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Cambridge Pseudocode Handout

  • 1 Style and layout
    1.1

    Keywords and case

    Pseudocode 伪代码 is the language Cambridge writes algorithms 算法 in. It is not a real programming language — no computer runs it — but the exam marks it as if it were, so the form matters.

    Every keyword 关键字 is written in upper case: IF, REPEAT, PROCEDURE, OUTPUT.

    DECLARE Count : INTEGER
    Count ← 3
    IF Count > 0
      THEN
        OUTPUT "Ready"
    ENDIF
    
    • Write IF, never if or If.
    • A keyword can never be used as a name of your own: you may not call a variable FOR.

    Common mistakes

    • Lower-case keywords. The mark scheme expects upper case.
    • Inventing keywords. Only the words in this handout are in the syllabus.
    Vocabulary
    EnglishChinesePinyin
    pseudocode/ˈsuːdəʊkəʊd/伪代码wěi dài mǎ
    algorithms/ˈælɡərɪθəmz/算法suàn fǎ
    keyword/ˈkiːwɜːd/关键字guān jiàn zì
    1.2

    Identifiers

    An identifier 标识符 is the name you give a variable 变量, a constant 常量, a procedure 过程 or a function 函数.

    DECLARE NumberOfPlayers : INTEGER
    NumberOfPlayers ← 4
    OUTPUT NumberOfPlayers
    

    Four rules, all from the syllabus:

    • It must start with a capital letter: Count, not count.
    • It may hold only letters and digits — no spaces, no punctuation.
    • It is not case-sensitive 不区分大小写, so Count and COUNT are the same name. Pick one spelling and keep it.
    • Make it mean something. NumberOfPlayers earns the reader's time; N does not.

    Common mistakes

    • count ← 0 — a lower-case start. 0478 requires the capital.
    • Number of players — spaces are not allowed inside a name.
    Vocabulary
    EnglishChinesePinyin
    identifier/aɪˈdentɪfaɪə/标识符biāo shí fú
    variable/ˈveərɪəbl/变量biàn liàng
    constant/ˈkɒnstənt/常量cháng liàng
    procedure/prəˈsiːdʒə/过程guò chéng
    function/ˈfʌŋkʃn/函数hán shù
    case-sensitive/keɪs ˈsensɪtɪv/不区分大小写bù qū fēn dà xiǎo xiě
    1.3

    Comments and indentation

    A comment 注释 starts with // and runs to the end of the line. It is for the human reader; the algorithm ignores it.

    // Swap the values of X and Y
    DECLARE X, Y, Temp : INTEGER
    X ← 1
    Y ← 2
    Temp ← X   // temporarily store X
    X ← Y
    Y ← Temp
    OUTPUT X, " ", Y
    

    Indentation 缩进 shows which statements are inside a structure. The syllabus asks for four spaces per level, with one exception you must know:

    DECLARE X, Y : INTEGER
    X ← 7
    Y ← 3
    IF X > Y
      THEN
        OUTPUT "X is bigger"
      ELSE
        OUTPUT "Y is bigger or equal"
    ENDIF
    
    • THEN and ELSE are indented two spaces from their IF.
    • The statements under them are indented four.
    • ENDIF lines up with its own IF.

    Common mistakes

    • Putting THEN on the IF line. That is the A-Level 9618 layout — see topic 11.
    • No indentation at all. A marker has to see the structure to award the structure marks.
    Vocabulary
    EnglishChinesePinyin
    comment/ˈkɒment/注释zhù shì
    indentation/ˌɪndenˈteɪʃn/缩进suō jìn
  • 2 Variables, constants and types
    2.1

    The five data types

    0478 pseudocode has exactly five data types 数据类型. Learn the list — naming a type that is not on it loses the mark.

    Type Holds Example
    INTEGER a whole number 整数 42, -7
    REAL a number with a decimal part 小数 3.14, -0.5
    CHAR a single character 单个字符 'A'
    STRING a sequence of characters 字符串 "Hello"
    BOOLEAN TRUE or FALSE 布尔值 TRUE
    DECLARE Age : INTEGER
    DECLARE Price : REAL
    DECLARE Grade : CHAR
    DECLARE Name : STRING
    DECLARE Passed : BOOLEAN
    Age ← 17
    Price ← 2.50
    Grade ← 'A'
    Name ← "Mei"
    Passed ← TRUE
    OUTPUT Name, " is ", Age, " and passed: ", Passed
    
    • A STRING is written in double quotes, a CHAR in single quotes.
    • TRUE and FALSE are keywords, so they are upper case and carry no quotes.

