Practice Question-1 (Chaining)
Duration: 3 min
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This lecture segment addresses a GATE 2014 Computer Science problem concerning hash tables and collision resolution. The instructor presents a scenario involving a hash table with 9 slots, indexed from 0 to 8. The core task requires applying the hash function h(k) = k mod 9 to a specific sequence of keys: 5, 28, 19, 15, 20, 33, 12, 17, and 10. The problem specifies that collisions are resolved using the chaining method. Students must determine the maximum, minimum, and average chain lengths resulting from these insertions.
Chapters
0:00 – 2:00 00:00-02:00
The instructor introduces the problem statement displayed on screen, defining a hash table with 9 slots and the modulo 9 hash function. He lists the nine keys to be inserted in order: 5, 28, 19, 15, 20, 33, 12, 17, and 10. The visual setup establishes the initial state of the table before any insertions occur, highlighting that collisions will be handled via chaining. The instructor begins demonstrating the sequential insertion process, starting with key 5 mapping to slot 5 and subsequent keys like 28 and 19 colliding at index 1, visually constructing the linked lists within the table structure.
2:00 – 2:48 02:00-02:48
The instructor completes the insertion of all keys, showing the final configuration where slot 6 contains a chain of length 2 (keys 15 and 33) and slot 1 contains a chain of length 2 (keys 28 and 19). He calculates the specific chain lengths for all slots: slot 0 is empty (length 0), slot 1 has length 2, slot 2 has length 1, slot 3 has length 1, slot 4 is empty (length 0), slot 5 has length 1, slot 6 has length 2, slot 7 is empty (length 0), and slot 8 has length 1. The instructor then computes the maximum chain length as 2, minimum as 0, and average by summing lengths to 9 and dividing by 9 slots, yielding an average of 1. He evaluates the multiple-choice options (A) through (D) to select the correct answer based on these calculated values.
The lecture demonstrates a practical application of hash table theory using chaining for collision resolution. The key takeaway is the systematic calculation of chain lengths after inserting a fixed set of keys using a modulo hash function. The problem requires careful tracking of each key's index to identify collisions and build the correct linked lists. By summing the lengths of all chains (which equals the total number of keys, 9) and dividing by the table size (9), the average chain length is derived as 1. The maximum and minimum values are determined by inspecting the populated slots versus empty ones, specifically identifying that slot 0 and others remain empty while specific indices accumulate multiple keys.