二叉堆

  1   class Program
  2   {
  3     static void Main(string[] args)
  4     {
  5       int[] unsorted = { 4, 9, 5, 2, 6, 3, 7, 1, 8 };
  6 
  7       HeapSortByMaxHeap(unsorted);
  8 
  9       foreach (var key in unsorted)
 10       {
 11         Console.Write("{0} ", key);
 12       }
 13 
 14       Console.Read();
 15     }
 16 
 17     static void HeapSortByMaxHeap(int[] unsorted)
 18     {
 19       // build the heap in array so that largest value is at the root
 20       BuildMaxHeap(unsorted);
 21 
 22       // swap root node and the last heap node
 23       for (int i = unsorted.Length - 1; i >= 1; i--)
 24       {
 25         // array[0] is the root and largest value. 
 26         // the swap moves it in front of the sorted elements
 27         int max = unsorted[0];
 28         unsorted[0] = unsorted[i];
 29         unsorted[i] = max; // now, the largest one is at the end
 30 
 31         // the swap ruined the heap property, so restore it
 32         // the heap size is reduced by one
 33         MaxHeapify(unsorted, 0, i - 1);
 34       }
 35     }
 36 
 37     static void BuildMaxHeap(int[] unsorted)
 38     {
 39       // put elements of array in heap order, in-place
 40       // start is assigned the index in array of the last parent node
 41       // the last element in 0-based array is at index count-1; 
 42       // find the parent of that element
 43       for (int i = (unsorted.Length / 2) - 1; i >= 0; i--)
 44       {
 45         // move a node down in the tree, as long as needed
 46         // shift down the node at index start to the proper place 
 47         // such that all nodes below the start index are in heap order
 48         MaxHeapify(unsorted, i, unsorted.Length - 1);
 49       }
 50       // after shifting down the root all nodes/elements are in heap order
 51     }
 52 
 53     static void MaxHeapify(int[] unsorted, int root, int bottom)
 54     {
 55       int rootValue = unsorted[root];
 56       int left = root * 2 + 1; // start from left child
 57 
 58       // while the root has at least one child
 59       while (left <= bottom)
 60       {
 61         // has more children
 62         if (left < bottom)
 63         {
 64           // if there is a right child and that child is greater
 65           if (unsorted[left] < unsorted[left + 1])
 66           {
 67             left = left + 1;
 68           }
 69         }
 70 
 71         // compare root and the older children
 72         if (rootValue < unsorted[left])
 73         {
 74           // swap
 75           unsorted[root] = unsorted[left];
 76           root = left;
 77 
 78           // repeat to continue sifting down the child now
 79           left = root * 2 + 1; // continue from left child
 80         }
 81         else
 82         {
 83           left = bottom + 1;
 84         }
 85       }
 86 
 87       unsorted[root] = rootValue;
 88     }
 89 
 90     static void HeapSortByMinHeap(int[] unsorted)
 91     {
 92       BuildMinHeap(unsorted);
 93 
 94       for (int i = unsorted.Length - 1; i >= 1; i--)
 95       {
 96         int min = unsorted[0];
 97         unsorted[0] = unsorted[i];
 98         unsorted[i] = min;
 99 
100         MinHeapify(unsorted, 0, i - 1);
101       }
102 
103       // reverse
104       for (int i = 0; i < (unsorted.Length / 2); i++)
105       {
106         int t = unsorted[i];
107         unsorted[i] = unsorted[unsorted.Length - 1 - i];
108         unsorted[unsorted.Length - 1 - i] = t;
109       }
110     }
111 
112     static void BuildMinHeap(int[] unsorted)
113     {
114       for (int i = (unsorted.Length / 2) - 1; i >= 0; i--)
115       {
116         MinHeapify(unsorted, i, unsorted.Length - 1);
117       }
118     }
119 
120     static void MinHeapify(int[] unsorted, int root, int bottom)
121     {
122       int rootValue = unsorted[root];
123       int left = root * 2 + 1; // start from left child
124 
125       // while the root has at least one child
126       while (left <= bottom)
127       {
128         // has more children
129         if (left < bottom)
130         {
131           // if there is a right child and that child is smaller
132           if (unsorted[left] > unsorted[left + 1])
133           {
134             left = left + 1;
135           }
136         }
137 
138         // compare root and the older children
139         if (rootValue > unsorted[left])
140         {
141           // swap
142           unsorted[root] = unsorted[left];
143           root = left;
144 
145           // repeat to continue sifting down the child now
146           left = root * 2 + 1; // continue from left child
147         }
148         else
149         {
150           left = bottom + 1;
151         }
152       }
153 
154       unsorted[root] = rootValue;
155     }
156   }