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: 5,598 Bytes
110b77f | 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 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 | use vstd::prelude::*;
fn main() {}
verus! {
pub struct Solution;
impl Solution {
pub open spec fn neg_inf() -> int {
-1_000_000_000_000
}
pub open spec fn min_int(a: int, b: int) -> int {
if a <= b { a } else { b }
}
pub open spec fn range_sum(a: Seq<i64>, start: int, len: int) -> int
decreases if len <= 0 { 0 } else { len },
{
if start < 0 || len <= 0 || start + len > a.len() {
0
} else {
a[start] as int + Self::range_sum(a, start + 1, len - 1)
}
}
pub open spec fn max_len_sum_upto(a: Seq<i64>, len: int, upto: int) -> int
decreases if upto <= 0 { 0 } else { upto },
{
if len <= 0 {
0
} else if upto <= 0 {
Self::neg_inf()
} else {
let prev = Self::max_len_sum_upto(a, len, upto - 1);
let cur = Self::range_sum(a, upto - 1, len);
if prev <= cur { cur } else { prev }
}
}
pub open spec fn max_len_sum(a: Seq<i64>, len: int) -> int {
if len == 0 {
0
} else if len < 0 || len > a.len() {
Self::neg_inf()
} else {
Self::max_len_sum_upto(a, len, a.len() as int - len + 1)
}
}
pub open spec fn candidate_value(a: Seq<i64>, x: int, k: int, len: int) -> int {
Self::max_len_sum(a, len) + x * Self::min_int(k, len)
}
pub open spec fn best_value_upto(a: Seq<i64>, x: int, k: int, upto: int) -> int
decreases if upto <= 0 { 0 } else { upto },
{
if upto <= 0 {
Self::neg_inf()
} else {
let prev = Self::best_value_upto(a, x, k, upto - 1);
let cur = Self::candidate_value(a, x, k, upto - 1);
if prev <= cur { cur } else { prev }
}
}
pub open spec fn best_value_for_k(a: Seq<i64>, x: int, k: int) -> int {
Self::best_value_upto(a, x, k, a.len() as int + 1)
}
pub open spec fn candidate_from_best(best: Seq<i64>, x: int, k: int, len: int) -> int {
if len < 0 || len >= best.len() {
Self::neg_inf()
} else {
best[len] as int + x * Self::min_int(k, len)
}
}
pub open spec fn best_from_best_upto(best: Seq<i64>, x: int, k: int, upto: int) -> int
decreases if upto <= 0 { 0 } else { upto },
{
if upto <= 0 {
Self::neg_inf()
} else {
let prev = Self::best_from_best_upto(best, x, k, upto - 1);
let cur = Self::candidate_from_best(best, x, k, upto - 1);
if prev <= cur { cur } else { prev }
}
}
pub open spec fn best_from_best(best: Seq<i64>, x: int, k: int) -> int {
Self::best_from_best_upto(best, x, k, best.len() as int)
}
fn max_sum_for_len(a: &Vec<i64>, len: usize) -> (res: i64)
requires
1 <= a.len() <= 5000,
1 <= len <= a.len(),
forall|i: int| 0 <= i < a.len() ==> -100000 <= #[trigger] a@[i] <= 100000,
ensures
res as int == Self::max_len_sum(a@, len as int),
-500000000 <= res as int <= 500000000,
{
let n = a.len();
let mut j: usize = 0;
let mut window_sum: i64 = 0;
while j < len {
let j0 = j;
window_sum = window_sum + a[j0];
j = j0 + 1;
}
let mut best_len = window_sum;
let mut start: usize = 0;
while start + len < n {
let start0 = start;
window_sum = window_sum - a[start0] + a[start0 + len];
start = start0 + 1;
if window_sum > best_len {
best_len = window_sum;
}
}
best_len
}
fn best_answer_from_best(best: &Vec<i64>, x: i64, k: usize) -> (res: i64)
requires
1 <= best.len() <= 5001,
0 <= x <= 100000,
0 <= k < best.len(),
forall|l: int| 0 <= l < best.len() ==> -500000000 <= #[trigger] best@[l] as int <= 500000000,
ensures
res as int == Self::best_from_best(best@, x as int, k as int),
Self::neg_inf() <= res as int <= 1000000000,
{
let n = best.len() - 1;
let mut cur: i64 = -1_000_000_000_000;
let mut used_len: usize = 0;
while used_len <= n {
let used0 = used_len;
let boosted = if used0 < k { used0 as i64 } else { k as i64 };
let cand = best[used0] + x * boosted;
if cand > cur {
cur = cand;
}
used_len = used0 + 1;
}
cur
}
pub fn increase_subarray_sums(a: Vec<i64>, x: i64) -> (res: Vec<i64>)
requires
1 <= a.len() <= 5000,
0 <= x <= 100000,
forall|i: int| 0 <= i < a.len() ==> -100000 <= #[trigger] a@[i] <= 100000,
ensures
res.len() == a.len() + 1,
forall|k: int| 0 <= k < res.len() ==> #[trigger] res@[k] as int == Self::best_value_for_k(a@, x as int, k),
{
let n = a.len();
let mut best: Vec<i64> = Vec::new();
best.push(0);
let mut len: usize = 1;
while len <= n {
let best_len = Solution::max_sum_for_len(&a, len);
best.push(best_len);
len = len + 1;
}
let mut ans: Vec<i64> = Vec::new();
let mut k: usize = 0;
while k <= n {
let cur = Solution::best_answer_from_best(&best, x, k);
ans.push(cur);
k = k + 1;
}
ans
}
}
}
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