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Skip List: Insertion and Deletion Algorithms, Lecture notes of Data Structures and Algorithms
The process of inserting and deleting keys in a skip list. A skip list is a probabilistic data structure that allows fast search within an ordered sequence of elements. The algorithm starts by initializing the skip list with a header node and then inserts or deletes keys by updating the pointers of the nodes at each level. The random depth of the node to be inserted or deleted determines the number of levels that need to be adjusted.
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2020/2021
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- (^) The skip list is initialized with a header node of level 0, whose forward pointer is set to null.
- (^) The top item shows the value associated with the skip list node. The head node is special so has the value "Hd".
- (^) Starting from level 0 of the head, we look for the first node whose pointer points to the largest key that is less than or equal to key:10 that we want to insert, and save it into a temporary update array at index level.
- (^) If no such key exists because the pointer is null, then update array will contain the last node at that level.
- (^) We save this highlighted node into our updated array since it will point to our new key: 10 if their height matches.
- (^) The update array actually contains a pointer to a node but we display the value of the node it is pointing to. To continue the process, we reduce level by one or stop if there are no more levels.
- (^) All of the pointers are now updated.
- (^) Insert value 30, assuming randomLevel returns 1.
- (^) The random depth of the node to be inserted is 1, so we must adjust the depth of the header node before inserting.
- (^) Starting from level 1 of the head, we look for the first node whose pointer points to the largest key that is less than or equal to key:30 that we want to insert, and save it into a temporary update array at index level.
- (^) If no such key exists because the pointer is null, then update array will contain the last node at that level.
- (^) We compare 30 to the next record 10. If it is less, we move forward, else we save this value.
- (^) We save this highlighted node into our updated array since it will point to our new key: 30 if their height matches.
- (^) The update array actually contains a pointer to a node but we display the value of the node it is pointing to.
- (^) To continue the process, we reduce level by one or stop if there are no more levels.
- (^) All of the pointers are now updated.
- (^) Insert value 20, assuming randomLevel returns 2.
- (^) Starting from level 2 of the head, we look for the first node whose pointer points to the largest key that is less than or equal to key:20 that we want to insert, and save it into a temporary update array at index level.
- (^) If no such key exists because the pointer is null, then update array will contain the last node at that level.
- (^) We save this highlighted node into our updated array since it will point to our new key: 20 if their height matches.
- (^) The update array actually contains a pointer to a node but we display the value of the node it is pointing to.
- (^) To continue the process, we reduce level by one or stop if there are no more levels.