There are n different sizes of boxes, from 1 to n. There is an unlimited supply of boxes of each size t, each with a value vt . A box of size t can hold several smaller boxes of sizes a1, a2, . . . , ak as long as the sum of sizes a1 + a2 + . . . + ak is strictly less than t. Each of these boxes may be filled with yet more boxes, and so on.Design an algorithm which runs in O(n2 ) time and finds the maximum value that can be attained by taking one box, potentially with smaller boxes nested inside it.

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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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There are n different sizes of boxes, from 1 to n. There is an unlimited supply of boxes of each size t, each with a value v_t . A box of size t can hold several smaller boxes of sizes a1, a2, . . . , ak as long as the sum of sizes a₁ + a₂ + . . . + a_k is strictly less than t. Each of these boxes may be filled with yet more boxes, and so on.

Design an algorithm which runs in O(n² ) time and finds the maximum value that can be attained by taking one box, potentially with smaller boxes nested inside it.

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