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: 2,275 Bytes
b2a430f | 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 | 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 <= #[trigger] 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
}
}
}
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