    Common mistakes

    • Writing FLOAT, DOUBLE or BOOL. Those are real languages, not this syllabus.
    • 'Hello' for a string — single quotes hold one character only.
    Vocabulary
    EnglishChinesePinyin
    data types/ˈdeɪtə taɪps/数据类型shù jù lèi xíng
    whole number/həʊl ˈnʌmbə/整数zhěng shù
    decimal part/ˈdesɪml pɑːt/小数xiǎo shù
    single character/ˈsɪŋɡl ˈkærɪktə/单个字符dān gè zì fú
    sequence of characters/ˈsiːkwəns ɒv ˈkærɪktəz/字符串zì fú chuàn
    TRUE` or `FALSE布尔值bù ěr zhí
    2.2

    DECLARE

    DECLARE names a variable 变量 and fixes its type before you use it.

    DECLARE <identifier> : <data type>
    
    DECLARE Counter : INTEGER
    DECLARE TotalToPay : REAL
    Counter ← 1
    TotalToPay ← 19.99
    OUTPUT "Item ", Counter, " costs ", TotalToPay
    

    Several names of one type go on a single line, separated by commas:

    DECLARE Length, Width, Area : INTEGER
    Length ← 6
    Width ← 4
    Area ← Length * Width
    OUTPUT "Area = ", Area
    
    • Declare a variable before its first use, near the top of the algorithm.
    • A variable keeps its type for the whole algorithm — an INTEGER never holds "Mei".

    Common mistakes

    • Leaving out the colon: DECLARE Counter INTEGER.
    • Using a variable that was never declared. The exam expects the declaration.
    Vocabulary
    EnglishChinesePinyin
    variable/ˈveərɪəbl/变量biàn liàng
    2.3

    CONSTANT

    A constant 常量 is a value that is fixed for the whole algorithm — a tax rate, π, the size of a class. Naming it once means a change is made in one place.

    CONSTANT <identifier> ← <value>
    
    CONSTANT TaxRate ← 0.20
    DECLARE Price, Tax : REAL
    Price ← 50.00
    Tax ← Price * TaxRate
    OUTPUT "Tax to pay: ", Tax
    
    • In 0478 the arrow is used, exactly as for an assignment.
    • The value must be a literal 字面量 — a number, a string, TRUE — never a calculation and never another variable.
    • A constant can never be given a new value later. That is the whole point of it.

    Common mistakes

    • CONSTANT TaxRate = 0.20. The = form is the A-Level 9618 spelling — see topic 11.
    • Assigning to a constant further down the algorithm.
    Vocabulary
    EnglishChinesePinyin
    constant/ˈkɒnstənt/常量cháng liàng
    literal/ˈlɪtərəl/字面量zì miàn liàng
  • 3 Assignment, input and output
    3.1

    The assignment arrow

    The assignment 赋值 operator is , a left-pointing arrow. It means take the value on the right and put it in the box on the left.

    <identifier> ← <value>
    
    DECLARE Counter : INTEGER
    Counter ← 0
    Counter ← Counter + 1
    Counter ← Counter + 1
    OUTPUT Counter
    

    Counter ← Counter + 1 looks impossible as mathematics and is ordinary as an instruction: work out the right-hand side with the value the box holds now, then store the result back.

    • If you cannot type , write <-. Both are accepted, here and in the exam.
    • The left side must be a single identifier or one array element. Never a calculation.

    Common mistakes

    • Counter = 0. In pseudocode = is a comparison, not an assignment — and confusing the two is the single commonest syntax error in this paper.
    • Counter + 1 ← Counter. The arrow points at the thing being changed.
    Vocabulary
    EnglishChinesePinyin
    assignment/əˈsaɪnmənt/赋值fù zhí
    3.2

    INPUT and OUTPUT

    INPUT reads a value from the user into a variable. OUTPUT displays one or more values.

    DECLARE Name : STRING
    DECLARE Age : INTEGER
    INPUT Name
    INPUT Age
    OUTPUT "Hello ", Name
    OUTPUT "Next year you will be ", Age + 1
    
    • INPUT takes exactly one variable, and that variable must already be declared.
    • OUTPUT takes any number of items separated by commas; they are printed one after another with nothing between them.
    • A literal 字面量 string in an OUTPUT goes in double quotes; a variable does not.

