C.1. Sum Notation

Sums can be concisely written using the upper-case Greek letter sigma. For example,

is read, "The sum, for i from 1 to 4, of 2i2." This is:

Often the upper limit of the index (written above the sigma) is some other variable involved in the analysis, such as n. For example, in Section C.3, we will see a formula for the sum of the first n positive integers:

In order to wrangle an expression into a form for which we have a formula, it is often useful to add or remove terms. For example:

Substitution of variables is another useful technique. For example, to evaluate the sum

we define n = 2m. Then:

Sum notation is sometimes used more casually. For example, to describe the total value of all of the cars on a sales lot, we might write:


Part I: Object-Oriented Programming

Encapsulation

Polymorphism

Inheritance

Part II: Linear Structures

Stacks and Queues

Array-Based Structures

Linked Structures

Part III: Algorithms

Analysis of Algorithms

Searching and Sorting

Recursion

Part IV: Trees and Sets

Trees

Sets

Part V: Advanced Topics

Advanced Linear Structures

Strings

Advanced Trees

Graphs

Memory Management

Out to the Disk

Part VI: Appendices

A. Review of Java

B. Unified Modeling Language

C. Summation Formulae

D. Further Reading

Index





Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
ISBN: 0131469142
EAN: 2147483647
Year: 2004
Pages: 216
Authors: Peter Drake
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