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| 1 | using System; | |
| 2 | using System.Collections.Generic; | |
| 3 | ||
| 4 | namespace Algorithms.Lib | |
| 5 | {
| |
| 6 | /// <summary> | |
| 7 | /// Doesn't support duplicate values! | |
| 8 | /// Yes, this breaks Liskov's principle. Sorry, Barbara! | |
| 9 | /// </summary> | |
| 10 | public class BinaryHeapWithUpdates<TKey, TValue> : BinaryHeap<TKey, TValue> | |
| 11 | {
| |
| 12 | protected readonly Dictionary<TValue, int> HeapIndexes; | |
| 13 | ||
| 14 | public BinaryHeapWithUpdates(IComparer<TKey> comparer, IEqualityComparer<TValue> valueComparer) : base(comparer) | |
| 15 | {
| |
| 16 | HeapIndexes = new Dictionary<TValue, int>(valueComparer); | |
| 17 | } | |
| 18 | ||
| 19 | public void UpdateKey(TValue value, TKey newKey) | |
| 20 | {
| |
| 21 | int index; | |
| 22 | if (!HeapIndexes.TryGetValue(value, out index)) | |
| 23 | {
| |
| 24 | throw new ArgumentException("Value was not found in the heap.");
| |
| 25 | } | |
| 26 | ||
| 27 | var oldKey = Keys[index]; | |
| 28 | int comp = Comparer.Compare(newKey, oldKey); | |
| 29 | Keys[index] = newKey; | |
| 30 | if (comp < 0) | |
| 31 | {
| |
| 32 | // decrease-key | |
| 33 | BubbleUp(index); | |
| 34 | } | |
| 35 | else if (comp > 0) | |
| 36 | {
| |
| 37 | // increase-key | |
| 38 | BubbleDown(index); | |
| 39 | } | |
| 40 | } | |
| 41 | ||
| 42 | public override void Insert(TKey key, TValue value) | |
| 43 | {
| |
| 44 | HeapIndexes.Add(value, Keys.Count); | |
| 45 | base.Insert(key, value); | |
| 46 | } | |
| 47 | ||
| 48 | public override KeyValuePair<TKey, TValue> ExtractMin() | |
| 49 | {
| |
| 50 | var min = base.ExtractMin(); | |
| 51 | HeapIndexes.Remove(min.Value); | |
| 52 | return min; | |
| 53 | } | |
| 54 | ||
| 55 | protected override void Swap(int i, int j) | |
| 56 | {
| |
| 57 | HeapIndexes[Values[i]] = j; | |
| 58 | HeapIndexes[Values[j]] = i; | |
| 59 | base.Swap(i, j); | |
| 60 | } | |
| 61 | } | |
| 62 | ||
| 63 | /// <summary> | |
| 64 | /// Supports duplicate keys, but without stable ordering guarantee. | |
| 65 | /// Stable ordering can be achieved by adding version counter to each node (as done in boost). | |
| 66 | /// </summary> | |
| 67 | public class BinaryHeap<TKey, TValue> | |
| 68 | {
| |
| 69 | protected readonly IComparer<TKey> Comparer; | |
| 70 | protected readonly List<TKey> Keys; | |
| 71 | protected readonly List<TValue> Values; | |
| 72 | ||
| 73 | public BinaryHeap(IComparer<TKey> comparer) | |
| 74 | {
| |
| 75 | this.Comparer = comparer; | |
| 76 | Keys = new List<TKey>(); | |
| 77 | Values = new List<TValue>(); | |
| 78 | } | |
| 79 | ||
| 80 | // O(N) | |
| 81 | public static BinaryHeap<TKey, TValue> Build(IEnumerable<KeyValuePair<TKey, TValue>> elements, IComparer<TKey> comparer) | |
| 82 | {
| |
| 83 | var heap = new BinaryHeap<TKey, TValue>(comparer); | |
| 84 | foreach (var element in elements) | |
| 85 | {
| |
| 86 | heap.Keys.Add(element.Key); | |
| 87 | heap.Values.Add(element.Value); | |
| 88 | } | |
| 89 | ||
| 90 | for (int i = (heap.Keys.Count - 2) >> 1; i >= 0; i--) | |
| 91 | {
| |
| 92 | heap.BubbleDown(i); | |
| 93 | } | |
| 94 | ||
| 95 | return heap; | |
| 96 | } | |
| 97 | ||
| 98 | // O(logN) | |
| 99 | public virtual void Insert(TKey key, TValue value) | |
| 100 | {
| |
| 101 | Keys.Add(key); | |
| 102 | Values.Add(value); | |
| 103 | BubbleUp(Keys.Count - 1); | |
| 104 | } | |
| 105 | ||
| 106 | // O(logN) | |
| 107 | public virtual KeyValuePair<TKey, TValue> ExtractMin() | |
| 108 | {
| |
| 109 | if (Keys.Count == 0) | |
| 110 | {
| |
| 111 | throw new InvalidOperationException("Cannot extract minimum from empty heap.");
| |
| 112 | } | |
| 113 | ||
| 114 | var p = new KeyValuePair<TKey, TValue>(Keys[0], Values[0]); | |
| 115 | - | Keys[0] = Keys[Keys.Count - 1]; |
| 115 | + | Swap(0, Keys.Count - 1); |
| 116 | - | Values[0] = Values[Values.Count - 1]; |
| 116 | + | |
| 117 | Values.RemoveAt(Values.Count - 1); | |
| 118 | BubbleDown(0); | |
| 119 | return p; | |
| 120 | } | |
| 121 | ||
| 122 | protected virtual void Swap(int i, int j) | |
| 123 | {
| |
| 124 | TKey tmpKey = Keys[i]; | |
| 125 | TValue tmpVal = Values[i]; | |
| 126 | ||
| 127 | Keys[i] = Keys[j]; | |
| 128 | Values[i] = Values[j]; | |
| 129 | ||
| 130 | Keys[j] = tmpKey; | |
| 131 | Values[j] = tmpVal; | |
| 132 | } | |
| 133 | ||
| 134 | protected void BubbleUp(int index) | |
| 135 | {
| |
| 136 | while (index > 0) | |
| 137 | {
| |
| 138 | int parent = (index - 1) >> 1; | |
| 139 | ||
| 140 | // stop condition: element is not less than it's parent | |
| 141 | if (Comparer.Compare(Keys[parent], Keys[index]) <= 0) return; | |
| 142 | Swap(index, parent); | |
| 143 | index = parent; | |
| 144 | } | |
| 145 | } | |
| 146 | ||
| 147 | // this is also called Heapify | |
| 148 | protected void BubbleDown(int index) | |
| 149 | {
| |
| 150 | int lastParent = (Keys.Count - 2) >> 1; | |
| 151 | while (index <= lastParent) | |
| 152 | {
| |
| 153 | int left = (index << 1) + 1; | |
| 154 | int right = left + 1; | |
| 155 | int min = index; | |
| 156 | if (left < Keys.Count && Comparer.Compare(Keys[left], Keys[min]) <= 0) min = left; | |
| 157 | if (right < Keys.Count && Comparer.Compare(Keys[right], Keys[min]) <= 0) min = right; | |
| 158 | ||
| 159 | // stop condition: index element is not less than both children | |
| 160 | if (min == index) return; | |
| 161 | Swap(index, min); | |
| 162 | index = min; | |
| 163 | } | |
| 164 | } | |
| 165 | } | |
| 166 | } |