Red-Black Tree Deletion is more complicated than insertion. The deletion may cause a violation of Red-Black properties. Here are the cases that we need to consider during deletion:

1. **Case 1: Node to be deleted is a leaf node.**
If the node to be deleted is a leaf node, then it can be directly removed from the tree.

2. **Case 2: Node to be deleted has one child.**
If the node to be deleted has one child, then the child node can replace the node to be deleted.

3. **Case 3: Node to be deleted has two children.**
If the node to be deleted has two children, then the in-order predecessor or the in-order successor of the node can replace the node to be deleted.

After deletion, the Red-Black Tree properties may be violated. We need to fix the tree by performing a series of rotations and color changes. The cases for fixing the tree are:

1. **Case 1: The sibling is red.**
In this case, we perform a rotation to change the sibling to black and the parent to red.

2. **Case 2: The sibling is black and both of sibling’s children are black.**
In this case, we change the sibling to red and move up to handle the parent.

3. **Case 3: The sibling is black, sibling’s left child is red, sibling’s right child is black.**
In this case, we perform a rotation to move the red child to right.

4. **Case 4: The sibling is black, sibling’s right child is red.**
In this case, we perform a rotation to move the red child up, change the sibling to the parent’s color, the parent to black, the sibling’s red child to black.

These are the cases that we need to consider during the deletion in a Red-Black Tree.

Question

Red-Black Tree Deletion is more complicated than insertion. The deletion may cause a violation of Red-Black properties. Here are the cases that we need to consider during deletion:

1. **Case 1: Node to be deleted is a leaf node.**
   If the node to be deleted is a leaf node, then it can be directly removed from the tree.

2. **Case 2: Node to be deleted has one child.**
   If the node to be deleted has one child, then the child node can replace the node to be deleted.

3. **Case 3: Node to be deleted has two children.**
   If the node to be deleted has two children, then the in-order predecessor or the in-order successor of the node can replace the node to be deleted.

After deletion, the Red-Black Tree properties may be violated. We need to fix the tree by performing a series of rotations and color changes. The cases for fixing the tree are:

1. **Case 1: The sibling is red.**
   In this case, we perform a rotation to change the sibling to black and the parent to red.

2. **Case 2: The sibling is black and both of sibling’s children are black.**
   In this case, we change the sibling to red and move up to handle the parent.

3. **Case 3: The sibling is black, sibling’s left child is red, sibling’s right child is black.**
   In this case, we perform a rotation to move the red child to right.

4. **Case 4: The sibling is black, sibling’s right child is red.**
   In this case, we perform a rotation to move the red child up, change the sibling to the parent’s color, the parent to black, the sibling’s red child to black.

These are the cases that we need to consider during the deletion in a Red-Black Tree.

Knowee AI · Accepted Answer