset_sum(nums@, sel, nums.len() as int) % 3 == 0 | |
| ==> subset_sum(nums@, sel, nums.len() as int) <= result as int, | |
| { | |
| let n = nums.len(); | |
| let mut dp0: i32 = 0; | |
| let mut dp1: i32 = 0; | |
| let mut dp2: i32 = 0; | |
| let mut i: usize = 0; | |
| while i < n { | |
| let a = nums[i]; | |
| let old0 = dp0; | |
| let old1 = dp1; | |
| let old2 = dp2; | |
| let r = a % 3; | |
| if r == 0 { | |
| dp0 = old0 + a; | |
| dp1 = if old1 > 0 { old1 + a } else { old1 }; | |
| dp2 = if old2 > 0 { old2 + a } else { old2 }; | |
| } else if r == 1 { | |
| let new_dp0 = if old2 > 0 && old2 + a > old0 { old2 + a } else { old0 }; | |
| let new_dp1 = if old0 + a > old1 { old0 + a } else { old1 }; | |
| let new_dp2 = if old1 > 0 && old1 + a > old2 { old1 + a } else { old2 }; | |
| dp0 = new_dp0; | |
| dp1 = new_dp1; | |
| dp2 = new_dp2; | |
| } else { | |
| let new_dp0 = if old1 > 0 && old1 + a > old0 { old1 + a } else { old0 }; | |
| let new_dp1 = if old2 > 0 && old2 + a > old1 { old2 + a } else { old1 }; | |
| let new_dp2 = if old0 + a > old2 { old0 + a } else { old2 }; | |
| dp0 = new_dp0; | |
| dp1 = new_dp1; | |
| dp2 = new_dp2; | |
| } | |
| i += 1; | |
| } | |
| dp0 | |
| } | |
| } | |
| } | |