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How many times will the innermost loop be iterated when the algorithm segment is implemented and run? Assume n, k, j, and i are positive integers. for k := 1 ton for j := k to n for i := j to n [Statements in the body of the inner loop, none containing branching statements that lead outside the loop] next i next j next k

How many times will the innermost loop be iterated when the algorithm segment is implemented and run? Assume n, k, j, and i are positive integers. for k := 1 ton for j := k to n for i := j to n [Statements in the body of the inner loop, none containing branching statements that lead outside the loop] next i next j next k

Database System Concepts
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
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How many times will the innermost loop be iterated when the algorithm segment is implemented and run? Assume n, k, j, and i are positive integers. for k := 1 to n for j := k to n for i:= j to n [Statements in the body of the inner loop, none containing branching statements that lead outside the loop] next i next j next k As in Example 9.6.4, sketch a trace table for the algorithm segment and notice that because i goes from j to n, it is always the case that i ? v j. Similarly, it is always the case that j ? v k and that k ? v 1. Thus, the number of iterations of the innermost loop is the same as the number of integer triples (i, i, k) that are related to each other in a certain way, and this is the same as the number of strings of ? ?v crosses, where the position of the crosses indicate which ? v integers from 1 to n are included in the triple. Thus, the answer is vertical bars and
Transcribed Image Text:How many times will the innermost loop be iterated when the algorithm segment is implemented and run? Assume n, k, j, and i are positive integers. for k := 1 to n for j := k to n for i:= j to n [Statements in the body of the inner loop, none containing branching statements that lead outside the loop] next i next j next k As in Example 9.6.4, sketch a trace table for the algorithm segment and notice that because i goes from j to n, it is always the case that i ? v j. Similarly, it is always the case that j ? v k and that k ? v 1. Thus, the number of iterations of the innermost loop is the same as the number of integer triples (i, i, k) that are related to each other in a certain way, and this is the same as the number of strings of ? ?v crosses, where the position of the crosses indicate which ? v integers from 1 to n are included in the triple. Thus, the answer is vertical bars and
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