    Prompting the user

    An INPUT on its own shows nothing on screen, so a well-written algorithm prints a prompt 提示 first:

    DECLARE Radius : REAL
    OUTPUT "Enter the radius: "
    INPUT Radius
    OUTPUT "The diameter is ", Radius * 2
    

    Common mistakes

    • INPUT "Enter a number", X — the prompt is a separate OUTPUT statement.
    • OUTPUT "Total: " + Total. 0478 joins output items with a comma; + is arithmetic and & belongs to A-Level 9618 (topic 11).
    • Forgetting the quotes: OUTPUT Hello looks for a variable called Hello.
    Vocabulary
    EnglishChinesePinyin
    literal/ˈlɪtərəl/字面量zì miàn liàng
    prompt/prɒmpt/提示tí shì
  • 4 Arithmetic and logic
    4.1

    Arithmetic operators

    Five arithmetic 算术 operators, in the order a calculator uses them.

    Operator Meaning A is 7, B is 2
    + add A + B is 9
    - subtract A - B is 5
    * multiply A * B is 14
    / divide A / B is 3.5
    ^ raise to a power A ^ B is 49
    DECLARE A, B : INTEGER
    A ← 7
    B ← 2
    OUTPUT "Sum: ", A + B
    OUTPUT "Product: ", A * B
    OUTPUT "Quotient: ", A / B
    OUTPUT "Power: ", A ^ B
    

    Brackets come first, then ^, then * and /, then + and - — the usual precedence 优先级. Use brackets whenever the reader would have to stop and think.

    DECLARE Total : REAL
    Total ← (12 + 18) / 2
    OUTPUT "Mean: ", Total
    

    Common mistakes

    • Expecting / to give a whole number. 7 / 2 is 3.5, not 3; for a whole number use DIV.
    • Writing A x B or A ÷ B. Use * and /.
    Vocabulary
    EnglishChinesePinyin
    arithmetic/əˈrɪθmətɪk/算术suàn shù
    add/æd/jiā
    subtract/sʌbˈtrækt/jiǎn
    multiply/ˌmʌltɪˈplaɪ/chéng
    divide/dɪˈvaɪd/chú
    raise to a power/reɪz tʊ ə ˈpaʊə/
    precedence/ˈpresɪdəns/优先级yōu xiān jí
    4.2

    DIV and MOD

    Integer division 整数除法 answers two different questions, and 0478 writes each of them as a function 函数, with the two values in brackets.

    • DIV(a, b) — how many whole times b goes into a, the quotient.
    • MOD(a, b) — what is left over, the remainder 余数.
    OUTPUT DIV(10, 3)
    OUTPUT MOD(10, 3)
    OUTPUT DIV(17, 5)
    OUTPUT MOD(17, 5)
    

    Both take integers, and both return an integer.

    What they are for

    MOD is the standard test for divides exactly, which makes it the way to ask whether a number is even 偶数:

    DECLARE Number : INTEGER
    Number ← 12
    IF MOD(Number, 2) = 0
      THEN
        OUTPUT Number, " is even"
      ELSE
        OUTPUT Number, " is odd"
    ENDIF
    

    DIV converts a total into whole units — seconds into minutes, pence into pounds:

    DECLARE Seconds : INTEGER
    Seconds ← 200
    OUTPUT DIV(Seconds, 60), " minutes and ", MOD(Seconds, 60), " seconds"
    

    Common mistakes

    • 10 MOD 3. That is the A-Level 9618 form; 0478 uses the function form MOD(10, 3).
    • Mixing the two up. DIV gives the whole part; MOD gives what does not fit.
    Vocabulary
    EnglishChinesePinyin
    Integer division/ˈɪntɪdʒə dɪˈvɪʒn/整数除法zhěng shù chú fǎ
    function/ˈfʌŋkʃn/函数hán shù
    quotient/ˈkwəʊʃənt/shāng
    remainder/rɪˈmeɪndə/余数yú shù
    even/ˈiːvən/偶数ǒu shù
    4.3

    Relational and logic operators

    A relational operator 关系运算符 compares two values and produces TRUE or FALSE.

