计算机科学导论Chap 05

Posttest loop: repeat (loop body) until(condition)
Pseudo Code: indentation
if (not raining)
then (if (temperature = hot) then (go swimming) else (play golf) ) else (watch television)
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Program 2 for XOR
Input: binary digits a,b Output: a XOR b 1. If a==b Return 0 2. Else Return 1 3. Halt
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, U. London
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Getting a Foot in the Door
Try working the problem backwards Solve an easier related problem Relax some of the problem constraints Solve pieces of the problem first (bottom up methodology) Stepwise refinement: Divide the problem into smaller problems (top-down methodology)
22 November 2011 Brookshear Section 5.1 6
Program 1 for XOR
Input: binary digits a,b Output: a XOR b If a==0 and b==0 Return 0 If a==0 and b==1 Return 1 If a==1 and b==0 Return 1 If a==1 and b==1 Return 0 Halt
Very useful informal representation of algorithms. Preferable to using program code when designing an algorithm. Basic structures (assignment, loops, arrays …) are similar across many programming languages.
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Figure 5.2 Folding a bird from a square piece of paper
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Figure 5.3 Origami primitives
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Pseudo Code for Algorithm Representation
if (not raining) then (if (temperature=hot) then (go
swimming) else (play golf)) else (watch television)
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Procedure
Definition: set of instructions which can be used as a single unit in different contexts. A procedure call contains the name of the procedure and any data supplied to the procedure A result calculated by the procedure can be obtained using a return statement.
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Pseudo Code: assignment
General form name <- expression Examples funds <- current + savings x <- 10
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Pseudo Code: conditional selection
halt.
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Algorithm Representation
Requires well-defined primitives A collection of primitives constitutes a programming language.
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Baidu Nhomakorabea
Terminology
Programming language: system for representing algorithms in a human readable form suitable for conversion to machine code. Program: representation of an algorithm in a programming language. Pseudo code: system for the informal representation of algorithms. Hardware: device to carry out the steps or instructions in a program.
Key or reserved words in bold
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Iterative Structures
Pretest loop: while (condition) do (loop body)
Example
while (tickets remain) do (sell a ticket)
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Solution: Exercise
procedure descending(A) j=0; flag=0; while flag==0 && j<Length[A]-1 do if A[j]<A[j+1] then flag=1; print(j); j=j+1; end while if flag==0 then print(-1); end procedure
An Introduction to Computer Science
计算机科学引论
XIANG， Hui 向辉 Shandong University
Chapter 5: Algorithms
5.1 The Concept of an Algorithm 5.2 Algorithm Representation 5.3 Algorithm Discovery 5.4 Iterative Structures 5.5 Recursive Structures 5.6 Efficiency and Correctness
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Definition of Algorithm
An algorithm is an ordered set of unambiguous, executable steps that defines a terminating process.
The steps are often called instructions. Termination is by a special instruction:
General form if (condition) then (activity) else (activity) Example if (year is leap year) then d <- total divided by 366 else d <- total divided by 365
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Program 3 for XOR
Input: binary digits a,b Output: a XOR b 1. Convert a to the integer ia 2. Convert b to the integer ib 3. ic=remainder on dividing ia+ib by 2 4. Return ic 5. Halt
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Pseudo Code: procedures
General type procedure name
Examples
procedure helloWorld //no parameters procedure sort (List) // parameter List
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Polya’s Problem Solving Steps
1. Understand the problem. 2. Devise a plan for solving the problem. 3. Carry out the plan. 4. Evaluate the solution for accuracy and its potential as a tool for solving other problems.
22 November 2011 Brookshear sections 5.1 and 5.2 5
Representation of an Algorithm
The same algorithm can be represented in many different ways:
F = (9/5)C+32 F <- (9*C)/5+32 To obtain F multiply C by (9/5) and then add 32. Lookup table for Fahrenheit and Centigrade
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Example of a Procedure
Definition of a procedure procedure temp(c) f=(9/5)*c+32; return f; endProcedure
Procedure call
f1=temp(34)
25 Brookshear, Section 5.3 25
Example: Evaluation of a Boolean expression
Suppose that A, B, C are Boolean variables such that A=0, B=1, C=0. Evaluate the Boolean expression (A AND B AND C) OR (A AND NOT(B))
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Bottom Up Strategy
Solve many small parts of the problem and gradually accumulate the information needed to solve the entire problem. Examples: evaluation of Boolean expressions, searching an unordered list.
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Figure 5.4 The procedure Greetings in pseudocode
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Exercise
Write an algorithm in pseudo code to carry out the following task: input: a 1-dimensional array A of integers output: the integer -1 if A[i]≥ A[i+1] for 0≤i≤Length[A]-2, otherwise the least integer j such that A[j]<A[j+1].