You are given n balls arranged in a row. Each ball i has a value v;. Give a polynomial time algorithm to pick a maxi- mum value subset S of the balls so that no three consecutive balls are in S. For example, say the ball values are 2 2 3 2 2 then, the maximum value subset has the first, second, fourth and the fifth ball, and their total value is 2+ 2+2+2 = 8. For this problem, you also need to write a proof of correctness of the recurrence.

You are given n balls arranged in a row. Each ball i has a value v;. Give a polynomial time algorithm to pick a maxi- mum value subset S of the balls so that no three consecutive balls are in S. For example, say the ball values are 2 2 3 2 2 then, the maximum value subset has the first, second, fourth and the fifth ball, and their total value is 2+ 2+2+2 = 8. For this problem, you also need to write a proof of correctness of the recurrence.

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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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.

Question

4 No three in a row
You are given n balls arranged in a row. Each ball i has a
value v;. Give a polynomial time algorithm to pick a maxi-
mum value subset S of the balls so that no three consecutive
balls are in S.
For example, say the ball values are
2 2 3 2 2
then, the maximum value subset has the first, second, fourth
and the fifth ball, and their total value is 2+2+ 2+2 = 8.
For this problem, you also need to write a proof
of correctness of the recurrence.

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