From 9f2347a0befb4f85cb4c58b81fdd052a242ae9f7 Mon Sep 17 00:00:00 2001 From: Lukas Kalbertodt Date: Wed, 4 Jan 2017 13:56:02 +0100 Subject: [PATCH] Add solution sheet8 --- aufgaben/sheet8/sol1/times.rs | 19 ++ aufgaben/sheet8/sol2/sort.rs | 345 ++++++++++++++++++++++++++++++++++ 2 files changed, 364 insertions(+) create mode 100755 aufgaben/sheet8/sol1/times.rs create mode 100755 aufgaben/sheet8/sol2/sort.rs diff --git a/aufgaben/sheet8/sol1/times.rs b/aufgaben/sheet8/sol1/times.rs new file mode 100755 index 0000000..efd8128 --- /dev/null +++ b/aufgaben/sheet8/sol1/times.rs @@ -0,0 +1,19 @@ +fn main() { + 3.times(|i| { + println!("Ferris ate {} cookies", i); + }); +} + +trait ChristmasExt { + fn times(&self, f: F); +} + +// We would somehow implement this for all integer types, but this is just +// a proof of concept, so one impl for `i32` is fine. +impl ChristmasExt for i32 { + fn times(&self, mut f: F) { + for i in 0..*self { + f(i); + } + } +} diff --git a/aufgaben/sheet8/sol2/sort.rs b/aufgaben/sheet8/sol2/sort.rs new file mode 100755 index 0000000..26e5184 --- /dev/null +++ b/aufgaben/sheet8/sol2/sort.rs @@ -0,0 +1,345 @@ +use std::cmp::Ordering; + +/// Sorts the array with either quick sort or insertion sort, depending on the +/// array's size. +fn hybrid_sort(arr: &mut [T], compare: &mut F) + where F: FnMut(&T, &T) -> Ordering, +{ + if arr.len() <= 32 { + insertion_sort(arr, compare); + } else { + quick_sort(arr, compare); + } +} + +/// Performs quick sort. +/// +/// Quick sort is a sorting algorithm running in O(n * log n) average case. The +/// worst case is O(n²), though. A lot depends on the choice of the pivot +/// element. This implementation chooses the pivot in a rather stupid manner, +/// so the worst-case is only "highly unlikely" and not "extremely unlikely". +/// +/// The algorithm works recursively by partitioning the array into two parts. +/// In the first, all elements have to be smaller than the pivot element, in +/// the second everything is greater than the pivot. Both parts can then be +/// sorted independent of each other. After the array has been partitioned it +/// looks somewhat like this: +/// +/// ``` +/// ▇ ▂ ▆ +/// ▃ ▅ ▃ ▅ ▁ █ █ ▇ █ ▆ +/// +/// \ / \ / +/// less greater +/// ``` +fn quick_sort(arr: &mut [T], compare: &mut F) + where F: FnMut(&T, &T) -> Ordering, +{ + // If the array only contains 0 or 1 element, we can stop, since it's + // already sorted. + if arr.len() <= 1 { + return; + } + + // Choose a pivot element. This is a crucial part in getting the + // performance right. This implementation just picks the element in the + // middle. This is usually not the best idea! We will run into an O(n²) + // worst case, if the pivot element is bad for partitioning. + // + // We reference the pivot element by index. Otherwise we would need to + // require `T: Clone` or use unsafe hackery. Always using the index is + // not the best solution regarding cache efficiency, but it works for us. + // The best solution would require special care, because of Ownership and + // Drop. We'll learn more about this later. + let mut pivot_pos = arr.len() / 2; + + // Partition