Beispiel 2-3-4-tree-10.cpp, 7.5.2018

20180507/2-3-4-tree-10.cpp

+#include <iostream>
+
+using namespace std;
+
+const int MaxLeaves = 4;
+const int MaxEntries = MaxLeaves - 1;
+
+template <typename TElement>
+class TTree
+{
+
+  struct TEntry
+  {
+    TElement Content;
+    bool empty;
+
+    TEntry ()
+    {
+      empty = true;
+    }
+  };
+
+  struct TNode
+  {
+    TEntry Entry[MaxEntries];
+    TNode *Child[MaxLeaves];
+
+    TNode ()
+    {
+      for (int i = 0; i < MaxLeaves; i++)
+        Child[i] = NULL;
+    }
+
+    void SetEntry (int i, TElement e)
+    {
+      Entry[i].Content = e;
+      Entry[i].empty = false;
+    }
+  };
+
+  TNode *Root;
+
+private:
+
+  void SplitNode (TNode *FullNode, TElement NewElement, TNode *&Left, TNode *&Right, TElement &Middle)
+  {
+    int i = 0;
+    while (i < MaxEntries && NewElement > FullNode->Entry[i].Content)
+      i++;
+    TElement Top;
+    if (i < MaxEntries)
+      {
+        Top = FullNode->Entry[MaxEntries - 1].Content;
+        for (int j = MaxEntries - 1; j > i; j--)
+          FullNode->Entry[j] = FullNode->Entry[j - 1];
+        FullNode->SetEntry (i, NewElement);
+      }
+    else
+      Top = NewElement;
+    // Achtung: Hier benutzen wir, daß MaxEntries = 3 ist!
+    Middle = FullNode->Entry[2].Content;
+    FullNode->Entry[2].empty = true;
+    Left = FullNode;
+    Right = new TNode ();
+    Right->SetEntry (0, Top);
+  }
+
+  void InsertNode (TNode *Node, TElement e)
+  {
+    if (Node->Child[0])
+      {
+        int i = 0;
+        while (i < MaxEntries && !Node->Entry[i].empty && e > Node->Entry[i].Content)
+          i++;
+        if (Node->Child[i])
+          InsertNode (Node->Child[i], e);  // @@@ Entartung möglich!
+        else
+          {
+            Node->Child[i] = new TNode ();
+            InsertNode (Node->Child[i], e);
+            // @@@ B-Baum-Bedingung: Knoten müssen immer mindestens zur Hälfte aufgefüllt sein!
+            // @@@ Hier automatisch erfüllt, weil "Hälfte" = 1, aber bei "größeren" Bäumen nicht.
+          }
+      }
+    else if (Node->Entry[MaxEntries - 1].empty)
+      {
+        int i = 0;
+        while (i < MaxEntries && !Node->Entry[i].empty && e > Node->Entry[i].Content)
+          i++;
+        if (i < MaxEntries)
+          {
+            if (!Node->Entry[i].empty)
+              for (int j = MaxEntries - 1; j > i; j--)
+                Node->Entry[j] = Node->Entry[j - 1];
+            Node->SetEntry (i, e);
+          }
+      }
+    else
+      {
+        TNode *Left, *Right;
+        TElement Middle;
+        SplitNode (Node, e, Left, Right, Middle);  // "zerstört" Node
+        Node = new TNode ();
+        Node->SetEntry (0, Middle);
+        Node->Child[0] = Left;
+        Node->Child[1] = Right;
+      }
+  }
+
+  void PrintNode (TNode *Node)
+  {
+    if (Node)
+      {
+        for (int i = 0; i < MaxEntries; i++)
+          {
+            PrintNode (Node->Child[i]);
+            if (!Node->Entry[i].empty)
+              cout << Node->Entry[i].Content << " ";
+          }
+        PrintNode (Node->Child[MaxLeaves - 1]);
+      }
+  }
+
+public:
+
+  TTree ()
+  {
+    Root = NULL;
+  }
+
+  void Insert (TElement e)
+  {
+    if (!Root)
+      Root = new TNode ();
+    InsertNode (Root, e);
+  }
+
+  void Print ()
+  {
+    PrintNode (Root);
+    cout << endl;
+  }
+
+};
+
+int main ()
+{
+  TTree <int> t;
+  t.Insert (42);
+  t.Insert (13);
+  t.Insert (137);
+  t.Insert (7);
+  t.Insert (1117);
+  t.Print ();
+  return 0;
+}