C.2. Sum of Constants
Our first formula is for a sum of n copies of a constant c.
This is fairly obvious, but for completeness we present Figure C-1.
Figure C-1. If each small rectangle has width c and height 1, the total area of the large rectangle is cn.
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C 3 Sum of First n Integers |
Part I: Object-Oriented Programming
Encapsulation
Polymorphism
Inheritance
- Inheritance
- Extending a Class
- The Object Class
- Packages and Access Levels
- Summary
- Vocabulary
- Problems
- Projects
Part II: Linear Structures
Stacks and Queues
- Stacks and Queues
- The Stack Interface
- The Call Stack
- Exceptions
- The Queue Interface
- Summary
- Vocabulary
- Problems
- Projects
Array-Based Structures
- Array-Based Structures
- Shrinking and Stretching Arrays
- Implementing Stacks and Queues
- The List Interface
- Iterators
- The Java Collections Framework: A First Look
- Summary
- Vocabulary
- Problems
- Projects
Linked Structures
- Linked Structures
- List Nodes
- Stacks and Queues
- The LinkedList Class
- The Java Collections Framework Revisited
- Summary
- Vocabulary
- Problems
- Projects
Part III: Algorithms
Analysis of Algorithms
- Analysis of Algorithms
- Timing
- Asymptotic Notation
- Counting Steps
- Best, Worst, and Average Case
- Amortized Analysis
- Summary
- Vocabulary
- Problems
- Projects
Searching and Sorting
- Searching and Sorting
- Linear Search
- Binary Search
- Insertion Sort
- The Comparable Interface
- Sorting Linked Lists
- Summary
- Vocabulary
- Problems
- Projects
Recursion
- Recursion
- Thinking Recursively
- Analyzing Recursive Algorithms
- Merge Sort
- Quicksort
- Avoiding Recursion
- Summary
- Vocabulary
- Problems
- Projects
Part IV: Trees and Sets
Trees
Sets
- Sets
- The Set Interface
- Ordered Lists
- Binary Search Trees
- Hash Tables
- The Java Collections Framework Again
- Summary
- Vocabulary
- Problems
- Projects
Part V: Advanced Topics
Advanced Linear Structures
- Advanced Linear Structures
- Bit Vectors
- Sparse Arrays
- Contiguous Representation of Multidimensional Arrays
- Advanced Searching and Sorting
- Summary
- Vocabulary
- Problems
- Projects
Strings
Advanced Trees
- Advanced Trees
- Heaps
- Disjoint Set Clusters
- Digital Search Trees
- Red-Black Trees
- Summary
- Vocabulary
- Problems
- Projects
Graphs
- Graphs
- Terminology
- Representation
- Graph Traversal
- Topological Sorting
- Shortest Paths
- Minimum Spanning Trees
- Summary
- Vocabulary
- Problems
- Projects
Memory Management
Out to the Disk
- Out to the Disk
- Interacting with Files
- Compression
- External Sorting
- B-Trees
- Summary
- Vocabulary
- Problems
- Projects
Part VI: Appendices
A. Review of Java
- A. Review of Java
- A.1. The First Program
- A.2. Variables and Types
- A.3. Loops
- A.4. Interacting with the User
- A.5. Branching
- A.6. Methods and Breaking Out
- A.7. Constants
- A.8. Operators
- A.9. Debugging
- A.10. Coding Conventions
B. Unified Modeling Language
C. Summation Formulae
- C. Summation Formulae
- C.1. Sum Notation
- C.2. Sum of Constants
- C.3. Sum of First n Integers
- C.4. Sums of Halves and Doubles
- C.5. Upper Limit on Sum of a Function
- C.6. Constant Factors
D. Further Reading
Index
EAN: 2147483647
Pages: 216
