Data StructureAlgorithm& Applications in C++
Chapter 15 Exercise 47

The initial configuration is:
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /  \            /    \
         /    \          /      \
        /      \        /        \
       2       6       10        14
     /  \    /   \    /  \      /  \
    1   3    5   7   9   11   13   15
The tree following the the deletion of 6 is shown below.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /  \            /    \
         /    \          /      \
        /      \        /        \
       2       5       10        14
     /  \       \     /  \      /  \
    1   3        7   9   11   13   15
5 becomes the splay node q, and p = 4 and gp = 8. An LR rotation is done and the splay node becomes the root. We get the following tree:
                    5
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               8
          /               /    \
         /               /      \
        /               /        \
       2               7         12
     /  \                       /   \
    1   3                     10    14
                             /  \   / \
                            9   11 13 15
The deletion of 7 results in the following tree.
                    5
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4                8
          /                    \
         /                      \
        /                        \
       2                         12
     /  \                       /   \
    1   3                     10    14
                             /  \   / \
                            9   11 13 15
The splay node is 8, and a type R rotation is done to get the following tree.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            5               12
          /               /    \
         /               /      \
        /               /        \
       4               10        14
     /                /  \      /  \
    2                9   11   13   15
   / \
  1   3


When 5 is deleted we get the following tree.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /               /    \
         /               /      \
        /               /        \
       2               10        14
     /  \             /  \      /  \
    1    3           9   11   13   15
8 is the splay node. Since the splay node is already the root, no rotation is done. The deletion of 10 results in the following tree.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /               /    \
         /               /      \
        /               /        \
       2               9         14
     /  \                \      /  \
    1    3               11   13   15
The splay node is 9, and an RL rotation is done to get the following tree.
                    9
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            8               12
          /               /    \
         /               /      \
        /               /        \
       4               11        14
     /                          /  \
    2                         13   15
   / \
  1  3
The deletion of 9 gives us the following tree.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /               /    \
         /               /      \
        /               /        \
       2               11        14
     /  \                       /  \
    1    3                    13   15
No rotation is done because the splay node, 8, is already the root.

When 11 is deleted we get the following tree.
                    8
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            4               12
          /                    \
         /                      \
        /                        \
       2                         14
     /  \                       /  \
    1    3                    13   15
The splay node is 12, and a type R rotation is done to get the following tree.
                  12
                 /  \
                /    \
               /      \
              8       14
             /       /  \
            4       13  15
           /      
          2      
        /  \    
       1    3  
The tree following the deletion of 15 is shown below.
                  12
                 /  \
                /    \
               /      \
              8       14
             /       /
            4       13 
           /      
          2      
        /  \    
       1    3  
14 is the splay node, and a type R rotation is done to get the following tree.
                   14
                   /
                  12   
                 /  \
                /    \
               /      \
              8       13
             /       
            4    
           /      
          2      
        /  \    
       1    3  
When 12 is deleted, the following tree results.
                   14
                   /
                  8   
                 /  \
                /    \
               /      \
              4       13
             /       
            2    
           / \
          1  3  
8 is the splay node and a tye L rotation is done to get the tree that is shown below.
                  8   
                 /  \
                /    \
               /      \
              4       14
             /       /
            2       13
           / \
          1  3  
The tree following the deletion of 13 is shown below.
                  8   
                 /  \
                /    \
               /      \
              4       14
             /
            2
           / \
          1  3  
14 is the splay node and a type R rotation is done to get the following tree.
                 14
                 /
                8   
               /
              4
             /
            2
           / \
          1  3  
When 14 is deleted we get the following tree.
                 14
                 /
                8   
               /
              4
             /
            2
           / \
          1  3  
This time, there is no rotation.