# Finding the Median and Mode of a slice in Rust

### Overview

I’m trying to learn Rust, so I’m reading The Rust Programming Language. At Chapter 8, there was a task to write a program that calculates the median and mode of a bunch of numbers. I originally skipped the task and kept reading but I’ve returned to it as I think it will give me some practice with the language. I’ve designed my solution as a library crate that provides a function pub fn median_and_mode<T: Ord + Eq + Hash + Clone>(values: &mut [T]) -> Option<MedianAndMode<T>>.

The directory structure is as follows:

src
├── common.rs
├── lib.rs
├── select_and_iterate
│   └── test.rs
├── select_and_iterate.rs
└── test.rs


I took a hopefully more efficient approach to the task than sorting the list, by using the median of medians algorithm and quickselect, which I largely copied from Wikipedia, but slightly modified to also count each element. To do this I used a point in the algorithm where it already looped over every element. However, I’m unsure of if my use of a closure to do this might slow things down, as later iterations are passed a noop closure, which might slow things down a bit.

I used the proptest crate to create property-based tests for my code.

Here are the source files from my project:

### lib.rs

mod common;
mod select_and_iterate;
#[cfg(test)]
mod test;

use std::{
collections::{HashMap, HashSet},
hash::Hash,
};

use crate::{common::noop, select_and_iterate::select_and_iterate};

#[derive(Debug, PartialEq, Eq)]
pub enum Median<T> {
At(T),
Between(T, T),
}

#[derive(Debug, PartialEq, Eq)]
pub struct Mode<T: Eq + Hash>(HashSet<T>);

#[derive(Debug, PartialEq, Eq)]
pub struct MedianAndMode<T: Eq + Hash> {
pub median: Median<T>,
pub mode: Mode<T>,
}

pub fn median_and_mode<T: Ord + Eq + Hash + Clone>(values: &mut [T]) -> Option<MedianAndMode<T>> {
let len = values.len();
if len == 0 {
return None;
}
let mut frequencies = HashMap::new();
let action = |x: &T| {
let frequency = frequencies.entry((*x).clone()).or_insert(0);
*frequency += 1;
};
let median;
if len % 2 == 1 {
let middle = len / 2;
let Some(median_index) = select_and_iterate(values, middle, action)
else { return None; };
median = Median::At(values[median_index].clone());
} else {
let middle_1 = len / 2 - 1;
let middle_2 = len / 2;
let Some(median_1_index) = select_and_iterate(values, middle_1, action)
else { return None; };
let median_1 = values[median_1_index].clone();
let Some(median_2_index) = select_and_iterate(values, middle_2, noop)
else { panic!() };
let median_2 = values[median_2_index].clone();
if median_1 == median_2 {
median = Median::At(median_1);
} else {
median = Median::Between(median_1, median_2);
}
}
let mode = Mode(get_mode(frequencies));
Some(MedianAndMode { median, mode })
}

fn get_mode<T: Eq + Hash>(frequencies: HashMap<T, usize>) -> HashSet<T> {
let mut modes = HashSet::new();
let mut highest_frequency = 0;
for (value, frequency) in frequencies {
match frequency.cmp(&highest_frequency) {
std::cmp::Ordering::Less => {}
std::cmp::Ordering::Equal => {
modes.insert(value);
}
std::cmp::Ordering::Greater => {
highest_frequency = frequency;
modes.clear();
modes.insert(value);
}
}
}
modes
}


### select_and_iterate.rs

#[cfg(test)]
mod test;

use std::cmp::{min, Ordering};

use crate::common::noop;

// Algorithm stolen wholesale from Wikipedia: https://en.wikipedia.org/wiki/Median_of_medians

pub fn select_and_iterate<T: Ord + Clone>(
values: &mut [T],
index: usize,
action: impl FnMut(&T),
) -> Option<usize> {
let len = values.len();
if len == 0 || index > len {
return None;
}
Some(select_and_iterate_inner(values, index, action))
}

fn select_and_iterate_inner<T: Ord + Clone>(
values: &mut [T],
index: usize,
mut action: impl FnMut(&T),
) -> usize {
let len = values.len();
debug_assert_ne!(len, 0);
if len == 1 {
debug_assert_eq!(index, 0);
action(&values[0]);
return 0;
}
let pivot_index = pivot(values);
let pivot_index = partition(values, pivot_index, index, action);
match index.cmp(&pivot_index) {
Ordering::Less => select_and_iterate_inner(&mut values[0..pivot_index], index, noop),
Ordering::Equal => pivot_index,
Ordering::Greater => {
select_and_iterate_inner(
&mut values[pivot_index + 1..len],
index - (pivot_index + 1),
noop,
) + (pivot_index + 1)
}
}
}

fn pivot<T: Ord + Clone>(values: &mut [T]) -> usize {
let len = values.len();
if len <= 5 {
return median_of_5(values);
}
for i in (0..len - 1).step_by(5) {
let right_index = min(i + 4, len - 1);
let median = median_of_5(&mut values[i..right_index]);
values.swap(median, i / 5);
}
select_and_iterate_inner(&mut values[0..len / 5], (len - 1) / 10, noop)
}

