What is the best case time complexity of deleting a key from a linear probe table?

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Question: What is the best case time complexity of deleting a key from a linear probe table?

Option a: O(1)
- In the best case, the key to delete is located in the first probe position without any collisions. If the slot is found immediately, the delete operation can be performed in constant time. This mirrors the optimal scenario for open addressing where the lookup and delete path is a single step.

Option b: O(N) where N is the number of keys in the hash table
- This would imply that deleting a key requires scanning all keys in the table, which is not necessary in linear probing when the target key is present and the probe path is short. A worst-case linear scan could occur if many consecutive collisions happen, but the best case does not require scanning all keys.

Option c: O(M) where M is the capacity of the table
- O(M) would mean the operation depends on the total array size, including empty slots. In typical linear probing, the delete operation is guided by the probe sequence used during insertion and lookup, not by the full capacity. The best case avoids traversing the entire table.

Option d: O(hash)
- The notation O(hash) is unconventional in this context. Time complexity is usually expressed in terms of N, M, or other problem parameters. Using a symbol like hash to denote a cost is ambiguous and not standard, making this option misleading for assessing best-case performance.

Summary: The best-case scenario occurs when the target key is found immediately at the initial probe position, yielding constant time O(1). The other options describe scenarios where more work is required, which do not apply to the best case. Regardless of the wording, the optimal path in linear probing aims for a single-step deletion when possible.

What is the best case time complexity of deleting a key from a linear probe table?

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What is the best case time complexity of deleting a key from a linear probe table?

View Explanation

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Similar Questions

Consider an implementation of a hash table with linear probing where the hash function runs in constant time and the cost of comparison is also constant. What is the best-case time complexity of the __getitem__ method? Consider n is the number of items in the hash table.

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Question at position 2 About how many steps would be needed when searching for a particular key in a hash map with 1000 nodes?1000150010

HT_Rev_6 A key 48 is to be inserted into a hash table using the hash function h(k)=k mod 10, open addressing, and linear probing for collision handling. Given the current state of the hash table below, where will key 48 be stored?​ ​

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Consider an implementation of a hash table with linear probing where the hash function runs in constant time and the cost of comparison is also constant. What is the best-case time complexity of the getitem method? Consider n is the number of items in the hash table.

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