Given an empty hash table of size 7 that uses open addressing, the following sequence of keys is to be inserted: 15 17 8 23 3 5 Insert these keys using each of the following approaches. h(x) = x % 7; linear probing 0   1   2   3   4   5   6     2. h(x) = x % 7; quadratic probing 0   1   2   3   4   5   6     3.h(x) = x % 7; double hashing with stepSize = 5 - (x % 5); 0   1   2   3   4   5   6

Let us consider a hash table with an underlying array of length 5. It is initially empty, and we then add consecutively the integers: 44, 7, 45, 21, 8, 23, 0, 33 Draw the resulting hashtable after all additions are made. Assume that the hash function used is the remainder of dividing by 5, that is: def hash(d): return d%5 You do not need to consider resizing the underlying array.

Consider a open bucket hash table and closed bucket hash table in which the keys are student identifiers (strings of 6 digits). Assume the following number of buckets and hash function:   m = 100; hash(id) = first two digits of id #. Starting with an empty hash table, show the effect of successively adding the following student identifiers: 000014, 990021, 990019, 970036, 000015, 970012, 970023. Use following function as second hash function hash(id) = last digit of id # Show the effect of deleting 000014 from the hash table. (Java Programming DSA)

Suppose you have a hash table of size N = 256, and you are using double hashing. The keys in your hash are 4-digit integers (0000 through 9999) and your hash function is h(k) = (k²)%N The second hash function (used for probing) is h₂(k) = (sum-of-digits (k) * 8)%N What are the first 4 values in the search sequence (starting with the home position) for a record with key k-2025?

The hash function h(k)= [(m(kA mod 1)] for A = 2-³ is used to insert the keys 61, 62, 63, 64, and 65 into a hash table of size m = 1000. The order of the hash codes in the table are given by a. 625, 125, 0, 750, 875 b. 625, 750, 625, 125, 0 c. 625,125, 0, 875, 750 d. 625, 750, 875, 0, 125 e. 625, 750, 125, 875, 0

Given a sequence of 5 keys < 53, 66, 32, 41, 88 > for searching task: a) Given the hash function H(k) = (3.k) mod 7, insert the keys above according to its original order (from left to right) into a hash table of 7 slots. Indicate the cases of collision. Clearly show the steps and calculation with a table. b) In case of any collisions found above in a) part, determine the new slot for each collided case using Linear Probing to solve the collision problem. Clearly show your answer for each identified case. No step of calculation required. o (Answer with “NO collision found”, in case there is no collisions found above) c) In case of any collisions found above in a) part, determine the new slot ONLY for the first collided case using Double-Hashing (with functions below) to solve the collision problem. Clearly show the steps of your calculation. d1 = H(k) = (3.k) mod 7 di = (di−1 + ((5·k) mod 6) + 1) mod 7 , i ≥ 2 o (Answer with “NO collision found”, in case there is no collisions…

Task - 1: Write a java program to implement the following algorithms for Open Addressing techniques for Hash Table data structure. (Use a simple array of integers to store integer key values only). HASH-SEARCH(T, k) HASH-INSERT (T, k) i = 0 repeat j = h (k, i) if T[j] == NIL T[j] = k return j else i = i + 1 ● i = 0 repeat until i == m error “hash table overflow" For both algorithms, to compute the index j, write the following methods: getLinear ProbIndex (key, i) getQuadraticProbIndex ● get DoubleHash (key, i) (key, i) j = h (k, i) if T[j] == k return j i = i + 1 until T[j] == NIL or i = m return NIL Linear Probing index is computed using following hash function: h(k, i) = (h₁(k) + i) mod m h₁(k)= k mod m Quadratic probing index is computed using following hash function: h(k, i) = (h₁(k) + i²) mod m h₁(k)= k mod m Double hashing index is computed using following hash function: h(k, i) = (h₁(k) + i h₂(k)) mod m h₁(k)= k mod m h₂(k) = 1 + (k mod m - 1)

Implement a commonly used hash table in a program that handles collision using linear probing. Using (K mod 13) as the hash function, store the following elements in the table: {1, 5, 21, 26, 39, 14, 15, 16, 17, 18, 19, 20, 111, 145, 146}.

Suppose you have a hash table of size N = 64, and you are using pseudo-random probing. The keys in your hash are 4-digit integers (0000 through 9999) and your hash function is h(k) = (the sum of the digits in k). Assume that the first 4 slots of your pseudo-random probing array contain: 5, 10, 60, 30 What are the first 4 values in the probe sequence (starting with the home position) for a record with key k=1948?

Suppose you have a hash table with seven entries (indexed 0 through 6). This table uses open addressing with the hash function that maps each letter to its alphabet code (a = A = 0, etc.) modulo 7. Rehashing is accomplished using linear-probing with a jump of 1. Describe the state of the table after each of the letters D, a, d, H, a, and h are added to the table.