    Operator Means
    = is equal to 等于
    <> is not equal to 不等于
    > is greater than 大于
    < is less than 小于
    >= is greater than or equal to 大于等于
    <= is less than or equal to 小于等于
    DECLARE Mark : INTEGER
    Mark ← 55
    OUTPUT "Pass: ", Mark >= 50
    OUTPUT "Perfect: ", Mark = 100
    OUTPUT "Not zero: ", Mark <> 0
    

    The three logic operators 逻辑运算符 join conditions:

    • AND — both sides must be TRUE.
    • OR — at least one side must be TRUE.
    • NOT — turns TRUE into FALSE and back.
    DECLARE Age : INTEGER
    DECLARE HasTicket : BOOLEAN
    Age ← 16
    HasTicket ← TRUE
    IF Age >= 15 AND HasTicket = TRUE
      THEN
        OUTPUT "Admitted"
    ENDIF
    IF NOT (Age > 18)
      THEN
        OUTPUT "Still a student rate"
    ENDIF
    

    Common mistakes

    • <> is the not equal sign here — not !=, which belongs to other languages.
    • IF Age >= 15 AND <= 18. Each side of AND needs its own complete comparison: Age >= 15 AND Age <= 18.
    • Calling these comparison operators in an answer. The syllabus term is relational.
    Vocabulary
    EnglishChinesePinyin
    relational operator/rɪˈleɪʃənl ˈɒpəreɪtə/关系运算符guān xì yùn suàn fú
    is equal to/ɪz ˈiːkwl tuː/等于děng yú
    is not equal to/ɪz nɒt ˈiːkwl tuː/不等于bù děng yú
    is greater than/ɪz ˈɡreɪtə ðən/大于dà yú
    is less than/ɪz les ðən/小于xiǎo yú
    is greater than or equal to/ɪz ˈɡreɪtə ðən ɔː ˈiːkwl tuː/大于等于dà yú děng yú
    is less than or equal to/ɪz les ðən ɔː ˈiːkwl tuː/小于等于xiǎo yú děng yú
    logic operators/ˈlɒdʒɪk ˈɒpəreɪtəz/逻辑运算符luó jí yùn suàn fú
  • 5 String operations
    5.1

    LENGTH, UCASE and LCASE

    0478 publishes four string 字符串 routines and no others. Three of them are here.

    LENGTH(<identifier>) returns how many characters 字符 a string holds — spaces included.

    OUTPUT LENGTH("Happy Days")
    OUTPUT LENGTH("")
    

    UCASE(<identifier>) returns the string in upper case 大写, LCASE(<identifier>) in lower case 小写. Neither changes the original 原值 — each hands back a new value.

    DECLARE Name : STRING
    Name ← "Happy"
    OUTPUT UCASE(Name)
    OUTPUT LCASE(Name)
    OUTPUT Name
    

    That last line still prints Happy: to keep the change you must assign it back.

    DECLARE Name : STRING
    Name ← "Happy"
    Name ← UCASE(Name)
    OUTPUT Name
    

    Comparing without worrying about case

    UCASE on both sides is the standard way to accept an answer however it was typed:

    DECLARE Answer : STRING
    Answer ← "yes"
    IF UCASE(Answer) = "YES"
      THEN
        OUTPUT "Accepted"
    ENDIF
    

    Common mistakes

    • Expecting UCASE(Name) to change Name. Assign the result back.
    • LENGTH counts characters, not words. LENGTH("Happy Days") is 10.
    Vocabulary
    EnglishChinesePinyin
    string/strɪŋ/字符串zì fú chuàn
    characters/ˈkærɪktəz/字符zì fú
    upper case/ˈʌpə keɪs/大写dà xiě
    lower case/ˈləʊə keɪs/小写xiǎo xiě
    original/əˈrɪdʒɪnl/原值yuán zhí
    5.2

    SUBSTRING

    SUBSTRING(<identifier>, <start>, <length>) pulls a piece out of a string — starting at position start, taking length characters.

    OUTPUT SUBSTRING("Happy Days", 1, 5)
    OUTPUT SUBSTRING("Happy Days", 7, 4)
    

    ⚠️ Counting starts at 1, not 0. The first character of "Happy Days" is at position 1.

    Taking one character, and the rest

    DECLARE Word : STRING
    Word ← "Computer"
    OUTPUT "First letter: ", SUBSTRING(Word, 1, 1)
    OUTPUT "Last letter: ", SUBSTRING(Word, LENGTH(Word), 1)
    OUTPUT "Without the first: ", SUBSTRING(Word, 2, LENGTH(Word) - 1)
    

    LENGTH inside SUBSTRING is what makes the last two lines work for a word of any size — hard-coding 8 would break the moment the word changed.

    Reading a string one character at a time

    DECLARE Word : STRING
    DECLARE Index : INTEGER
    Word ← "Cat"
    FOR Index ← 1 TO LENGTH(Word)
        OUTPUT SUBSTRING(Word, Index, 1)
    NEXT Index
    

    Common mistakes

    • Starting at 0. Position 1 is the first character.
    • Reading the third argument as an end position. It is a countSUBSTRING(W, 2, 3) takes three characters beginning at the second.
    • Asking for more characters than the string has.
  • 6 Selection
    6.1

    IF, THEN, ELSE, ENDIF

    Selection 选择 runs one group of statements or another, depending on a condition 条件.

