To determine the probability Q k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

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Answer 1

Question

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

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Given a matrix of dimension m*n where each cell in the matrix can have values 0, 1 or 2 which has the following meaning: 0: Empty cell 1: Cells have fresh oranges 2: Cells have rotten oranges So we have to determine what is the minimum time required so that all the oranges become rotten. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1], [i,j+1] (up, down, left and right). If it is impossible to rot every orange then simply return -1. Examples: Input: arr[][C] = { {2, 1, 0, 2, 1}, {1, 0, 1, 2, 1}, {1, 0, 0, 2, 1}}; Output: All oranges cannot be rotten. Below is algorithm. 1) Create an empty Q. 2) Find all rotten oranges and enqueue them to Q. Also enqueue a delimiter to indicate beginning of next time frame. 3) While Q is not empty do following 3.a) While delimiter in Q is not reached (i) Dequeue an orange from queue, rot all adjacent oranges. While rotting the adjacents, make sure that time frame is incremented only once. And time frame is…

Problem 2: In this problem we assume that h: U → {0, 1, . . . , m − 1} is a good hashfunction, that is, every key k has the same probability 1/m to map to any place in the tableT of length m.(i) What is the probability that three pairwise distinct elements u1, u2, u3 ∈ U aremapped by the function h to the same place in the table (that is, h(u1) = h(u2) =h(u3))?(ii) We insert three elements into an empty hash table T using the hash function h. Ifcollision is solved by chaining, what is the probability that T[0] and T[1] are empty?

Given an n×n matrix M in which every entry is either a 0 or 1. Present an algorithm that determines if ∃i, 1 ≤ i ≤ n, such that M[i, j] = 0 and M[j, i] = 1, ∀j, 1 ≤ j ≤ n ∧ j 6= i, using examining an entry of M as the key operation. Your algorithm must examine at most 3n − ⌊lg n⌋ − 3 entries of M.

Answer 2

Question

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Expert Solution & Answer

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Answer 3

Question

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Expert Solution & Answer

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Answer 5

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Answer 6

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

Answer 7

Chapter 11, Problem 2P

(a)

Program Plan Intro

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

Answer 8

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

Answer 9

(b)

Program Plan Intro

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

Answer 10

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

Answer 11

(c)

Program Plan Intro

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

Answer 12

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Answer 13

(d)

Program Plan Intro

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E

To determine the probability Q k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

Solution Summary: The author explains how the probability of slot contacting maximum keys is less than or equals to n times of probability for exactly k keys present in the particular slot.

Concept explainers

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.

Want to see the full answer?

Chapter 11 Solutions

To determine the probability Q k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

Solution Summary: The author explains how the probability of slot contacting maximum keys is less than or equals to n times of probability for exactly k keys present in the particular slot.

Concept explainers

To determine the probability Qk of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

To show that the probability of slot contacting maximum keys is less then or equals to n times of probability of exactly k keys present in the particular slot.

Show that the probability of a slot having maximum k keys Qk is less than ek/kk by using Stirling approximation.

Show that the probability Pkof a slot having maximum number of k keys is less than 1/n2, where is equals to total no. of slots.

Want to see the full answer?

Chapter 11 Solutions

To determine the probability Q_k of exactly k keys hash present in to a particular slot of the hash table having n number of slots and n keys.

Show that the probability of a slot having maximum k keys Q_k is less than ek/kk by using Stirling approximation.

Show that the probability P_kof a slot having maximum number of k keys is less than 1/n², where is equals to total no. of slots.