The off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n} under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT- MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S be represented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) of INSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtained from insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m, extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n) for i = 1 to n determine j such that i ∈ Kj if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, destoying Kj return extracted Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where each number stands for its insertion. Draw a table showing the building process of extracted[1..6]. You have to show all Kj from Ij in the table and how they change (e.g. some have more elements due to merge and some disappeared due to merge).
The off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n} under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT- MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S be represented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) of INSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtained from insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m, extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n) for i = 1 to n determine j such that i ∈ Kj if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, destoying Kj return extracted Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where each number stands for its insertion. Draw a table showing the building process of extracted[1..6]. You have to show all Kj from Ij in the table and how they change (e.g. some have more elements due to merge and some disappeared due to merge).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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The off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n}
under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-
MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S be
represented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) of
INSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtained
from insertions in Ij. Thealgorithm to build an array extracted[1..m], where for i = 1, 2, ..., m,
extracted[i] is the key returned by the ith EXTRACT-MIN call is given below:
under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-
MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S be
represented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) of
INSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtained
from insertions in Ij. The
extracted[i] is the key returned by the ith EXTRACT-MIN call is given below:
Off-Line-Minimum(m, n)
for i = 1 to n
determine j such that i ∈ Kj
if j ≠ m + 1
extracted[j] = i
let L be the smallest value greater than j for which KL exists
KL = KL U Kj, destoying Kj
return extracted
KL = KL U Kj, destoying Kj
return extracted
Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where each
number stands for its insertion. Draw a table showing the building process of extracted[1..6].
number stands for its insertion. Draw a table showing the building process of extracted[1..6].
You have to show all Kj from Ij in the table and how they change (e.g. some have more elements due to merge
and some disappeared due to merge).
and some disappeared due to merge).
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