    IF <condition>
      THEN
        <statements>
    ENDIF
    
    DECLARE Mark : INTEGER
    Mark ← 72
    IF Mark >= 50
      THEN
        OUTPUT "Pass"
    ENDIF
    

    Add ELSE for the other case. Exactly one of the two branches 分支 runs — never both, never neither.

    DECLARE Mark : INTEGER
    Mark ← 41
    IF Mark >= 50
      THEN
        OUTPUT "Pass"
      ELSE
        OUTPUT "Fail"
    ENDIF
    

    The layout is the one part students lose marks on, so learn it as a shape:

    • IF and its condition on one line, nothing after the condition.
    • THEN and ELSE on their own lines, indented two spaces.
    • The statements indented four.
    • ENDIF back at the column of its IF.

    Nesting 嵌套

    An IF inside an IF handles more than two outcomes. Each one needs its own ENDIF.

    DECLARE Mark : INTEGER
    Mark ← 85
    IF Mark >= 80
      THEN
        OUTPUT "Distinction"
      ELSE
        IF Mark >= 50
          THEN
            OUTPUT "Pass"
          ELSE
            OUTPUT "Fail"
        ENDIF
    ENDIF
    

    Common mistakes

    • Forgetting ENDIF. Every IF closes, and a missing one is a syntax error 语法错误 the marker will see at a glance.
    • IF Mark >= 50 THEN OUTPUT "Pass" on one line. No such form exists in either syllabus; write the three lines.
    • IF Mark = 50 THEN written as IF Mark ← 50. The arrow assigns; = compares.
    Vocabulary
    EnglishChinesePinyin
    Selection/sɪˈlekʃn/选择xuǎn zé
    condition/kənˈdɪʃn/条件tiáo jiàn
    branches/ˈbræntʃɪz/分支fēn zhī
    Nesting/ˈnestɪŋ/嵌套qiàn tào
    syntax error/ˈsɪntæks ˈerə/语法错误yǔ fǎ cuò wù
    6.2

    CASE OF

    When one variable is tested against several single values, CASE OF says it far more clearly than a stack of nested IFs.

    CASE OF <identifier>
        <value 1> : <statement>
        <value 2> : <statement>
        OTHERWISE <statement>
    ENDCASE
    
    DECLARE Choice : INTEGER
    Choice ← 2
    CASE OF Choice
        1 : OUTPUT "You chose north"
        2 : OUTPUT "You chose south"
        3 : OUTPUT "You chose east"
        4 : OUTPUT "You chose west"
        OTHERWISE OUTPUT "That is not a direction"
    ENDCASE
    
    • Each branch is a value, a colon, then what to do.
    • OTHERWISE catches everything the listed values missed. It is optional, and writing one is good practice — it is what happens when the user types something unexpected.
    • The first matching branch runs, and the rest are skipped.

    A range, and a character

    DECLARE Grade : CHAR
    Grade ← 'B'
    CASE OF Grade
        'A' : OUTPUT "Excellent"
        'B' : OUTPUT "Good"
        'C' : OUTPUT "Satisfactory"
        OTHERWISE OUTPUT "Unclassified"
    ENDCASE
    

    Common mistakes

    • Using CASE OF for a condition. It tests one variable against values; Mark >= 50 needs an IF.
    • Forgetting ENDCASE.
    • Leaving out OTHERWISE and then wondering why an unexpected value does nothing at all.
  • 7 Iteration
    7.1

    FOR, the counted loop

    Iteration 迭代 repeats statements. Use a FOR loop when you know before you start how many times — a count-controlled 计数控制 loop.

    FOR <identifier> ← <value1> TO <value2>
        <statements>
    NEXT <identifier>
    
    DECLARE Index : INTEGER
    FOR Index ← 1 TO 5
        OUTPUT "Line ", Index
    NEXT Index
    

    The counter 计数器 starts at the first value, and the loop runs once for every value up to and including the second. 1 TO 5 runs five times.

    STEP

    STEP changes the size of each jump. A negative step counts down.

    DECLARE Index : INTEGER
    FOR Index ← 2 TO 10 STEP 2
        OUTPUT Index
    NEXT Index
    FOR Index ← 3 TO 1 STEP -1
        OUTPUT "Countdown ", Index
    NEXT Index
    

    Running totals

    The commonest use: a variable outside the loop that the loop adds to.

