Rotation of AVL tree

Catalog

Selection of single rotation and double rotation ：

Left spin

Right single spin

Right left double rotation

Double left and right

AVL Verification of trees

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Selection of single rotation and double rotation ：

 

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Left spin

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Right single spin

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Right left double rotation

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Double left and right

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AVL Verification of trees

• AVL The tree is based on the binary search tree and adds the restriction of balance , So verify AVL Trees , There are two steps ：
  • 1. Verify that it is a binary search tree
    • If the middle order traversal can get an ordered sequence , It is explained as a binary search tree
  • 2. Verify that it is a balanced tree
    • The absolute value of the height difference of each node subtree shall not exceed 1( Note that if there is no balance factor in the node )
    • Whether the balance factor of the node is calculated correctly

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  • Special scenes 2
    • {4, 2, 6, 1, 3, 5, 15, 7, 16, 14}
    • The value found during validation is 6 There is an error in the balance factor of the node , The balance factor should have been -1, But the result is 0;
    • Cause analysis ：
      • Right left double rotation ：

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      • Problem solving ：
        • You can rotate it according to SubRL The equilibrium factor of , Modify the rotation after it is completed ：

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      • Double left and right

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      • Problem solving ：
        • You can rotate it according to SubLR The equilibrium factor of , Modify the rotation after it is completed ：

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• AVL Complex tree implementation :
  • 1. The implementation is more complex , because AVL Maintain the balance factor for nodes in , The balance factor needs to be updated after each insertion , After the double rotation is completed, the balance factor also needs to be updated
  • 2. Delete : The most inserted case should always be updated or rotated to the root position