| | 1 | | using System.Collections; |
| | 2 | |
|
| | 3 | | namespace MoreStructures.PriorityQueues.LinkedList; |
| | 4 | |
|
| | 5 | | /// <summary> |
| | 6 | | /// An <see cref="IPriorityQueue{T}"/> implementation based on a <b>sorted linked list</b> of its items. |
| | 7 | | /// On top of basic operations it also supports <see cref="IUpdatablePriorityQueue{T}"/>, |
| | 8 | | /// <see cref="IPeekKthPriorityQueue{T}"/> and <see cref="IMergeablePriorityQueue{T, TPQTarget}"/>. |
| | 9 | | /// operations. |
| | 10 | | /// </summary> |
| | 11 | | /// <typeparam name="T"><inheritdoc cref="IPriorityQueue{T}"/></typeparam> |
| | 12 | | /// <remarks> |
| | 13 | | /// <para id="advantages"> |
| | 14 | | /// ADVANTAGES AND DISADVANTAGES |
| | 15 | | /// <br/> |
| | 16 | | /// This represents one of the simplest implementations of a Priority Queue. |
| | 17 | | /// <br/> |
| | 18 | | /// It provides O(1) count and amortized extraction, at the cost of all other operations, which are O(n). |
| | 19 | | /// <br/> |
| | 20 | | /// Runtime behavior is specular to <see cref="ArrayList.ArrayListPriorityQueue{T}"/>, which can perform an |
| | 21 | | /// insertion in constant time, but requires a linear amount of time to extract a value. |
| | 22 | | /// <br/> |
| | 23 | | /// If extraction performance is the only highly critical operation, to the point that a constant time performance |
| | 24 | | /// is the only acceptable runtime, and not even the logarithmic time extraction of a tree-based solution can be |
| | 25 | | /// applied, this implementation may be the best choice. |
| | 26 | | /// <br/> |
| | 27 | | /// An advantage over <see cref="ArrayList.ArrayListPriorityQueue{T}"/> is that this solution can also offer |
| | 28 | | /// constant-time merging and still similar simplicity of implementation. |
| | 29 | | /// <br/> |
| | 30 | | /// When data insertion performance is also a concern, or the main concern, a more balanced solution in terms of |
| | 31 | | /// complexity of its operations should be preferred. |
| | 32 | | /// </para> |
| | 33 | | /// </remarks> |
| | 34 | | public sealed class SortedLinkedListPriorityQueue<T> |
| | 35 | | : IUpdatablePriorityQueue<T>, IPeekKthPriorityQueue<T>, IMergeablePriorityQueue<T, SortedLinkedListPriorityQueue<T>> |
| | 36 | | where T : notnull |
| | 37 | | { |
| | 38 | | /// <summary> |
| | 39 | | /// A non-negative, zero-based, monotonically strictly increasing counter, incremented at every insertion into this |
| | 40 | | /// data structure by a <see cref="Push(T, int)"/>. |
| | 41 | | /// </summary> |
| 14223 | 42 | | private int CurrentPushTimestamp { get; set; } = 0; |
| | 43 | |
|
| | 44 | | /// <summary> |
| | 45 | | /// The <see cref="LinkedList{T}"/> of <see cref="PrioritizedItem{T}"/> backing the linked list heap. |
| | 46 | | /// </summary> |
| 14682 | 47 | | private LinkedList<PrioritizedItem<T>> Items { get; set; } |
| | 48 | |
|
| | 49 | | private LinkedListNode<PrioritizedItem<T>>? FindOccurrenceWithHighestPrioritySmallerThan(PrioritizedItem<T> item) |
| 4045 | 50 | | { |
| 4045 | 51 | | LinkedListNode<PrioritizedItem<T>>? current = Items.First; |
| 4045 | 52 | | if (current == null) |
| 251 | 53 | | return null; |
| | 54 | |
|
| 3794 | 55 | | LinkedListNode<PrioritizedItem<T>>? previous = null; |
| 880513 | 56 | | while (current != null && current.Value.CompareTo(item) > 0) |
| 876719 | 57 | | { |
| 876719 | 58 | | previous = current; |
| 876719 | 59 | | current = current.Next; |
