Rust’s compiler catches many ownership and lifetime errors; algorithmic correctness still rests on invariants and numeric bounds. A small single-file solution, tested against the judge’s toolchain, provides a reliable baseline before adding contest automation.
Complexity and integer bounds
For input size \(n\), \(O(n\log n)\) bounds growth up to constants for sufficiently large \(n\), not elapsed time. Repeated allocation can make an \(O(n)\) implementation slower than an \(O(n\log n)\) one on small inputs. Constant-factor tuning cannot make an \(O(n^2)\) algorithm near-linear.
At \(n=200{,}000\), a double loop performs roughly \(4\times10^{10}\) iterations; sorting takes on the order of \(n\log_2 n\approx3.52\times10^6\) comparison-scale operations. These are operation estimates, not Rust or CPU measurements.
Summing \(n\) values bounded in absolute value by \(B\) gives
\[\left\vert \sum_{i=1}^{n}a_i\right\vert \le nB.\]With \(n\le2\times10^5\) and \(B\le10^9\), the sum can reach \(2\times10^{14}\): within i64, beyond i32. A signed \(b\)-bit integer represents \([-2^{b-1},2^{b-1}-1]\). Intermediate products need bounds too: multiplying two i64 operands and casting afterward cannot undo overflow.
A single-file solution
This program reads \(n\) signed integers and prints their sum. Input consists of valid whitespace-separated integers satisfying \(n\le200{,}000\) and \(\vert a_i\vert \le10^9\).
use std::io::{self, Read};
fn main() {
let mut input = String::new();
io::stdin().read_to_string(&mut input).unwrap();
let mut it = input.split_whitespace();
let n: usize = it.next().unwrap().parse().unwrap();
let mut sum: i64 = 0;
for _ in 0..n {
let x: i64 = it.next().unwrap().parse().unwrap();
sum += x;
}
println!("{sum}");
}
The input string occupies \(O(L)\) memory for \(L\) bytes, with \(O(L)\) parsing work under the usual fixed-width integer model. Reading to EOF suits non-interactive problems; interactive judges need streaming input and output flushing.
An example compilation is
rustc --edition=2021 -O main.rs -o main
./main < input.txt
Edition 2021 is illustrative; the edition, compiler version, and crates must follow the judge’s requirements. Stable Rust suffices for standard algorithms; a dependency may explicitly require nightly. Optimization changes execution, not the correctness argument.
Ownership and graph storage
Safe Rust prevents broad classes of memory misuse, but a wrong recurrence, bounds panic, deadlock, or arithmetic error remains possible. Debug overflow checks and release wrapping defaults differ; explicit checked arithmetic detects overflow when required. Rust integer overflow.
A Vec<T> owns its allocation; &T allows shared reading and &mut T grants exclusive access for its lifetime. Storing indices avoids holding references across vector growth: reallocation can move elements, explaining the borrowing conflict when pushing while a reference remains live.
Vec<Vec<usize>> is a straightforward adjacency list. Compressed sparse row storage instead uses one contiguous neighbor array and \(n+1\) offsets, occupying \(O(n+m)\) for \(n\) vertices and \(m\) directed edges. Its locality benefit depends on the traversal.
Breadth-first search
For an unweighted graph \(G=(V,E)\) and source \(s\), BFS finds the minimum edge count from \(s\) to each reachable vertex. dist[v] = None marks an undiscovered vertex; the FIFO queue holds discovered vertices awaiting expansion.
use std::collections::VecDeque;
fn bfs(graph: &[Vec<usize>], source: usize) -> Vec<Option<usize>> {
let mut dist = vec![None; graph.len()];
let mut queue = VecDeque::new();
dist[source] = Some(0);
queue.push_back(source);
while let Some(v) = queue.pop_front() {
let next = dist[v].unwrap() + 1;
for &u in &graph[v] {
if dist[u].is_none() {
dist[u] = Some(next);
queue.push_back(u);
}
}
}
dist
}
Vertices leave the queue in nondecreasing distance order. The source starts at zero. When \(v\) leaves with shortest distance \(d\), an undiscovered neighbor receives \(d+1\). A shorter path would have a predecessor at distance at most \(d-1\), already expanded, contradicting the neighbor’s undiscovered state. Each vertex enters once and each stored edge is inspected once, giving time \(O(\vert V\vert +\vert E\vert )\) and auxiliary space \(O(\vert V\vert )\).
Weighted paths require different assumptions: Dijkstra needs nonnegative weights, while negative edges need another algorithm and negative cycles can leave shortest distances undefined.
Modular arithmetic
For integer modulus \(M\ge2\), arithmetic in \(\mathbb Z/M\mathbb Z\) satisfies
\[(a+b)\bmod M=((a\bmod M)+(b\bmod M))\bmod M\]The implementation must still hold the intermediate sum, using a wider type or overflow-safe calculation. Division by \(a\) uses an inverse, existing exactly when \(\gcd(a,M)=1\). Fermat’s formula \(a^{M-2}\bmod M\) additionally requires prime \(M\) and \(a\not\equiv0\pmod M\).
Signed % returns a remainder; rem_euclid yields a canonical nonnegative residue for positive modulus. Boundary cases include \(0\), \(M-1\), \(M\), permitted negative inputs, and the largest intermediate value.
Small oracles
An exhaustive solver makes an effective reference for small random inputs. Tiny shortest-path cases allow enumeration or a cubic all-pairs solver; subset optimization allows all \(2^n\) subsets for small \(n\). Saving the seed and failing input makes counterexamples reproducible.
Tests cover parsing, indexing, and boundaries; the invariant covers the stated domain. Debug and optimized binaries exercise different checks and execution modes. Graph cases include isolated vertices, disconnected components, parallel edges, self-loops, and long chains that expose recursive stack use.
Contest tools
The original workspace used rust-competitive-helper and Competitive Companion. Their installation, ports, judge support, and toolchain requirements belong to their current READMEs; pinned revisions make the setup reproducible.
The underlying workflow remains a problem directory, single-file implementation, samples and oracle tests, judge-compatible compilation, and source submission. A generated Cargo workspace must also fit the judge’s dependency and entry-point restrictions. Local IDE success alone does not establish portability. No compiler benchmark or execution of these helpers is reported here.
References
- The Rust Programming Language: ownership, borrowing, types, and errors.
- Rust standard library: collections, I/O, and numeric operations.
- rust-competitive-helper and Competitive Companion.