Improve performance of A6 algorithm and input code

Cargo.toml

@@ -7,6 +7,7 @@ members = [
     "a4",
     "a5",
     "a6",
+    "a6/a6_benchgen",
     "read_u32",
     "test_run_bin",
 ]

README.md

@@ -37,9 +37,11 @@ The following procedures may require familiarity with the comamnd line.
 1. [Install Git](https://git-scm.com/downloads) if it hasn't been installed.
 
 2. Install Rust using `rustup` from
-   [Rust's official installation page](https://www.rust-lang.org/tools/install).
-   (There are some benchmarks that require nightly Rust to compile.
-   To use nightly Rust, choose the `nightly` channel when installing with `rustup`.)
+   [Rust's official installation page](https://www.rust-lang.org/tools/install).<br>
+   (Some code requires nightly Rust to compile.
+   To use nightly Rust, choose the `nightly` channel when installing with `rustup`.<br>
+   While we will try to use stabilized APIs only, we may include stabilized APIs
+   that have not entered the `stable` channel yet, so `nightly` is still required.)
 
 3. Clone this repository:
    ```

a5/src/main.rs

@@ -7,13 +7,13 @@ fn main() {
 
 // Input routine.
 fn input_price_wallet() -> impl Iterator<Item = (u32, u32)> {
-    let reader = read_u32::U32Reader::new();
+    let mut reader = read_u32::U32Reader::with_stdin();
 
-    let test_case_count = reader.read_until(b'\n');
+    let test_case_count = reader.read_until_newline();
 
     std::iter::repeat_with(move || {
-        let price = reader.read_until(b' ');
-        let wallet = reader.read_until(b'\n');
+        let price = reader.read_until_space();
+        let wallet = reader.read_until_newline();
         (price, wallet)
     })
     .take(test_case_count as usize)

a6/Cargo.toml

@@ -14,7 +14,8 @@ read_u32 = { path = "../read_u32" }
 [dev-dependencies]
 test_run_bin = { path = "../test_run_bin" }
 criterion = "0.3"
-primal = "0.3"
+a6_benchgen = { path = "./a6_benchgen" }
+rand = "0.8"
 
 [[bench]]
 name = "solve_bad_case"

a6/a6_benchgen/Cargo.toml

@@ -0,0 +1,15 @@
+[package]
+name = "a6_benchgen"
+version = "0.1.0"
+authors = ["ivan-shrimp"]
+edition = "2021"
+license = "MIT OR Apache-2.0"
+description = "Input data generator for SPCC Kickstart Problem A6"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+primal = "0.3"
+rand = "0.8"
+anyhow = "1.0"
+clap = { version = "3.1.6", features = ["derive"] }

a6/a6_benchgen/src/lib.rs

@@ -0,0 +1,47 @@
+//! A generator of bad case data that most A6 solutions will likely take a long time to solve.
+
+/// Maximum input value for Problem A6.
+pub const A6_MAX: u32 = 1_000_000;
+const SQRT_A6_MAX: u32 = 1_000;
+
+/// Minimum input value for Problem A6.
+pub const A6_MIN: u32 = 2;
+
+/// Returns a set of bad case data for A6, which contains:
+/// - All numbers with 2, 3, 7, 8, 12, 13, 17, 18, 22, 23, 27 or 28 total prime factors; and
+/// - Primes above `A6_MAX / 4`. (4 is the smallest number in this set)
+pub fn bad_case() -> impl Iterator<Item = u32> {
+    const WANTED_NUMBER_OF_PRIME_FACTORS: [u32; 12] = [2, 3, 7, 8, 12, 13, 17, 18, 22, 23, 27, 28];
+
+    let count_prime_factors = prime_counter();
+
+    (A6_MIN..=A6_MAX).filter(move |&n| {
+        let prime_factors = count_prime_factors(n);
+        WANTED_NUMBER_OF_PRIME_FACTORS.contains(&prime_factors)
+            || (n > A6_MAX / 4 && prime_factors == 1)
+    })
+}
+
+/// Creates a function that counts the number of prime factors of any number below `A6_MAX`.
+/// e.g.: `prime_counter()(6)` is 2, `prime_counter()(9)` is also 2.
+/// This is known as the "big omega" variant of the "prime omega function", see
+/// <https://en.wikipedia.org/wiki/Prime_omega_function>.
+#[allow(clippy::cast_possible_truncation, clippy::cast_sign_loss)]
+fn prime_counter() -> impl Fn(u32) -> u32 {
+    // A sieve to `sqrt(N)` can factorize numbers up to `N`.
+    let sieve = primal::Sieve::new(SQRT_A6_MAX as usize);
+
+    move |num: u32| {
+        sieve
+            // Factorize the number.
+            // Does not truncate as we're not running on 16-bit targets. We don't.
+            .factor(num as usize)
+            // The input, which should not be more than `A6_MAX`, can always be factorized by `sieve`.
+            .unwrap()
+            .into_iter()
+            // Sum up the exponents of each prime factor.
+            // Does not truncate because a number can't have more prime factors than itself.
+            .map(|(_, exp)| exp as u32)
+            .sum()
+    }
+}