INT-102_Lecture_01

Part I

• Some Well-known Computational Problems

  • Sorting
  • Searching
  • Graph and Combinatorial Problems
    • Shortest paths in a graph---【最短路】
    • Minimum spanning tree
    • Traveling salesman problem
    • Knapsack problem
    • ...
  • Problem in Number Theory
    • Primality testing
    • ...

• What is an algorithm?

  • A sequence of precise and concise 【精确且简洁】instructions that guide you (or a computer) to solve a class of specific problem
  • 

• Learning Aims

  • To give an overview of the study of algorithms in terms of their efficiency
  • To introduce the standard algorithmic design patterns 【设计模式】employed in the development of efficient algorithmic solutions
  • To describe the analysis of algorithms in terms of the use of formal models of Time and Space
  • To give a brief introduction to the subject of computational complexity theory 【计算复杂度】and its use in classifying computational problems

Part II: How to represent algorithms

• Pseudo Code

  • Trace Table & Statement

    • 

    • p = 1
      for i = 1 to n do
          p = p * x
      output p
      

  •  Statement
    • Assignment statement【赋值语句】 

      • Variable = Expression

      • e.g., assign the expression 3 * 4 to the variable result :

        • result = 3 * 4

    • Compound statements 【复合语句】

      • begin
            statement1
            statement2
        end

    • Conditional statement 【条件语句】

      • if condition then
            statement

      • if condition then
            statement1
        else
            statement2

      • Example:

        • if a < 0 then    
              a = -a
              abs = a
          output abs

        • if a > 0 then
              abs = a
          else
              abs = -a 
          output abs

    • Iterative statement 【迭代语句】
      • For Loop 【For 循环】

        • for var = start_value to end_value do
              statement

        • Example: Computing sum of the first n numbers

          • input n
            sum = 0
            for i = 1 to n do
            begin
                sum = sum + i
            end
            output sum

          • 
          • 
          • The loop is executed for n times
      • While Loop 【While循环】

        • while condition do
              statement

        • Condition__CONTINUE the loop
        • Example_01: Computing sum of the first n numbers

          • input n
            sum = 0
            i = 1 
            while i <= n do
            begin
                sum = sum + i
                i = i + 1
            end
            output sum

        • Example_02: Computing sum of all (keyboard) input numbers

          • sum = 0
            while (user wants to continue) do
            begin
                ask for a number
                sum = sum + number
            end
            output sum

          • 
          • This loop is executed for an undetermined number of times
      • Repeat-until Statement 【Repeat循环】

        • repeat
              statement
          until condition

        • Condition__STOP the loop
        • Example: Computing sum of all (keyboard) input numbers

          • sum = 0
            repeat
                ask for a number
                sum = sum + number
            until (user wants to stop)
            output sum

          • 

• Computing the n-th power

  • Input
    • A number x & A non-negative integer n
  • Output
    • The n-th power of x
  • Algorithm
    • Set a temporary variable p to 1
    • Repeat the multiplication p = p * x for n times
    • Output the result p

• Algorithm vs Program

  • Algorithms
    • Free from grammatical rules
    • Content is more important than form
    • Acceptable as long as it tells people how to perform a task
  • Programs
    • Must follow some syntax rules
    • Form is important
    • Even if the idea is correct, it is still not acceptable if there is a syntax error
  • More Generally: Program = Data Structure + Algorithm

Part III: Pseudo Code_Exercise

• Ex_01:List all factors of a given positive integer x
  •  For Loop

    • for i = 1 to x do
      begin
          if (x%i == 0) then
              output i
      end

  • While Loop

    • i = 1
      while i <= x do
      begin
          if x%i == 0 then
              output i
          i = i+1
      end
      
      

  • Repeat Loop

    • i = 1
      repeat
          if x%i == 0 then
              output i
          i = i+1
      until i > x

• Ex_02:Find the product of all integers in the interval [x, y], assuming that x and y are both integers
  • For Loop

    • product = 1
      for i = x to y do
      begin
          product = product * i
      end
      output product
      

  • While Loop

    • product = 1
      i = x
      while i <= y do
      begin
          product = product * i
          i = i+1
      end
      output product
      

  • Repeat Loop

    • product = 1
      if x <= y then begin
          i = x
          repeat
              product = product * i
              i = i+1
          until i > y
          output product
      end

Part IV: Summary

• While
  • 判断==>执行
  • 满足条件，执行，继续循环
• Repeat
  • 执行==>判断
  • 满足条件，不执行，结束循环
• Loop
  • 执行==>判断
  • 满足条件，不执行，结束循环
• 当条件为False时，Repeat循环也能执行一次，类似于 java中的 Do While 循环； 而 While、Loop 循环无法执行

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来源： https://blog.csdn.net/Astronaut_WHY/article/details/123221502