the array by maintaining two indices. Afterwards we want to + // have two parts. In the first, all elements have to be smaller than the + // pivot element, in the second everything is greater than the pivot. + // + // Note: This could be done by `Iterator::partition()`, but we can do it + // without any additional memory requirement. + let (mut i, mut j) = (0, arr.len() - 1); + while i <= j { + while compare(&arr[i], &arr[pivot_pos]) == Ordering::Less { + i += 1; + } + while compare(&arr[j], &arr[pivot_pos]) == Ordering::Greater { + j -= 1; + } + + if i <= j { + // Now we found two elements that can be swapped! + arr.swap(i, j); + + // Check if we just swapped the pivot element and fix the index + // accordingly. + if i == pivot_pos { + pivot_pos = j; + } else if j == pivot_pos { + pivot_pos = i; + } + + i += 1; + j -= 1; + } + } + + // The partitioning is done, i and j tell us the bounds of both parts. We + // call `hybrid_sort()` to allow for algorithm dispatching. We want to sort + // small arrays with another algoritm than big arrays. + hybrid_sort(&mut arr[..j + 1], compare); + hybrid_sort(&mut arr[i..], compare); +} + +/// Performs insertion sort. +/// +/// Insertion sort runs in O(n²) worst case, but is extremly fast on nearly +/// sorted or small inputs. It's commonly used to handle the small sub-arrays +/// of recursive algorithms such as quick sort or merge sort. +/// +/// Insertion sort splits the array in two parts: a sorted first part and an +/// unsorted second part. In each iteration the first element of the unsorted +/// part is inserted at the correct position into the sorted part. The array +/// may look like this during the algorithm: +/// +/// ``` +/// ▂ ▆ ▇ +/// ▃ ▆ ▇ █ █ ▅ ▁ █ ▅ ▃ +/// +/// \ / \ / +/// sorted unsorted +/// ``` +/// +/// # Performance +/// +/// To insert the next element at the correct position in the sorted part, we +/// have multiple possibilities: +/// +/// 1. Always swap the element with the element left to it, if the former is +/// smaller. This is what this implementation does. It's fairly easy but +/// we do quite a few unnecessary writes. This method is *slow*! +/// +/// 2. We can first find the correct position to insert by searching through +/// all elements first, then shift all elements to the right and insert the +/// new element. This is way better than the first method. +/// +/// 3. Like (2.) but we already shift all elements to the right while searching +/// for the right insertion-position. This is the best method. +/// +/// Sadly, (2.) and (3.) require some unsafe hackery. Why? Ownership and Drop! +/// +/// We don't know what `Drop` is, yet, but we know that each resource should +/// have one owner. We *can't* move out of an array, so we can't really get +/// out the new element to do the shift with the rest. We will learn how to +/// theoretically optimize this method later. +/// +fn insertion_sort(arr: &mut [T], compare: &mut F) + where F: FnMut(&T, &T) -> Ordering +{ + for mut new in 0..arr.len() { + while new > 0 && compare(&arr[new - 1], &arr[new]) == Ordering::Greater { + arr.swap(new, new - 1); + new -= 1; + } + } +} + +/// Sorts