Solve by greedy algorithm 3.Consider the activity selection problem as discussed in class where we are given nintervals (1,91), ..., (En, Yn) and we would like to select a maximum number of pairwise disjointintervals. Consider the following greedy algorithm for this problem:Algorithm 1 Activity Selection((x₁, y₁),..., (En, Yn))A = {1,...,n}S + Øwhile A # 0 doPick i € A that minimizes |{j € A | (xi, Yi) (xj, Yj) #0}| breaking ties arbitrarily ▷ i-thinterval has smallest number of intersectionsS + SU {i}A+ A- {i}A+ A-{je A | (xi, yi) (xj, Yj) # 0} ▷ Removes i and all its intersecting intervals from Aend whilereturn(S)Prove or disprove that this greedy algorithm always outputs the optimal answer. To disproveyou would need to provide a counter-example. To prove you need to prove that for all possibleinputs it provides the optimal answer.

Given: A Greedy Algorithm to find maximum number of pairwise disjoint intervals. To Find: To…

3. Consider the activity selection problem as discussed in class where we are given n intervals (21, 31),..., (n. Yn) and we would like to select a maximum number of pairwise disjoint intervals. Consider the following greedy algorithm for this problem: Algorithm 1 Activity Selection((x₁, y₁),..., (En, Yn)) A = {1,...,n} S-0 while A # ) do Pick i € A that minimizes |{j € A | (xi, yi) (xj, yj) #0}| breaking ties arbitrarily interval has smallest number of intersections S SU{i} ▷ i-th A+ A- {i} A+ A-{je A | (xi, yi) (x, yj) #0} > Removes i and all its intersecting intervals from A end while return(S) Prove or disprove that this greedy algorithm always outputs the optimal answer. To disprove you would need to provide a counter-example. To prove you need to prove that for all possible inputs it provides the optimal answer.

3. Consider the activity selection problem as discussed in class where we are given n intervals (21, 31),..., (n. Yn) and we would like to select a maximum number of pairwise disjoint intervals. Consider the following greedy algorithm for this problem: Algorithm 1 Activity Selection((x₁, y₁),..., (En, Yn)) A = {1,...,n} S-0 while A # ) do Pick i € A that minimizes |{j € A | (xi, yi) (xj, yj) #0}| breaking ties arbitrarily interval has smallest number of intersections S SU{i} ▷ i-th A+ A- {i} A+ A-{je A | (xi, yi) (x, yj) #0} > Removes i and all its intersecting intervals from A end while return(S) Prove or disprove that this greedy algorithm always outputs the optimal answer. To disprove you would need to provide a counter-example. To prove you need to prove that for all possible inputs it provides the optimal answer.

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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