fn median_of_5<T: Ord>(values: &mut [T]) -> usize {
values.sort();
(values.len() - 1) / 2
}

fn partition<T: Ord + Clone>(
values: &mut [T],
pivot_index: usize,
target_index: usize,
mut action: impl FnMut(&T),
) -> usize {
let len = values.len();
let pivot_value_ref = &values[pivot_index];
action(pivot_value_ref);
let pivot_value = pivot_value_ref.clone();
values.swap(pivot_index, len - 1);
let mut store_index = 0;
for i in 0..len - 1 {
action(&values[i]);
if values[i] < pivot_value {
values.swap(store_index, i);
store_index += 1;
}
}
let mut store_index_eq = store_index;
for i in store_index..len - 1 {
if values[i] == pivot_value {
values.swap(store_index_eq, i);
store_index_eq += 1;
}
}
values.swap(len - 1, store_index_eq);
if target_index < store_index {
store_index
} else if target_index <= store_index_eq {
target_index
} else {
store_index_eq
}
}


### common.rs

pub fn noop<T>(_: &T) {}


### test.rs

use super::{median_and_mode, Median, MedianAndMode, Mode};
use proptest::{collection::vec, prop_assert, prop_assert_eq, prop_assert_ne, proptest};
use std::collections::HashSet;
// See https://github.com/proptest-rs/proptest/issues/256

#[test]
fn test_median_and_mode_empty_array() {
let mut values: [i128; 0] = [];
let None = median_and_mode(&mut values)
else { panic!("Wrong result pattern") };
}
#[test]
fn test_median_and_mode_1() {
let mut values: [i128; 12] = [
30050, 17767, 12534, -24364, 20538, -17, 690, -7966, -40, -1172, -25598, 34,
];
let Some(MedianAndMode { median, mode }) = median_and_mode(&mut values)
else { panic!() };
assert_eq!(median, Median::Between(-17, 34));
assert_eq!(mode, Mode(HashSet::from_iter(values.iter().copied())))
}
#[test]
fn test_median_and_mode_2() {
let mut values: [i128; 9] = [
7952,
19412,
-1450,
6978825196251534519,
11125,
5270098434161345047,
-13739,
-27060,
-467,
];
let Some(MedianAndMode { median, mode }) = median_and_mode(&mut values)
else { panic!("Wrong result pattern") };
assert_eq!(median, Median::At(7952));
assert_eq!(mode, Mode(HashSet::from_iter(values.iter().copied())));
}

proptest! {
#[test]
fn proptest_median_and_mode(mut values in vec(i8::MIN..i8::MAX, 1..32768)) {
let len = values.len();
if len == 0 {
let None = median_and_mode(&mut values)
else { panic!("Wrong result pattern") };
} else {
let Some(MedianAndMode { median, mode }) = median_and_mode(&mut values)
else { panic!("Wrong result pattern") };
values.sort();
match median {
Median::At(x) => {
prop_assert_eq!(x, values[len / 2]);
},
Median::Between(x, y) => {
prop_assert_eq!(x, values[len / 2 - 1]);
prop_assert_eq!(y, values[len / 2]);
},
}
let Mode(mode) = mode;
prop_assert_ne!(mode.len(), 0);
let mut frequencies = Vec::new();
for value in mode {
frequencies.push(values.iter().filter(|n| **n == value).count())
};
let first_frequency = frequencies[0];
prop_assert!(first_frequency <= len);
prop_assert!(frequencies.iter().all(|n| *n == first_frequency));
}
}

#[test]
fn proptest_median_and_mode_singleton_vec(value in i128::MIN..i128::MAX) {
let mut values = vec![value];
let Some(MedianAndMode { median, mode }) = median_and_mode(&mut values)
else { panic!("Wrong result pattern") };
prop_assert_eq!(median, Median::At(value));
prop_assert_eq!(mode, Mode(HashSet::from([value])))
}
}


### select_and_iterate/test.rs

use super::select_and_iterate;
use crate::common::noop;
use proptest::{collection::vec, prop_assert, prop_assert_eq, proptest};
use std::collections::HashMap;

#[test]
fn test_select_empty_vec() {
let mut values: Vec<i128> = vec![];
let None = select_and_iterate(&mut values, 0, noop)
else { panic!("Wrong result pattern") };
}

proptest! {
#[test]
fn proptest_select(mut values in vec(i8::MIN..i8::MAX, 1..32768), index in 0..usize::MAX) {
let len = values.len();
if len == 0 {
let None = select_and_iterate(&mut values, index, noop)
else { panic!("Wrong result pattern") };
} else {
let index = index % len;
let mut frequencies = HashMap::new();
let action = |x: &i8| {
let frequency = frequencies.entry(*x).or_insert(0);
*frequency += 1;
};
let Some(value_index) = select_and_iterate(&mut values, index, action)
else { panic!() };
let value = values[value_index];
values.sort();
prop_assert_eq!(value, values[index]);
for (value, frequency) in frequencies {
prop_assert!(values.contains(&value));
prop_assert!(frequency <= len);
}
}
}