    DECLARE Index, Total : INTEGER
    Total ← 0
    FOR Index ← 1 TO 10
        Total ← Total + Index
    NEXT Index
    OUTPUT "Sum of 1 to 10 is ", Total
    

    Total ← 0 must sit before the loop. Inside, it would reset on every pass.

    Common mistakes

    • NEXT naming the wrong counter. Nested loops must close in the reverse order they opened: the inner NEXT first.
    • Assuming 1 TO 5 runs four times. Both ends are included.
    • Changing the counter inside the loop. Let FOR own it.
    Vocabulary
    EnglishChinesePinyin
    Iteration/ˌɪtəˈreɪʃn/迭代dié dài
    count-controlled/kaʊnt kənˈtrəʊld/计数控制jì shù kòng zhì
    counter/ˈkaʊntə/计数器jì shù qì
    7.2

    WHILE, the pre-condition loop

    A WHILE loop tests before each pass, so it can run zero times. Use it when the number of repeats depends on something that happens while the loop runs.

    WHILE <condition> DO
        <statements>
    ENDWHILE
    
    DECLARE Total : INTEGER
    Total ← 1
    WHILE Total < 100 DO
        Total ← Total * 2
    ENDWHILE
    OUTPUT "First power of two past 100: ", Total
    

    Something inside the loop must eventually make the condition false, or the loop never ends — an infinite loop 无限循环.

    DECLARE Count : INTEGER
    Count ← 5
    WHILE Count > 0 DO
        OUTPUT Count
        Count ← Count - 1
    ENDWHILE
    OUTPUT "Lift off"
    

    Common mistakes

    • Forgetting to change the variable the condition tests, giving an infinite loop.
    • Leaving out DO or ENDWHILE.
    • Using WHILE where the count is known. A FOR says what you mean in one line.
    Vocabulary
    EnglishChinesePinyin
    infinite loop/ˈɪnfɪnət luːp/无限循环wú xiàn xún huán
    7.3

    REPEAT, the post-condition loop

    A REPEAT loop tests after each pass, so it always runs at least once.

    REPEAT
        <statements>
    UNTIL <condition>
    

    That "at least once" is the reason to choose it: validating 验证 input, where you must ask before you can judge the answer.

    DECLARE Number : INTEGER
    Number ← 0
    REPEAT
        Number ← Number + 25
        OUTPUT "Trying ", Number
    UNTIL Number >= 100
    OUTPUT "Reached ", Number
    

    ⚠️ UNTIL states the condition that stops the loop; WHILE states the one that keeps it going. They are opposites, and swapping them is the classic error.

    Tests Runs at least once? Condition means
    FOR a counter no (an empty range runs zero times)
    WHILE before no keep going while this is true
    REPEAT after yes stop when this becomes true

    Common mistakes

    • Writing UNTIL Number < 100 when you mean UNTIL Number >= 100.
    • Using REPEAT where the body must be able to run zero times.
    • Forgetting that UNTIL ends the structure — there is no ENDREPEAT.
    Vocabulary
    EnglishChinesePinyin
    validating/ˈvælɪdeɪtɪŋ/验证yàn zhèng
  • 8 Arrays
    8.1

    One-dimensional arrays

    An array 数组 holds many values of one type under one name. Each value sits at an index 下标.

    DECLARE <identifier> : ARRAY[<lower>:<upper>] OF <data type>
    
    DECLARE Names : ARRAY[1:3] OF STRING
    Names[1] ← "Mei"
    Names[2] ← "Sam"
    Names[3] ← "Ana"
    OUTPUT Names[2]
    
    • The bounds 边界 are written lower:upper, and both are included[1:3] has three elements 元素.
    • Cambridge arrays normally start at 1, not 0.
    • Every element has the same type, fixed by OF.

    Filling and reading with a FOR loop

    An array and a counted loop belong together: the counter is the index.

    DECLARE Scores : ARRAY[1:5] OF INTEGER
    DECLARE Index, Total : INTEGER
    FOR Index ← 1 TO 5
        Scores[Index] ← Index * 10
    NEXT Index
    Total ← 0
    FOR Index ← 1 TO 5
        Total ← Total + Scores[Index]
    NEXT Index
    OUTPUT "Total: ", Total
    OUTPUT "Mean: ", Total / 5
    

    Finding the largest

    DECLARE Scores : ARRAY[1:5] OF INTEGER
    DECLARE Index, Largest : INTEGER
    Scores[1] ← 42
    Scores[2] ← 17
    Scores[3] ← 93
    Scores[4] ← 8
    Scores[5] ← 55
    Largest ← Scores[1]
    FOR Index ← 2 TO 5
        IF Scores[Index] > Largest
          THEN
            Largest ← Scores[Index]
        ENDIF
    NEXT Index
    OUTPUT "Largest: ", Largest
    

    Start Largest at the first element, never at 0 — with negative data, 0 would win and the answer would be wrong.

