1. Asymptotics. Given an array A of n integers, you'd like to output a two-dimensional n x n array B in which B[i, j] = max {A[i], A[i + 1],..., A[j]} for each i < j. For i j the value of B[i, j] can be left as is. for i = 1,2, η for j = i + 1, n " Compute the maximum of the entries A[i], A[i + 1], , A[j]. Store the maximum value in B[i, j]. (a) Find a function of such that the running time of the algorithm is O(f(n)), and clearly explain why. (b) For the same function f argue that the running time of the algorithm is also (f(n)). (This establishes an asymptotically tight bound (f(n)).) (c) Design and analyze a faster algorithm for this problem. You should give an algorithm with running O(g(n)), where lim→∞ g(n)/f(n) = 0.
1. Asymptotics. Given an array A of n integers, you'd like to output a two-dimensional n x n array B in which B[i, j] = max {A[i], A[i + 1],..., A[j]} for each i < j. For i j the value of B[i, j] can be left as is. for i = 1,2, η for j = i + 1, n " Compute the maximum of the entries A[i], A[i + 1], , A[j]. Store the maximum value in B[i, j]. (a) Find a function of such that the running time of the algorithm is O(f(n)), and clearly explain why. (b) For the same function f argue that the running time of the algorithm is also (f(n)). (This establishes an asymptotically tight bound (f(n)).) (c) Design and analyze a faster algorithm for this problem. You should give an algorithm with running O(g(n)), where lim→∞ g(n)/f(n) = 0.
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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![1. Asymptotics. Given an array A of n integers, you'd like to output a two-dimensional n x n
array B in which B[i, j] = max {A[i], A[i + 1],..., A[j]} for each i < j.
For i j the value of B[i, j] can be left as is.
for i = 1,2, η
for j = i + 1, n
"
Compute the maximum of the entries A[i], A[i + 1], , A[j].
Store the maximum value in B[i, j].
(a) Find a function of such that the running time of the algorithm is O(f(n)), and clearly
explain why.
(b) For the same function f argue that the running time of the algorithm is also (f(n)).
(This establishes an asymptotically tight bound (f(n)).)
(c) Design and analyze a faster algorithm for this problem. You should give an algorithm
with running O(g(n)), where lim→∞ g(n)/f(n) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30aa2789-1fd1-4400-ac44-9e05193a01ce%2Fb9c848e2-fdaf-4b6b-8b1f-257f61717903%2Fg90ks6v_processed.png&w=3840&q=75)
Transcribed Image Text:1. Asymptotics. Given an array A of n integers, you'd like to output a two-dimensional n x n
array B in which B[i, j] = max {A[i], A[i + 1],..., A[j]} for each i < j.
For i j the value of B[i, j] can be left as is.
for i = 1,2, η
for j = i + 1, n
"
Compute the maximum of the entries A[i], A[i + 1], , A[j].
Store the maximum value in B[i, j].
(a) Find a function of such that the running time of the algorithm is O(f(n)), and clearly
explain why.
(b) For the same function f argue that the running time of the algorithm is also (f(n)).
(This establishes an asymptotically tight bound (f(n)).)
(c) Design and analyze a faster algorithm for this problem. You should give an algorithm
with running O(g(n)), where lim→∞ g(n)/f(n) = 0.
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