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...ti-tests/tests/verify_overflow/pass/competitve_programming/dp/TheJackpot_10684_failing.rs
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//https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1625 | ||
use prusti_contracts::*; | ||
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pub struct VecWrapperI32 { | ||
v: Vec<i32>, | ||
} | ||
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impl VecWrapperI32 { | ||
#[trusted] | ||
#[pure] | ||
#[ensures (0 <= result)] | ||
pub fn len(&self) -> usize { | ||
self.v.len() | ||
} | ||
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#[trusted] | ||
#[ensures (result.len() == 0)] | ||
pub fn new() -> Self { | ||
VecWrapperI32 { v: Vec::new() } | ||
} | ||
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#[trusted] | ||
#[pure] | ||
#[requires (0 <= index && index < self.len())] | ||
pub fn lookup(&self, index: usize) -> i32 { | ||
self.v[index] | ||
} | ||
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#[trusted] | ||
#[ensures (self.len() == old(self.len()) + 1)] | ||
#[ensures (self.lookup(old(self.len())) == value)] | ||
#[ensures (forall(|i: usize| (0 <= i && i < old(self.len())) ==> | ||
self.lookup(i) == old(self.lookup(i))))] | ||
pub fn push(&mut self, value: i32) { | ||
self.v.push(value); | ||
} | ||
} | ||
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#[pure] | ||
#[ensures (result >= a && result >= b)] | ||
#[ensures (result == a || result == b)] | ||
fn max(a: i32, b: i32) -> i32 { | ||
if a < b { | ||
b | ||
} else { | ||
a | ||
} | ||
} | ||
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// Recursive solution | ||
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#[pure] | ||
#[requires (i >= 0)] | ||
#[requires (i < seq.len())] | ||
#[requires (seq.len() > 0)] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
fn max_seq_sum_rec(seq: &VecWrapperI32, i: usize) -> i32 { | ||
if i == 0 { | ||
seq.lookup(0) | ||
} else { | ||
let prev = max_seq_sum_rec(seq, i - 1); | ||
if prev > 0 { | ||
prev + seq.lookup(i) | ||
} else { | ||
seq.lookup(i) | ||
} | ||
} | ||
} | ||
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#[pure] | ||
#[requires (seq.len() > 0)] | ||
#[requires (idx >= 0)] | ||
#[requires (idx < seq.len())] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
fn solve_rec(seq: &VecWrapperI32, idx: usize) -> i32 { | ||
if idx == 0 { | ||
max_seq_sum_rec(seq, idx) | ||
}else { | ||
max(max_seq_sum_rec(seq, idx), solve_rec(seq, idx - 1)) | ||
} | ||
} | ||
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#[pure] | ||
#[requires (seq.len() > 0)] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
fn the_jackpot_rec(seq: &VecWrapperI32) -> i32 { | ||
max(0, solve_rec(seq, seq.len() - 1)) | ||
} | ||
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// Naive Solution | ||
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#[requires (seq.len() > 0)] | ||
#[requires (start >= 0)] | ||
#[requires (start <= end)] | ||
#[requires (end < seq.len())] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result <= max_seq_sum_rec(seq, end))] | ||
fn seq_sum(seq: &VecWrapperI32, start: usize, end: usize) -> i32 { | ||
if end == start { | ||
seq.lookup(end) | ||
} else { | ||
seq.lookup(end) + seq_sum(seq, start, end - 1) | ||
} | ||
} | ||
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#[requires (seq.len() > 0)] | ||
#[requires (start >= 0)] | ||
#[requires (start <= end)] | ||
#[requires (end < seq.len())] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
fn seq_sum_iter(seq: &VecWrapperI32, start: usize, end: usize) -> i32 { | ||
let mut sum = seq.lookup(start); | ||