    Common mistakes

    • Reading Scores[6] from an array declared [1:5]. That is out of bounds 越界.
    • Writing Scores(3). Arrays use square brackets; round brackets call a function.
    • Declaring [1:5] and then looping 0 TO 4.
    Vocabulary
    EnglishChinesePinyin
    array/əˈreɪ/数组shù zǔ
    index/ˈɪndeks/下标xià biāo
    bounds/baʊndz/边界biān jiè
    elements/ˈelɪmənts/元素yuán sù
    out of bounds/ˈaʊtəv baʊndz/越界yuè jiè
    8.2

    Two-dimensional arrays

    A 2-D array 二维数组 is a table: rows and columns, two indexes.

    DECLARE <identifier> : ARRAY[<lower1>:<upper1>, <lower2>:<upper2>] OF <data type>
    
    DECLARE Grid : ARRAY[1:2, 1:3] OF INTEGER
    Grid[1,1] ← 1
    Grid[1,2] ← 2
    Grid[1,3] ← 3
    Grid[2,1] ← 4
    Grid[2,2] ← 5
    Grid[2,3] ← 6
    OUTPUT Grid[2,3]
    

    The first index is the row, the second the column.

    Nested loops walk a table

    One loop per dimension 维度. The inner loop finishes a whole row before the outer moves on.

    DECLARE Grid : ARRAY[1:2, 1:3] OF INTEGER
    DECLARE Row, Col : INTEGER
    FOR Row ← 1 TO 2
        FOR Col ← 1 TO 3
            Grid[Row, Col] ← Row * Col
        NEXT Col
    NEXT Row
    FOR Row ← 1 TO 2
        FOR Col ← 1 TO 3
            OUTPUT "Grid[", Row, ",", Col, "] = ", Grid[Row, Col]
        NEXT Col
    NEXT Row
    

    ⚠️ The inner NEXT closes the inner counter. NEXT Row before NEXT Col crosses the loops over and is nonsense — a marker spots it instantly.

    Common mistakes

    • Swapping row and column. Grid[2,3] is row 2, column 3.
    • Grid[Row][Col]. Cambridge writes one pair of brackets with a comma inside.
    • Crossing the NEXT lines over, as above.
    Vocabulary
    EnglishChinesePinyin
    2-D array/tuː diː əˈreɪ/二维数组èr wéi shù zǔ
    row/rəʊ/xíng
    column/ˈkɒlʌm/liè
    dimension/daɪˈmenʃn/维度wéi dù
  • 9 Procedures and functions
    9.1

    PROCEDURE and CALL

    A procedure 过程 is a named block of statements. Writing one once and calling it from several places is decomposition 分解 — the idea the whole of paper 2 rests on.

    PROCEDURE <identifier>
        <statements>
    ENDPROCEDURE
    

    A procedure is called by name, with the keyword CALL:

    PROCEDURE DefaultLine
        OUTPUT "------------------------------"
    ENDPROCEDURE
    
    CALL DefaultLine
    OUTPUT "Report"
    CALL DefaultLine
    
    • The definition 定义 does nothing on its own. Only CALL runs it.
    • Control returns to the line after the CALL when the procedure ends.
    • A procedure does not give a value back. If you need one, you want a function.

    Common mistakes

    • Writing DefaultLine on its own to run it. 0478 requires CALL.
    • Leaving out ENDPROCEDURE.
    • Expecting the procedure's own variables to exist outside it.
    Vocabulary
    EnglishChinesePinyin
    procedure/prəˈsiːdʒə/过程guò chéng
    decomposition/ˌdiːkɒmpəˈzɪʃn/分解fēn jiě
    definition/ˌdefɪˈnɪʃn/定义dìng yì
    9.2

    FUNCTION and RETURN

    A function 函数 is a procedure that hands a value back. It is written where that value is needed — inside an OUTPUT, on the right of an assignment, inside a condition.