| 876719 | 60 | | } |
| | 61 | |
|
| 3794 | 62 | | return previous; |
| 4045 | 63 | | } |
| | 64 | |
|
| | 65 | | private LinkedListNode<PrioritizedItem<T>>? FindOccurrenceWithHighestPriorityOf(T item) |
| 120 | 66 | | { |
| 2306 | 67 | | for (var current = Items.First; current != null; current = current.Next) |
| 1143 | 68 | | if (Equals(current.Value.Item, item)) |
| 110 | 69 | | return current; |
| | 70 | |
|
| 10 | 71 | | return null; |
| 120 | 72 | | } |
| | 73 | |
|
| | 74 | | /// <summary> |
| | 75 | | /// Builds a priority queue using the provided linked list as <b>direct</b> backing structure. |
| | 76 | | /// </summary> |
| | 77 | | /// <param name="items">The <see cref="LinkedList{T}"/> structure to be used as backing structure.</param> |
| | 78 | | /// <remarks> |
| | 79 | | /// The provided linked list is not copied over: it is used directly as backing structure for the queue. |
| | 80 | | /// <br/> |
| | 81 | | /// Therefore, operations mutating the queue such as <see cref="Push(T, int)"/> will alter the content of the |
| | 82 | | /// <paramref name="items"/> linked list. |
| | 83 | | /// </remarks> |
| 221 | 84 | | public SortedLinkedListPriorityQueue(LinkedList<PrioritizedItem<T>> items) |
| 221 | 85 | | { |
| 221 | 86 | | Items = items; |
| 221 | 87 | | } |
| | 88 | |
|
| | 89 | | /// <summary> |
| | 90 | | /// Builds an empty priority queue. |
| | 91 | | /// </summary> |
| 219 | 92 | | public SortedLinkedListPriorityQueue() : this(new List<PrioritizedItem<T>>()) |
| 219 | 93 | | { |
| 219 | 94 | | } |
| | 95 | |
|
| | 96 | | /// <summary> |
| | 97 | | /// Builds a priority queue using the provided items to populate its backing structure. |
| | 98 | | /// </summary> |
| | 99 | | /// <param name="items">The items to be added to the queue.</param> |
| | 100 | | /// <remarks> |
| | 101 | | /// The provided sequence is enumerated, sorted in descending order of priority (taking into account |
| | 102 | | /// <see cref="PrioritizedItem{T}.PushTimestamp"/> to break ties), then copied over onto a dedicated linked list. |
| | 103 | | /// <br/> |
| | 104 | | /// So, the provided sequence is not used directly as backing structure for the queue. |
| | 105 | | /// <br/> |
| | 106 | | /// Therefore, operations mutating the queue won't alter the provided <paramref name="items"/> sequence. |
| | 107 | | /// </remarks> |
| | 108 | | public SortedLinkedListPriorityQueue(IEnumerable<PrioritizedItem<T>> items) |
| 224 | 109 | | : this(new LinkedList<PrioritizedItem<T>>(items.OrderByDescending(i => i))) |
| 220 | 110 | | { |
| 220 | 111 | | } |
| | 112 | |
|
| | 113 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 114 | | /// <remarks> |
| | 115 | | /// Calls <see cref="Count"/> on the underlying list. |
| | 116 | | /// <br/> |
| | 117 | | /// Time and Space Complexity are O(1). |
| | 118 | | /// </remarks> |
| 236 | 119 | | public int Count => Items.Count; |
| | 120 | |
|
| | 121 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 122 | | /// <remarks> |
| | 123 | | /// Returns the items in the underlying linked list, which is already sorted in descending order of priority. |
| | 124 | | /// <br/> |
| | 125 | | /// Time Complexity is O(n) (when fully enumerated). Space Complexity is O(1). |
| | 126 | | /// </remarks> |
| 3037 | 127 | | public IEnumerator<T> GetEnumerator() => Items.Select(n => n.Item).GetEnumerator(); |
| | 128 | |
|
| | 129 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 130 | | /// <remarks> |