the given slice with the given comparator, which determines the +/// relation between two elements. +pub fn sort_by(arr: &mut [T], mut f: F) + where F: FnMut(&T, &T) -> Ordering, +{ + hybrid_sort(arr, &mut f); +} + +/// Sorts the given slice by comparing the keys for each element according to +/// the given closure. +pub fn sort_by_key(arr: &mut [T], mut map: F) + where F: FnMut(&T) -> K, + K: Ord, +{ + hybrid_sort(arr, &mut |a, b| map(a).cmp(&map(b))) +} + +/// Sorts the array in natural order (with the `Ord::cmp` method). +pub fn sort(arr: &mut [T]) { + hybrid_sort(arr, &mut Ord::cmp); +} + +fn main() { + let mut arr = [ + 90, 39, 49, 18, 43, 17, 38, 76, 24, 74, 56, 19, 32, 54, 33, 24, 47, 75, + 68, 22, 70, 58, 72, 89, 14, 69, 61, 84, 45, 44, 7, 96, 95, 22, 83, 93, + 14, 97, 17, 86, 92, 81, 79, 32, 30, 82, 8, 40, 7, 24, 87, 38, 27, 70, + 9, 18, 44, 89, 86, 17, 60, 93, 43, 39, 74, 42, 38, 40, 13, 29, 87, 95, + 73, 3, 75, 97, 87, 2, 96, 66, 37, 1, 73, 23, 43, 93, 20, 51, 40, 44, + 39, 13, 56, 38, 16, 90, 5, + ]; + // let mut arr = [90, 39, 49, 18, 43, 17, 38, 76, 24, 74, 56, 19, 54, 33]; + + println!("Before: {:?}", &arr[..]); + println!("After: {:?}", &arr[..]); +} + +#[test] +fn sort_short() { + let mut a: [i32; 0] = []; + let mut b = [27]; + + sort(&mut a); + sort(&mut b); + assert_eq!(a, []); + assert_eq!(b, [27]); + + sort_by(&mut a, |a, b| a.cmp(b)); + sort_by(&mut b, |a, b| a.cmp(b)); + assert_eq!(a, []); + assert_eq!(b, [27]); + + sort_by_key(&mut a, |x| *x); + sort_by_key(&mut b, |x| *x); + assert_eq!(a, []); + assert_eq!(b, [27]); +} + +#[test] +fn sort_medium_long() { + let arr = [-30, 31, 22, 21, 59, -64, -77, 98, -58, 55, -41, 49]; + let mut a = arr.to_vec(); + let mut b = arr.to_vec(); + let mut c = arr.to_vec(); + + sort(&mut a); + assert_eq!(a, &[-77, -64, -58, -41, -30, 21, 22, 31, 49, 55, 59, 98]); + + sort_by(&mut b, |a, b| b.cmp(a)); // reverse order + assert_eq!(b, &[98, 59, 55, 49, 31, 22, 21, -30, -41, -58, -64, -77]); + + sort_by_key(&mut c, |x: &i64| x.abs()); + assert_eq!(c, &[21, 22, -30, 31, -41, 49, 55, -58, 59, -64, -77, 98]); +} + +#[test] +fn sort_long() { + let arr = [ + -27, -62, -21, 1, 0, 6, 17, -14, -98, -49, 8, 67, -82, -65, -53, 56, + 32, 0, 59, -12, 39, 15, 90, -80, 40, -63, 65, -69, -74, 56, 91, 63, + -61, 68, -95, 17, -81, 35, 7, 77, 28, 76, 16, -81, -53, -25, -45, -27, + 60, -81, 86, 95, 85, -32, -53, -53, -98, 50, -92, 66, 44, 85, -52, 54, + 48, -14, 92, -80, -59, 20, 61, -36, -76, -34, 20, 76, 87, -38, -61, 12, + -54, 6, 26, 48, 81, 98, -30, 31, 22, 21, 59, -64, -77, 98, 49, -58, + -27, -44, 49, 55, -41, 49, -78, 50, -38, -8, -68, -31, 64, -52, 22, 0, + 58, -88, 90, -19, 42, 3, 54, -68, -24, 73, 0, 11, 77, -75, -48, -51, + -52, 29, 12, 59, 50, -14, -70, 29, -18, 92, 0, -88, -73, -25, -32, -39, + 67, 18, -87, 93, 24, -80, 34, 92, 34, 60, 68, -79, 60, 72, 17, 82, -39, + 47, -83, -44, -57, 91, 33, 93, 41, 5, -26, 59, -25, 57, -39, -49, 84, + -44, -39, 97, 12, -12, 85, 83, -11, -59, -60, -36, 98, -46, -18, 64, + -88, -67, -24, 42, 39, 61, -63, 89, 39, 72, -12, 54, 87, 33, 92, -56, + -6, -76, 73, -63, -58, 28, 86, -49, -11, 78, 38, 39, 26, -13, -73, 