AL

• Induction


  The inductive step is the part where to generalize your basis and take it a step further
• Data type


  Refers to the kinds of data that a variable may hold in a given programming language
• Theorem


  A mathematical statement which is proven to be true
• O(log n)


  Logarithmic if the largest term in the formula is a constant times a logarithm of n, then the algorithm is "Big- O on the logarithm of n"
• Lemma


  A statement that has been proven true in order to further help in proving another statement
• Array


  Allocated sequentially in contiguous memory locations
• Proof


  A logical argument that tries to show that a statement is true
• Array information


  • One dimensional
  • Two dimensional
• Implies


  One method for proving the existence of such an object is to prove that P ⇒ Q (P implies Q)
• Informal


  Pseudo-Language is a combination of the informal English statements and the constructs of a programming language
• Inductive


  The inductive step is the part where to generalize your basis and take it a step further
• Data Structure


  A way to organize data
• Odd number


  Can be characterized by n = 2k + 1
• Debugging should not be the most-time consuming part of programming
• Contradiction


  A common form of proving a theorem is assuming the theorem is false, and then show that the assumption is false itself
• Pseudocode


  The textual representation of an algorithm's flowchart. It is an English-like representation of the code required for an algorithm
• Outputs


  Data items resulting from the execution of an algorithm
• How to design/create programs


  1. Input and Output Specification

  2. Algorithm and Data Structure Design

  3. Translation of Algorithm to a certain Programming Language

  4. Program Testing and Debugging
• Algorithm


  A finite sequence of instructions that can be performed in a finite length of time in order to solve a problem(s)
• Pseudo-Language


  A combination of the informal English statements and the constructs of a programming language
• Data type refers to the kinds of data that a variable may hold in a given programming language
• Data Structure is simply a way to organize data
• Designing Data Structure and Algorithm is expressed in pseudocode or pseudo-language
• Once we have designed a data structure and an algorithm, we have now a program expressed in pseudocode or pseudo-language. And yet, we cannot run this program on a computer unless we translate that pseudo code into a programming language of your choice
• Criteria for Algorithms


  • Input
  • Output
  • Definiteness
  • Finiteness
  • Effectiveness
• A computer cannot perform an instruction if it has insufficient information or if the result of the execution could be inherently undefined
• Big-O Notation


  • Quadratic
  • Linear
  • Logarithmic
• Rules for Big-O Notation


  1. Rule 1 - for loops

  2. Rule 2 - Nested for loops

  3. Rule 3 - Consecutive statements

  4. Rule 4 - if else
• Pseudocode is the textual representation of an algorithm's flowchart. It is an English-like representation of the code required for an algorithm
• Data Types and Values in Algorithmic Language


  • Real Number
  • Character String or String Constant
• One-dimensional Array


  Start + k (i-1)
• Two-dimensional Array


  • Row-major: Start + k ( [ ( i - 1) n] + [ j - 1] )
  • Column-major: Start + k ( [ ( j - 1) m] + [ i - 1] )