| | 131 | | /// <inheritdoc cref="GetEnumerator"/> |
| | 132 | | /// </remarks> |
| 1 | 133 | | IEnumerator IEnumerable.GetEnumerator() => GetEnumerator(); |
| | 134 | |
|
| | 135 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 136 | | /// <remarks> |
| | 137 | | /// Returns the first item in the underlying linked list, raising <see cref="InvalidOperationException"/> when the |
| | 138 | | /// list is empty. |
| | 139 | | /// <br/> |
| | 140 | | /// Time Complexity is O(1). Space Complexity is O(1). |
| | 141 | | /// </remarks> |
| | 142 | | public PrioritizedItem<T> Peek() |
| 1319 | 143 | | { |
| 1319 | 144 | | if (Items.Count == 0) |
| 3 | 145 | | throw new InvalidOperationException($"Can't ${nameof(Peek)} on an empty queue."); |
| | 146 | |
|
| 1316 | 147 | | return Items.First(); |
| 1316 | 148 | | } |
| | 149 | |
|
| | 150 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 151 | | /// <remarks> |
| | 152 | | /// <see cref="Peek"/> the item with the highest priority from the underlying linked lists, which is the first item |
| | 153 | | /// in the chain. |
| | 154 | | /// <br/> |
| | 155 | | /// Then removes such an the item from the front of the linked list and returns it as result. |
| | 156 | | /// <br/> |
| | 157 | | /// Time Complexity is O(1). Space Complexity is O(1). |
| | 158 | | /// </remarks> |
| | 159 | | public PrioritizedItem<T> Pop() |
| 1258 | 160 | | { |
| 1258 | 161 | | if (Items.Count == 0) |
| 3 | 162 | | throw new InvalidOperationException($"Can't ${nameof(Pop)} on an empty queue."); |
| | 163 | |
|
| 1255 | 164 | | var result = Peek(); |
| 1255 | 165 | | Items.RemoveFirst(); |
| 1255 | 166 | | return result; |
| 1255 | 167 | | } |
| | 168 | |
|
| | 169 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 170 | | /// <remarks> |
| | 171 | | /// Finds the item I in the linked list with the highest priority, smaller than the priority of the provided |
| | 172 | | /// <paramref name="priority"/>. |
| | 173 | | /// <br/> |
| | 174 | | /// Then adds a new <see cref="LinkedListNode{T}"/> instance, having as value a new |
| | 175 | | /// <see cref="PrioritizedItem{T}"/> with the provided <paramref name="item"/> and <paramref name="priority"/>, |
| | 176 | | /// just before the item I. |
| | 177 | | /// <br/> |
| | 178 | | /// If such a I doesn't exist, prepend the new <see cref="LinkedListNode{T}"/> at the front of the linked list. |
| | 179 | | /// <br/> |
| | 180 | | /// Time Complexity is O(n). Space Complexity is O(1). |
| | 181 | | /// <br/> |
| | 182 | | /// Remark: while the linked list is sorted by priority, binary search it's not possible, due to lack of direct |
| | 183 | | /// random access support. |
| | 184 | | /// </remarks> |
| | 185 | | public void Push(T item, int priority) |
| 4045 | 186 | | { |
| 4045 | 187 | | var prioritizedItem = new PrioritizedItem<T>(item, priority, CurrentPushTimestamp++); |
| 4045 | 188 | | var highestSmallerNode = FindOccurrenceWithHighestPrioritySmallerThan(prioritizedItem); |
| 4045 | 189 | | if (highestSmallerNode == null) |
| 686 | 190 | | Items.AddFirst(prioritizedItem); |
| | 191 | | else |
| 3359 | 192 | | Items.AddAfter(highestSmallerNode, prioritizedItem); |
| 4045 | 193 | | } |
| | 194 | |
|
| | 195 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 196 | | /// <remarks> |
| | 197 | | /// Linearly scans the underlying linked list, looking for <see cref="PrioritizedItem{T}"/> having an item equals |