44, + -46, -78, -61, -62, 19, 27, 96, 22, -86, -4, -1, -33, 74, 91, 83, 23, + -40, -29, 90, 7, 30, -27, -90, 65, 79, 47, 45, 19, -27, 20, 11, -73, + -84, -27, 58, -88, 94, -58, 56, -93, 86, 22, -43, 1, -21, -20, -64, + -18, 54, -97, -63, -32, 57, -24, 29, 27, -53, -86, 17, -7, -78, -36, + 65, -9, 52, -86, 62, 21, 82, 10, -53, 80, 2, -87, -85, -51, 2, 45, 42, + -85, 17, -63, -76, -46, 26, 55, 94, 80, -53, -26, -73, -43, 72, -45, + 14, -83, -69, -3, -77, 96, -95, -15, 4, -12, -54, 99, -94, 88, -56, + -11, -36, -72, -91, -42, 95, 41, 23, 41, 44, -49, 93, 91, 22, 38, 96, + 7, -63, 55, -74, -77, -50, -90, 78, -56, -2, 30, 79, -42, -12, -46, + -28, -73, -28, 61, -13, 4, -15, -96, -62, 93, -91, 41, -79, 1, 65, -49, + 35, -24, 88, 60, 24, -36, 27, 85, 80, -80, -65, 87, 14, 18, 79, 44, 39, + -91, 81, -89, 70, 27, 49, -65, -33, 93, 60, -65, 85, 57, -62, -72, -90, + -42, -62, 69, 40, 86, -43, -81, -52, 66, -5, -96, -47, -92, 36, 38, + -21, 62, -35, 27, 65, 87, 68, -33, 0, -13, 89, -55, -95, 80, -14, 13, + 71, -95, -52, -60, -46, 14, 26, -89, -77, -52, -49, -53, -95, 60, 2, + 45, -98, -19, 49, -24, 1, -63, -51, 24, 83, 60, -92, 8, 17, -55, -64, + 42, 12, 3, 86, 78, 28, -36, 6, 55, -90, -33, -84, 34, 29, 47, 57, -80, + -24, -31, -95, -8, -8, 21, -34, -68, + ]; + + let mut a = arr.to_vec(); + let mut b = arr.to_vec(); + let mut c = arr.to_vec(); + + // a.sort(); + sort(&mut a); + assert_eq!(a, &[ + -98i64, -98, -98, -97, -96, -96, -95, -95, -95, -95, -95, -95, -94, + -93, -92, -92, -92, -91, -91, -91, -90, -90, -90, -90, -89, -89, -88, + -88, -88, -88, -87, -87, -86, -86, -86, -85, -85, -84, -84, -83, -83, + -82, -81, -81, -81, -81, -80, -80, -80, -80, -80, -79, -79, -78, -78, + -78, -77, -77, -77, -77, -76, -76, -76, -75, -74, -74, -73, -73, -73, + -73, -73, -72, -72, -70, -69, -69, -68, -68, -68, -67, -65, -65, -65, + -65, -64, -64, -64, -63, -63, -63, -63, -63, -63, -63, -62, -62, -62, + -62, -62, -61, -61, -61, -60, -60, -59, -59, -58, -58, -58, -57, -56, + -56, -56, -55, -55, -54, -54, -53, -53, -53, -53, -53, -53, -53, -53, + -52, -52, -52, -52, -52, -52, -51, -51, -51, -50, -49, -49, -49, -49, + -49, -49, -48, -47, -46, -46, -46, -46, -46, -45, -45, -44, -44, -44, + -43, -43, -43, -42, -42, -42, -41, -40, -39, -39, -39, -39, -38, -38, + -36, -36, -36, -36, -36, -36, -35, -34, -34, -33, -33, -33, -33, -32, + -32, -32, -31, -31, -30, -29, -28, -28, -27, -27, -27, -27, -27, -27, + -26, -26, -25, -25, -25, -24, -24, -24, -24, -24, -24, -21, -21, -21, + -20, -19, -19, -18, -18, -18, -15, -15, -14, -14, -14, -14, -13, -13, + -13, -12, -12, -12, -12, -12, -11, -11, -11, -9, -8, -8, -8, -7, -6, + -5, -4, -3, -2, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, + 5, 6, 6, 6, 7, 7, 7, 8, 8, 10, 11, 11, 12, 12, 12, 12, 13, 14, 14, 14, + 15, 16, 17, 17, 17, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, + 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 26, 26, 26, 26, 27, 27, + 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31, 32, 33, 33, 34, + 34, 34, 35, 35, 36, 38, 38, 38, 39, 39, 39, 39, 39, 40, 40, 41, 41, + 41, 41, 42, 42, 42, 42, 44, 44, 44, 44, 45, 45, 45, 47, 47, 47, 