|
| 1 | +using System; |
| 2 | + |
| 3 | +namespace PriorityQueue |
| 4 | +{ |
| 5 | + /// <summary> |
| 6 | + /// 前序堆排序类，提供堆排序的静态方法。 |
| 7 | + /// </summary> |
| 8 | + /// <typeparam name="T">需要排序的元素类型。</typeparam> |
| 9 | + public static class HeapPreorder |
| 10 | + { |
| 11 | + /// <summary> |
| 12 | + /// 利用堆排序对数组进行排序。 |
| 13 | + /// </summary> |
| 14 | + /// <param name="pq">需要排序的数组。</param> |
| 15 | + public static void Sort<T>(T[] pq) where T : IComparable<T> |
| 16 | + { |
| 17 | + int n = pq.Length; |
| 18 | + BuildTree(pq, 0, pq.Length); |
| 19 | + // 排序 |
| 20 | + while (n > 1) |
| 21 | + { |
| 22 | + int tail = GetTail(pq, 0, n); |
| 23 | + T temp = pq[tail]; |
| 24 | + for (int i = tail + 1; i < n; i++) |
| 25 | + pq[i - 1] = pq[i]; |
| 26 | + n--; |
| 27 | + Exch(pq, 0, n); |
| 28 | + pq[0] = temp; |
| 29 | + Sink(pq, 0, n); |
| 30 | + } |
| 31 | + } |
| 32 | + |
| 33 | + private static int GetTail<T>(T[] pq, int p, int n) |
| 34 | + { |
| 35 | + if (n <= 1) |
| 36 | + return p; |
| 37 | + int k = (int)(Math.Log10(n) / Math.Log10(2)); // 高度 |
| 38 | + |
| 39 | + int left = (int)Math.Pow(2, k - 1) - 1; |
| 40 | + int right = left; |
| 41 | + if (n - left <= (int)Math.Pow(2, k)) |
| 42 | + { |
| 43 | + // 叶子结点全在左侧 |
| 44 | + left = n - right - 1; |
| 45 | + return GetTail(pq, p + 1, left); |
| 46 | + } |
| 47 | + else |
| 48 | + { |
| 49 | + left = (int)Math.Pow(2, k) - 1; |
| 50 | + right = n - left - 1; |
| 51 | + return GetTail(pq, p + 1 + left, right); |
| 52 | + } |
| 53 | + } |
| 54 | + |
| 55 | + /// <summary> |
| 56 | + /// 递归建堆。 |
| 57 | + /// </summary> |
| 58 | + /// <typeparam name="T">堆中元素。</typeparam> |
| 59 | + /// <param name="pq">堆所在的数组。</param> |
| 60 | + /// <param name="p">堆的起始下标。</param> |
| 61 | + /// <param name="n">堆的元素数目。</param> |
| 62 | + private static void BuildTree<T>(T[] pq, int p, int n) where T : IComparable<T> |
| 63 | + { |
| 64 | + if (n <= 1) |
| 65 | + return; |
| 66 | + int k = (int)(Math.Log10(n) / Math.Log10(2)); // 高度 |
| 67 | + |
| 68 | + int left = (int)Math.Pow(2, k - 1) - 1; |
| 69 | + int right = left; |
| 70 | + if (n - left <= (int)Math.Pow(2, k)) |
| 71 | + { |
| 72 | + // 叶子结点全在左侧 |
| 73 | + left = n - right - 1; |
| 74 | + } |
| 75 | + else |
| 76 | + { |
| 77 | + left = (int)Math.Pow(2, k) - 1; |
| 78 | + right = n - left - 1; |
| 79 | + } |
| 80 | + |
| 81 | + BuildTree(pq, p + 1, left); |
| 82 | + BuildTree(pq, p + 1 + left, right); |
| 83 | + Sink(pq, p, n); |
| 84 | + } |
| 85 | + |
| 86 | + /// <summary> |
| 87 | + /// 令堆中的元素下沉。 |
| 88 | + /// </summary> |
| 89 | + /// <param name="pq">需要执行操作的堆。</param> |
| 90 | + /// <param name="p">需要执行下沉的结点下标。</param> |
| 91 | + /// <param name="n">堆中元素的数目。</param> |
| 92 | + private static void Sink<T>(T[] pq, int p, int n) where T : IComparable<T> |
| 93 | + { |
| 94 | + if (n <= 1) |
| 95 | + return; |
| 96 | + int k = (int)(Math.Log10(n) / Math.Log10(2)); // 高度 |
| 97 | + |
| 98 | + int left = (int)Math.Pow(2, k - 1) - 1; |
| 99 | + int right = left; |
| 100 | + if (n - left <= (int)Math.Pow(2, k)) |
| 101 | + { |
| 102 | + // 叶子结点全在左侧 |
| 103 | + left = n - right - 1; |
| 104 | + } |
| 105 | + else |
| 106 | + { |
| 107 | + left = (int)Math.Pow(2, k) - 1; |
| 108 | + right = n - left - 1; |
| 109 | + } |
| 110 | + |
| 111 | + // 找出较大的子结点 |
| 112 | + int j = p + 1, size = left; |
| 113 | + if (right != 0) // 有右结点 |
| 114 | + { |
| 115 | + if (Less(pq, j, p + left + 1)) |
| 116 | + { |
| 117 | + j = p + left + 1; |
| 118 | + size = right; |
| 119 | + } |
| 120 | + } |
| 121 | + |
| 122 | + // 与根结点比较 |
| 123 | + if (!Less(pq, p, j)) |
| 124 | + return; |
| 125 | + |
| 126 | + // 交换，继续下沉 |
| 127 | + Exch(pq, p, j); |
| 128 | + Sink(pq, j, size); |
| 129 | + } |
| 130 | + |
| 131 | + /// <summary> |
| 132 | + /// 比较堆中下标为 <paramref name="a"/> 的元素是否小于下标为 <paramref name="b"/> 的元素。 |
| 133 | + /// </summary> |
| 134 | + /// <param name="pq">元素所在的数组。</param> |
| 135 | + /// <param name="a">需要比较是否较小的结点序号。</param> |
| 136 | + /// <param name="b">需要比较是否较大的结点序号。</param> |
| 137 | + /// <returns></returns> |
| 138 | + private static bool Less<T>(T[] pq, int a, int b) where T : IComparable<T> => pq[a].CompareTo(pq[b]) < 0; |
| 139 | + |
| 140 | + /// <summary> |
| 141 | + /// 交换堆中的两个元素。 |
| 142 | + /// </summary> |
| 143 | + /// <param name="pq">要交换的元素所在堆。</param> |
| 144 | + /// <param name="a">要交换的结点序号。</param> |
| 145 | + /// <param name="b">要交换的结点序号。</param> |
| 146 | + private static void Exch<T>(T[] pq, int a, int b) |
| 147 | + { |
| 148 | + T temp = pq[a]; |
| 149 | + pq[a] = pq[b]; |
| 150 | + pq[b] = temp; |
| 151 | + } |
| 152 | + } |
| 153 | +} |
0 commit comments