let mut i = start + 1; | ||
let mut dp = VecWrapperI32::new(); | ||
dp.push(sum); | ||
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while i <= end { | ||
body_invariant!(i > start); | ||
body_invariant!(i <= end); | ||
body_invariant!(dp.len() == i - start); | ||
body_invariant!(forall(|k: usize| (k >= start && k < i) ==> dp.lookup(k - start) <= max_seq_sum_rec(seq, k))); | ||
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vakaras
Contributor
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sum += seq.lookup(i); | ||
dp.push(sum); | ||
i+=1; | ||
} | ||
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sum | ||
} | ||
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#[requires (seq.len() > 0)] | ||
#[requires (start >= 0)] | ||
#[requires (start <= end)] | ||
#[requires (end < seq.len())] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result <= solve_rec(seq, end))] | ||
fn max_seq_sum(seq: &VecWrapperI32, start: usize, end: usize) -> i32 { | ||
if start == end { | ||
seq_sum(seq, start, end) | ||
}else { | ||
max(max_seq_sum(seq, start + 1, end), seq_sum(seq, start, end)) | ||
} | ||
} | ||
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#[requires (seq.len() > 0)] | ||
#[requires (end >= 0)] | ||
#[requires (end < seq.len())] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result <= solve_rec(seq, end))] | ||
fn solve_naive(seq: &VecWrapperI32, end: usize) -> i32 { | ||
if end == 0 { | ||
max_seq_sum(seq, 0, end) | ||
} else { | ||
max(solve_naive(seq, end - 1), max_seq_sum(seq, 0, end)) | ||
} | ||
} | ||
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#[requires (seq.len() > 0)] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result <= the_jackpot_rec(seq))] | ||
fn the_jackpot_naive(seq: &VecWrapperI32) -> i32 { | ||
max(0, solve_naive(seq, seq.len() - 1)) | ||
} | ||
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// Solution >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | ||
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#[requires (seq.len() > 0)] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result.len() == seq.len())] | ||
#[ensures (forall(|k:usize| (k >= 0 && k < seq.len()) ==> (result.lookup(k) == max_seq_sum_rec(seq, k))))] | ||
fn solve(seq: &VecWrapperI32) -> VecWrapperI32 { | ||
let mut dp = VecWrapperI32::new(); | ||
dp.push(seq.lookup(0)); | ||
let mut i = 1usize; | ||
let len = seq.len(); | ||
while i < len { | ||
body_invariant!(i >= 1); | ||
body_invariant!(i < seq.len()); | ||
body_invariant!(dp.len() == i); | ||
body_invariant!(forall(|k: usize| (k < i && k >= 0) ==> dp.lookup(k) == max_seq_sum_rec(seq, k))); | ||
let prev = dp.lookup(i - 1); | ||
if prev > 0 { | ||
dp.push(prev + seq.lookup(i)); | ||
} else { | ||
dp.push(seq.lookup(i)); | ||
} | ||
i += 1; | ||
} | ||
dp | ||
} | ||
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#[requires (seq.len() > 0)] | ||
#[requires (forall(|k: usize| (k >= 0 && k < seq.len()) ==> (seq.lookup(k) >= -1000 && seq.lookup(k) <= 1000)))] | ||
#[requires (seq.len() <= 10000)] | ||
#[ensures (result == the_jackpot_rec(seq))] | ||
fn the_jackpot(seq: &VecWrapperI32) -> i32 { | ||
let dp = solve(seq); | ||
let mut answer = seq.lookup(0); | ||
let len = seq.len(); | ||
let mut idx = 1; | ||
while idx < len { | ||
body_invariant!(idx >= 1); | ||
body_invariant!(idx < len); | ||
body_invariant!(answer == solve_rec(seq, idx - 1)); | ||
answer = max(answer, dp.lookup(idx)); | ||
idx+=1; | ||
} | ||
max(0, answer) | ||
} | ||
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pub fn main() { | ||
} |
@kammola After three hours of debugging, I found that this invariant seems to work:
where
sub
is defined as: