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Properties of BST delete We first do the normal BST deletion: – 0 children: just delete it – 1 child: delete it, connect child to parent – 2 children:

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Presentation on theme: "Properties of BST delete We first do the normal BST deletion: – 0 children: just delete it – 1 child: delete it, connect child to parent – 2 children:"— Presentation transcript:

1 Properties of BST delete We first do the normal BST deletion: – 0 children: just delete it – 1 child: delete it, connect child to parent – 2 children: put successor in your place, delete successor Which nodes’ heights may have changed: – 0 children: path from deleted node to root – 1 child: path from deleted node to root – 2 children: path from deleted successor to root Will rebalance as we return along the “path in question” to the root 1CSE332: Data Abstractions 20 92 155 12 7 10

2 Case #1 Left-left due to right deletion CSE332: Data Abstractions2 Start with some subtree where if right child Z becomes shorter we are unbalanced due to height of left-left grandchild X A delete in the right child Z could cause this right-side shortening h a Z Y b X h+1 h h+2 h+3

3 Case #1: Left-left due to right deletion CSE332: Data Abstractions3 h a Z Y b X h+1 h h+2 h+3 b ZY a h+1 h h+2 X h h+1 Same single rotation as when an insert in the left-left grandchild X caused imbalance due to X becoming taller But here the “height” at the top decreases, so more rebalancing farther up the tree might still be necessary

4 Case #2: Left-right due to right deletion a h-1 h h V U h+1 h+2 h+3 Z X b c h+1 h c X h-1 h+1 h V U h+2 Z a b h h+1 h Same double rotation when an insert in the left-right grandchild caused imbalance due to c becoming taller But here the “height” at the top decreases, so more rebalancing farther up the tree might still be necessary

5 No third right-deletion case needed So far we have handled these two cases: left-leftleft-right 5CSE332: Data Abstractions h a Z Y b X h+1 h h+2 h+3 a h-1 h h V U h+1 h+2 h+3 Z X b c h+1 h But what if the two left grandchildren X & Y are now both too tall (h+1)? Then it turns out left-left solution still works The children of the “new top node” will have heights differing by 1 instead of 0, but that’s fine

6 Mirror Image cases For each of the cases described above, we can also have the mirror image: deletion in the left side of the tree, and needing to compare the heights of the right grandchildren

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