48, + 48, 49, 49, 49, 49, 49, 50, 50, 50, 52, 54, 54, 54, 54, 55, 55, 55, + 55, 56, 56, 56, 57, 57, 57, 57, 58, 58, 59, 59, 59, 59, 60, 60, 60, + 60, 60, 60, 60, 61, 61, 61, 62, 62, 63, 64, 64, 65, 65, 65, 65, 65, + 66, 66, 67, 67, 68, 68, 68, 69, 70, 71, 72, 72, 72, 73, 73, 74, 76, + 76, 77, 77, 78, 78, 78, 79, 79, 79, 80, 80, 80, 80, 81, 81, 82, 82, + 83, 83, 83, 84, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 87, 87, 87, + 87, 88, 88, 89, 89, 90, 90, 90, 91, 91, 91, 91, 92, 92, 92, 92, 93, + 93, 93, 93, 93, 94, 94, 95, 95, 96, 96, 96, 97, 98, 98, 98, 99, + ] as &[_]); + + // b.sort_by(|a, b| b.cmp(a)); + sort_by(&mut b, |a, b| b.cmp(a)); // reverse order + assert_eq!(b, &[ + 99i64, 98, 98, 98, 97, 96, 96, 96, 95, 95, 94, 94, 93, 93, 93, 93, 93, + 92, 92, 92, 92, 91, 91, 91, 91, 90, 90, 90, 89, 89, 88, 88, 87, 87, 87, + 87, 86, 86, 86, 86, 86, 85, 85, 85, 85, 85, 84, 83, 83, 83, 82, 82, 81, + 81, 80, 80, 80, 80, 79, 79, 79, 78, 78, 78, 77, 77, 76, 76, 74, 73, 73, + 72, 72, 72, 71, 70, 69, 68, 68, 68, 67, 67, 66, 66, 65, 65, 65, 65, 65, + 64, 64, 63, 62, 62, 61, 61, 61, 60, 60, 60, 60, 60, 60, 60, 59, 59, 59, + 59, 58, 58, 57, 57, 57, 57, 56, 56, 56, 55, 55, 55, 55, 54, 54, 54, 54, + 52, 50, 50, 50, 49, 49, 49, 49, 49, 48, 48, 47, 47, 47, 45, 45, 45, 44, + 44, 44, 44, 42, 42, 42, 42, 41, 41, 41, 41, 40, 40, 39, 39, 39, 39, 39, + 38, 38, 38, 36, 35, 35, 34, 34, 34, 33, 33, 32, 31, 30, 30, 29, 29, 29, + 29, 28, 28, 28, 27, 27, 27, 27, 27, 26, 26, 26, 26, 24, 24, 24, 23, 23, + 22, 22, 22, 22, 22, 21, 21, 21, 20, 20, 20, 19, 19, 18, 18, 17, 17, 17, + 17, 17, 17, 16, 15, 14, 14, 14, 13, 12, 12, 12, 12, 11, 11, 10, 8, 8, + 7, 7, 7, 6, 6, 6, 5, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, + -1, -2, -3, -4, -5, -6, -7, -8, -8, -8, -9, -11, -11, -11, -12, -12, + -12, -12, -12, -13, -13, -13, -14, -14, -14, -14, -15, -15, -18, -18, + -18, -19, -19, -20, -21, -21, -21, -24, -24, -24, -24, -24, -24, -25, + -25, -25, -26, -26, -27, -27, -27, -27, -27, -27, -28, -28, -29, -30, + -31, -31, -32, -32, -32, -33, -33, -33, -33, -34, -34, -35, -36, -36, + -36, -36, -36, -36, -38, -38, -39, -39, -39, -39, -40, -41, -42, -42, + -42, -43, -43, -43, -44, -44, -44, -45, -45, -46, -46, -46, -46, -46, + -47, -48, -49, -49, -49, -49, -49, -49, -50, -51, -51, -51, -52, -52, + -52, -52, -52, -52, -53, -53, -53, -53, -53, -53, -53, -53, -54, -54, + -55, -55, -56, -56, -56, -57, -58, -58, -58, -59, -59, -60, -60, -61, + -61, -61, -62, -62, -62, -62, -62, -63, -63, -63, -63, -63, -63, -63, + -64, -64, -64, -65, -65, -65, -65, -67, -68, -68, -68, -69, -69, -70, + -72, -72, -73, -73, -73, -73, -73, -74, -74, -75, -76, -76, -76, -77, + -77, -77, -77, -78, -78, -78, -79, -79, -80, -80, -80, -80, -80, -81, + -81, -81, -81, -82, -83, -83, -84, -84, -85, -85, -86, -86, -86, -87, + -87, -88, -88, -88, -88, -89, -89, -90, -90, -90, -90, -91, -91, -91, + -92, -92, -92, -93, -94, -95, -95, -95, -95, -95, -95, -96, -96, -97, + -98, -98, -98 + ] as &[_]); + + // c.sort_by_key(|x: &i64| x.abs()); + sort_by_key(&mut c, |x: &i64| x.abs()); + assert!( + c.iter() + .zip(&c[1..]) + .all(|(&a, &b)| a.abs() <= b.abs()) + ); +}