Published at Sep 27 2019
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Instructions

Test suite

Solution

A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,

```
a**2 + b**2 = c**2
```

and such that,

```
a < b < c
```

For example,

```
3**2 + 4**2 = 9 + 16 = 25 = 5**2.
```

Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`

.

For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`

: `{200, 375, 425}`

.

Refer to the exercism help page for Rust installation and learning resources.

Execute the tests with:

```
$ cargo test
```

All but the first test have been ignored. After you get the first test to
pass, open the tests source file which is located in the `tests`

directory
and remove the `#[ignore]`

flag from the next test and get the tests to pass
again. Each separate test is a function with `#[test]`

flag above it.
Continue, until you pass every test.

If you wish to run all ignored tests without editing the tests source file, use:

```
$ cargo test -- --ignored
```

To run a specific test, for example `some_test`

, you can use:

```
$ cargo test some_test
```

If the specific test is ignored use:

```
$ cargo test some_test -- --ignored
```

To learn more about Rust tests refer to the online test documentation

Make sure to read the Modules chapter if you haven't already, it will help you with organizing your files.

After you have solved the exercise, please consider using the additional utilities, described in the installation guide, to further refine your final solution.

To format your solution, inside the solution directory use

```
cargo fmt
```

To see, if your solution contains some common ineffective use cases, inside the solution directory use

```
cargo clippy --all-targets
```

Generally you should submit all files in which you implemented your solution (`src/lib.rs`

in most cases). If you are using any external crates, please consider submitting the `Cargo.toml`

file. This will make the review process faster and clearer.

The exercism/rust repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the rust track team are happy to help!

If you want to know more about Exercism, take a look at the contribution guide.

Problem 9 at Project Euler http://projecteuler.net/problem=9

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
use pythagorean_triplet::find;
use std::{collections::HashSet, iter::FromIterator};
fn process_tripletswithsum_case(sum: u32, expected: &[[u32; 3]]) {
let triplets = find(sum);
if !expected.is_empty() {
let expected = HashSet::from_iter(expected.iter().cloned());
assert_eq!(expected, triplets);
} else {
assert!(triplets.is_empty());
}
}
#[test]
fn test_triplets_whose_sum_is_12() {
process_tripletswithsum_case(12, &[[3, 4, 5]]);
}
#[test]
#[ignore]
fn test_triplets_whose_sum_is_108() {
process_tripletswithsum_case(108, &[[27, 36, 45]]);
}
#[test]
#[ignore]
fn test_triplets_whose_sum_is_1000() {
process_tripletswithsum_case(1000, &[[200, 375, 425]]);
}
#[test]
#[ignore]
fn test_no_matching_triplets_for_1001() {
process_tripletswithsum_case(1001, &[]);
}
#[test]
#[ignore]
fn test_returns_all_matching_triplets() {
process_tripletswithsum_case(90, &[[9, 40, 41], [15, 36, 39]]);
}
#[test]
#[ignore]
fn test_several_matching_triplets() {
process_tripletswithsum_case(
840,
&[
[40, 399, 401],
[56, 390, 394],
[105, 360, 375],
[120, 350, 370],
[140, 336, 364],
[168, 315, 357],
[210, 280, 350],
[240, 252, 348],
],
);
}
#[test]
#[ignore]
fn test_triplets_for_large_number() {
process_tripletswithsum_case(
30_000,
&[
[1200, 14_375, 14_425],
[1875, 14_000, 14_125],
[5000, 12_000, 13_000],
[6000, 11_250, 12_750],
[7500, 10_000, 12_500],
],
);
}
```

```
use std::collections::HashSet;
//Given the sum {}, return all possible Pythagorean triplets, which produce the said sum, or an empty HashSet if there are no such triplets. Note that you are expected to return triplets in [a, b, c] order, where a < b < c
pub fn find(sum: u32) -> HashSet<[u32; 3]> {
// Euclid formula a = m2 -n2 ; b = 2mn; c = m2+n2 ; m>n
// and a+b+c = m2 - n2 +2mn + m2 +n2 = 2m2 + 2mn = 2(m2+mn)
let mut sol = HashSet::new();
let max = (sum as f32).sqrt() as u32;
for n in 1..=max {
for m in n + 1..=max {
let mut a = m * m - n * n;
let mut b = 2 * m * n;
let mut c = m * m + n * n;
let s = a + b + c;
// need to check also for non primitive triplets
if sum % s == 0 {
let k = sum / s;
a = k * a;
b = k * b;
c = k * c;
if a < b {
sol.insert([a, b, c]);
} else {
sol.insert([b, a, c]);
}
}
}
}
sol
}
```

Using Euklid's formula to generate triplets so it's much faster then naive iteration over a an b, but still significantly slower (~50x) then best solution :-(

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