| | 198 | | /// to the provided <paramref name="item"/> (<see cref="object.Equals(object?, object?)"/> is used to compare the |
| | 199 | | /// two items of type <typeparamref name="T"/>). |
| | 200 | | /// <br/> |
| | 201 | | /// It then selects all priorities found for <paramref name="item"/> and builds a |
| | 202 | | /// <see cref="SortedLinkedListPriorityQueue{T}"/> of <see cref="int"/> values out of them. |
| | 203 | | /// <br/> |
| | 204 | | /// Such a priority queue is returned as result. |
| | 205 | | /// <br/> |
| | 206 | | /// Time Complexity is O(n * Teq) and Space Complexity is O(Seq), where Teq and Seq are the time and space cost of |
| | 207 | | /// comparing two items of type <typeparamref name="T"/>. |
| | 208 | | /// </remarks> |
| | 209 | | public IEnumerable<int> GetPrioritiesOf(T item) |
| 41 | 210 | | { |
| 41 | 211 | | var priorities = Items |
| 78 | 212 | | .Where(prioritizedItem => Equals(prioritizedItem.Item, item)) |
| 85 | 213 | | .Select(prioritizedItem => prioritizedItem.Priority); |
| 41 | 214 | | var priorityQueue = new SortedLinkedListPriorityQueue<int>(); |
| 211 | 215 | | foreach (var priority in priorities) |
| 44 | 216 | | priorityQueue.Push(priority, priority); |
| 41 | 217 | | return priorityQueue; |
| 41 | 218 | | } |
| | 219 | |
|
| | 220 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 221 | | /// <remarks> |
| | 222 | | /// Removes the occurrence of <paramref name="item"/> with highest priority from the underlying linked list (the |
| | 223 | | /// first encountered while navigating the list). |
| | 224 | | /// <br/> |
| | 225 | | /// If no occurrence of <paramref name="item"/> is found, an <see cref="InvalidOperationException"/> is thrown. |
| | 226 | | /// <br/> |
| | 227 | | /// Then pushes the provided <paramref name="item"/> with the given <paramref name="newPriority"/>. |
| | 228 | | /// <br/> |
| | 229 | | /// Both removal and push operations require linked list traversal and update. |
| | 230 | | /// <br/> |
| | 231 | | /// Therefore, Time Complexity is O(n). Space Complexity is O(1). |
| | 232 | | /// </remarks> |
| | 233 | | public PrioritizedItem<T> UpdatePriority(T item, int newPriority) |
| 97 | 234 | | { |
| 97 | 235 | | var oldItem = Remove(item); |
| 97 | 236 | | if (oldItem == null) |
| 3 | 237 | | throw new InvalidOperationException("The specified item is not in the queue."); |
| 94 | 238 | | Push(item, newPriority); |
| 94 | 239 | | return oldItem.Value; |
| 94 | 240 | | } |
| | 241 | |
|
| | 242 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 243 | | /// <remarks> |
| | 244 | | /// Linearly scans the underlying linked list, looking for the first node with the item equals to the provided |
| | 245 | | /// <paramref name="item"/> (<see cref="object.Equals(object?, object?)"/> is used to compare the two items of type |
| | 246 | | /// <typeparamref name="T"/>). |
| | 247 | | /// <br/> |
| | 248 | | /// If multiple occurrences of <paramref name="item"/> are present with the same highest priority, the one with the |
| | 249 | | /// lowest <see cref="PrioritizedItem{T}.PushTimestamp"/> is considered of higher priority, and comes before any |
| | 250 | | /// other in the list. That guarantees <b>stability</b>. |
| | 251 | | /// <br/> |
| | 252 | | /// If no such node is found, nothing is changed and <see langword="null"/> is returned. |
| | 253 | | /// <br/> |
| | 254 | | /// Otherwise the node is removed from the list and returned as result. |
| | 255 | | /// <br/> |