#[test]
fn proptest_select_singleton_vec(value in i128::MIN..i128::MAX) {
let mut counter = 0;
let action = |_: &i128| {
counter += 1;
};
let mut values = vec![value];
let Some(0) = select_and_iterate(&mut values, 0, action)
else { panic!("Wrong result pattern") };
prop_assert_eq!(counter, 1);
}
}


### Questions

In particular, I’m interested in these questions:

• Is this code actually notably faster than the sorting method? In my tests it seemed to perform O(n), as Wikipedia suggested
• Does the use of a closure and passing noop to later iterations slow down the code notably?
• Is the structure and organization of the code sensible?
• Is the Clone requirement for median_and_mode sensible? I ran into issues with the borrow checker, which I still don’t fully understand, and used Clone, but I’m not sure if it’s a sensible requirement
• Is the Clone requirement for select_and_iterate sensible? It comes from the call to clone in pivot, where I assume it’s because the compiler must assume that the mutable borrow in swap might result in a dangling pointer. Would this be a good place to use unsafe? Or is there some hack I’m not aware of that might circumvent this need? I assume it’s not that big of a deal as any other use of the same code could just pass references to be compared

The code looks good overall, it's well-organized, and easily readable. A pleasure to review.

### Separation of concerns

While the exercise does suggest computing the median and the mode, I do not think it expects you to compute both in a single function. Unlike a minmax function, there's little to no synergy between the two.

As such, I would suggest splitting the two calculations.

Relatedly, the MedianAndMode struct is overkill, since you already designed two strong types (Median and Mode) a simple tuple would have been enough. And with the split function, Mode becomes overkill too.

### Separation of concerns (2)

By splitting the top-level function, you can also split the select_and_iterate to be just select.

This removes the use of the closure.

### Expression, Expression, Expression

Rust is an Expression-Oriented language, almost everything is an expression!

For example, in your calculation of the median you write:

let median;
if ... {
...
median = <a>;
} else {
...
median = <b>;
}


Which is statement oriented.

But in Rust, { ... } is an expression (returning the value of the expression after the last ;) and if ... { ... } else { ... } is also an expression!

Thus, idiomatically it would be:

let median = if ... {
...
<a>
} else {
...
<b>
};


It's shorter, to boot.

### Impossible code-paths

Your code contains impossible code-path in the median calculation.

The only reason for select_and_iterate to return None are an empty slice and an erroneous index, neither of which should ever occur in the calls from median_and_mode.

It's distracting to have those impossible code-paths, so it may be worth spending a bit of time trying to see if there's a sensible way to express the inputs of select_and_iterate so as to avoid them.

(I am afraid I can't think of any, off the top of my hat)

Is this code actually notably faster than the sorting method? In my tests it seemed to perform O(n), as Wikipedia suggested

I'll trust Wikipedia on this one.

Does the use of a closure and passing noop to later iterations slow down the code notably?

It's not optimal.

Rust uses monomorphization, it's a fancy term to say that each generic function is "copy/pasted" for each unique set of generic parameters, and optimized separately.

Thus, calling select_and_iterate with action or noop is, each time, maximally efficient. There is, however, a slight inefficiency in calling both: each one is a specifically different block of code. And a complex one at that. Expect more cache misses, decoding stalls, etc... It won't be noticeable on large inputs, but it will be on short ones.

Is the structure and organization of the code sensible?

Yes.

I wouldn't bother splitting the tests in their own separate files unless they get really big, however, as that's a lot of ceremonial, and many folders (at scale), I typically just shove them at the bottom of the file.

And if the file gets really big due to lots of tests, I'll split the "production" code in it into several files, and split the tests to match.

Is the Clone requirement for median_and_mode sensible? I ran into issues with the borrow checker, which I still don’t fully understand, and used Clone, but I’m not sure if it’s a sensible requirement.

It's avoidable, but you'll have to structure the code differently.

First of all, you can't avoid it as long as you return copies. You could, instead, return indices or references.

However, to return indices or references, you must index into or refer to an immutable slice: if the elements are shuffled after the fact, suddenly you index or reference points to another element!

This naturally suggests how to play it:

• First mutate the slice in order to compute the median.
• Then memorize the median.
• Then calculate the mode.
• Return median and mode.

Is the Clone requirement for select_and_iterate sensible?

It's avoidable by using indexes instead of the element itself.

Doing so does open you to accidentally having the elements being shuffled under your feet, and your index suddenly referring to another element, which is a logical bug, but not a memory safety one, and thus which tests should be able to somewhat reliably detect.

I assume it’s not that big of a deal as any other use of the same code could just pass references to be compared.

It's possible to pass references but this requires an extra allocation for the Vec that will hold the references, so it's not great and it'd be better to remove the requirement if possible.