Which of the following most accurately describes the "load factor"?

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Question restatement: Which of the following most accurately describes the 'load factor'?

Option 1: 'The load factor is defined as the total number of elements n added, and hence the same as the number of keys.' This is incorrect in general. The load factor is typically defined as the number of elements divided by the table capacity (n / m). It does not necessarily equal the number of keys, unless by coincidence n equals m, which is not the standard definition.

Option 2: 'When using quadratic probing, the load factor describes the total number of values defined for the hash function, but not necessarily related to the number of keys.' This is misleading. The load factor still measures how full the table is (n/m) regardless of the collision resolution strategy (linear, quadratic probing, or double hashing). It does relate to the number of keys (n) and the table length (m). The phrasing here obscures the core meaning and is therefore incorrect.

Option 3: 'For a hash table with open addressing, the load factor is the size of the array.' This statement confuses two concepts. The load factor is not the table size itself; it is the ratio n/m, where n is the number of keys stored and m is the array size. The actual size of the array is just m, not the load factor value.

Option 4: 'For a hash table with chaining, it is the average chain length (avg length of the linked lists)' This option correctly describes the load factor in the chaining scheme. In chaining, keys are stored in linked lists at each bucket, so the load factor corresponds to the average number of elements per bucket, i.e., the average chain length. This aligns with the standard definition where load factor α = n/m, which in chaining translates to average list length.

Additional notes:
- Across probing schemes, the fundamental idea of load factor as n/m remains central, but the practical performance implications differ as the load factor grows.
- Misconceptions commonly arise from equating load factor with the total capacity or with the number of keys alone; remember it is a ratio reflecting how full the table is relative to its capacity.
- The only option that faithfully matches the conventional definition for chaining is the one describing average chain length, since that directly corresponds to the expected number of elements per bucket in a chained hash table.

DATA STRUCTURES (CS_261_001_S2025) Quiz 4

Which of the following most accurately describes the "load factor"?

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DATA STRUCTURES (CS_261_001_S2025) Quiz 4

Which of the following most accurately describes the "load factor"?

View Explanation

Log in for full answers

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

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?​ ​

HTables_3 Double hashing is a form of open addressing.

HTables_8 During open addressing, if the number of probes exceeds 1, expected run time complexity of the hash table becomes O(____). (number of probes = k, size of table =n)

More Practical Tools for Students Powered by AI Study Helper

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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.

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?