| | 256 | | /// Time Complexity is O(n * Teq) and Space Complexity is O(Seq), where Teq and Seq are the time and space cost of |
| | 257 | | /// comparing two items of type <typeparamref name="T"/>. |
| | 258 | | /// </remarks> |
| | 259 | | public PrioritizedItem<T>? Remove(T item) |
| 120 | 260 | | { |
| 120 | 261 | | var itemNode = FindOccurrenceWithHighestPriorityOf(item); |
| | 262 | |
|
| 120 | 263 | | if (itemNode == null) |
| 10 | 264 | | return null; |
| | 265 | |
|
| 110 | 266 | | Items.Remove(itemNode); |
| 110 | 267 | | return itemNode.Value; |
| 120 | 268 | | } |
| | 269 | |
|
| | 270 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 271 | | /// <remarks> |
| | 272 | | /// Takes advantage of the fact that the underlying linked list of items is already sorted in descending order by |
| | 273 | | /// priority, and returns the <paramref name="k"/>-th item of the list. |
| | 274 | | /// <br/> |
| | 275 | | /// Time Complexity is O(k). Space Complexity is O(1). |
| | 276 | | /// <br/> |
| | 277 | | /// The <paramref name="k"/>-th item of the list cannot be accessed in constant time, because linked lists don't |
| | 278 | | /// support direct random access. |
| | 279 | | /// </remarks> |
| | 280 | | public PrioritizedItem<T>? PeekKth(int k) |
| 26 | 281 | | { |
| 26 | 282 | | if (k < 0) |
| 2 | 283 | | throw new ArgumentException("Must be non-negative.", nameof(k)); |
| 24 | 284 | | if (k >= Items.Count) |
| 8 | 285 | | return null; |
| 16 | 286 | | if (k == 0) |
| 5 | 287 | | return Peek(); |
| | 288 | |
|
| 11 | 289 | | return Items.ElementAt(k); |
| 24 | 290 | | } |
| | 291 | |
|
| | 292 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 293 | | /// <remarks> |
| | 294 | | /// Does 2-way merging on the underlying linked lists, which are already sorted in descending order of priority. |
| | 295 | | /// <br/> |
| | 296 | | /// Time and Space Complexity are O(n + m), where n and m are the number of items in this queue and in the target, |
| | 297 | | /// respectively. |
| | 298 | | /// </remarks> |
| | 299 | | public void MergeFrom(SortedLinkedListPriorityQueue<T> targetPriorityQueue) |
| 119 | 300 | | { |
| 119 | 301 | | var first = Items.First; |
| 119 | 302 | | var second = targetPriorityQueue.Items.First; |
| 119 | 303 | | var merged = new LinkedList<PrioritizedItem<T>>(); |
| 3075 | 304 | | while (first != null || second != null) |
| 2956 | 305 | | { |
| | 306 | | PrioritizedItem<T> prioritizedItem; |
| 2956 | 307 | | if (second == null || (first != null && first.Value.Priority >= second.Value.Priority)) |
| 1639 | 308 | | { |
| 1639 | 309 | | prioritizedItem = new(first!.Value.Item, first.Value.Priority, CurrentPushTimestamp++); |
| 1639 | 310 | | first = first.Next; |
| 1639 | 311 | | } |
| | 312 | | else |
| 1317 | 313 | | { |
| 1317 | 314 | | prioritizedItem = new(second.Value.Item, second.Value.Priority, CurrentPushTimestamp++); |
| 1317 | 315 | | second = second.Next; |
| 1317 | 316 | | } |
| 2956 | 317 | | merged.AddLast(prioritizedItem); |
| 2956 | 318 | | } |
| | 319 | |
|
| 119 | 320 | | Items = merged; |
| 119 | 321 | | targetPriorityQueue.Clear(); |
| 119 | 322 | | } |
| | 323 | |
|
| | 324 | | /// <inheritdoc path="//*[not(self::remarks)]"/> |
| | 325 | | /// <remarks> |
| | 326 | | /// Just clears the underlying linked list. |
| | 327 | | /// <br/> |
| | 328 | | /// Time and Space Complexity is O(1). |
| | 329 | | /// </remarks> |
| | 330 | | public void Clear() |
| 174 | 331 | | { |
| 174 | 332 | | Items.Clear(); |
| 174 | 333 | | } |
| | 334 | | } |