    FUNCTION <identifier>(<parameters>) RETURNS <data type>
        <statements>
        RETURN <value>
    ENDFUNCTION
    
    FUNCTION SumSquare(Number1 : INTEGER, Number2 : INTEGER) RETURNS INTEGER
        RETURN Number1 * Number1 + Number2 * Number2
    ENDFUNCTION
    
    OUTPUT "Sum of squares = ", SumSquare(10, 20)
    
    • RETURNS <data type> on the header says what type comes back. It is not optional.
    • RETURN ends the function immediately — nothing after it runs.
    • A function is never called with CALL; it is used wherever its value belongs.

    A function inside a condition

    FUNCTION IsEven(Number : INTEGER) RETURNS BOOLEAN
        RETURN MOD(Number, 2) = 0
    ENDFUNCTION
    
    DECLARE Index : INTEGER
    FOR Index ← 1 TO 6
        IF IsEven(Index)
          THEN
            OUTPUT Index, " is even"
        ENDIF
    NEXT Index
    

    Common mistakes

    • CALL SumSquare(10, 20) — that throws the answer away.
    • A function with no RETURN on some path. Every route out must return a value.
    • Leaving RETURNS INTEGER off the header.
    Vocabulary
    EnglishChinesePinyin
    function/ˈfʌŋkʃn/函数hán shù
    9.3

    Parameters

    A parameter 参数 is a value a procedure or function is given when it is called. Each one carries its own type.

    PROCEDURE Line(Size : INTEGER)
        DECLARE Index : INTEGER
        FOR Index ← 1 TO Size
            OUTPUT "-"
        NEXT Index
    ENDPROCEDURE
    
    CALL Line(5)
    CALL Line(20)
    

    Several parameters are separated by commas, and the order at the call must match the order in the definition:

    PROCEDURE Greet(Name : STRING, Times : INTEGER)
        DECLARE Index : INTEGER
        FOR Index ← 1 TO Times
            OUTPUT "Hello ", Name
        NEXT Index
    ENDPROCEDURE
    
    CALL Greet("Mei", 2)
    CALL Greet("Sam", 1)
    

    ⚠️ In 0478 every parameter is passed by value 传值: the procedure works on a copy, so changing it inside changes nothing outside. To get a value back, use a FUNCTION and RETURN it. (A-Level 9618 adds BYREF for the other behaviour — topic 11.)

    FUNCTION Doubled(Number : INTEGER) RETURNS INTEGER
        RETURN Number * 2
    ENDFUNCTION
    
    DECLARE Value : INTEGER
    Value ← 7
    Value ← Doubled(Value)
    OUTPUT Value
    

    Common mistakes

    • PROCEDURE Line(Size) with no type.
    • Calling with the arguments in the wrong order — Greet(2, "Mei") is a type error.
    • Expecting a procedure to change the variable you passed in. In 0478 it cannot.
    Vocabulary
    EnglishChinesePinyin
    parameter/pəˈræmɪtə/参数cān shù
    passed by value/pæst baɪ ˈvæljuː/传值chuán zhí
  • 10 File handling
    10.1

    Writing to a file

    A file 文件 keeps data after the program ends. 0478 uses four commands, and every one names the file it works on.

    OPENFILE <file identifier> FOR WRITE
    WRITEFILE <file identifier>, <data>
    CLOSEFILE <file identifier>
    
    OPENFILE "names.txt" FOR WRITE
    WRITEFILE "names.txt", "Mei"
    WRITEFILE "names.txt", "Sam"
    CLOSEFILE "names.txt"
    OUTPUT "Saved"
    

    Three file modes 文件模式:

    Mode What it does
    WRITE start a new file — anything already there is lost
    APPEND add to the end of what is there 追加
    READ read from the start
    OPENFILE "log.txt" FOR WRITE
    WRITEFILE "log.txt", "first"
    CLOSEFILE "log.txt"
    OPENFILE "log.txt" FOR APPEND
    WRITEFILE "log.txt", "second"
    CLOSEFILE "log.txt"
    OUTPUT "Both lines saved"
    
    • One WRITEFILE writes one line.
    • CLOSEFILE is not optional. An unclosed file can lose the data still waiting to be written, and that is a stock exam answer.

    Common mistakes

    • FOR WRITE when you meant FOR APPEND, which silently destroys the old contents.
    • Forgetting CLOSEFILE.
    • Opening a file that is already open.
    Vocabulary
    EnglishChinesePinyin
    file/faɪl/文件wén jiàn
    file modes/faɪl məʊdz/文件模式wén jiàn mó shì
    to the end of what is there/tə ðɪ end ɒv wɒt ɪz ðeə/追加zhuī jiā
    10.2

    Reading a file to the end

    READFILE takes one line into a variable. The variable must be declared first.

    OPENFILE <file identifier> FOR READ
    READFILE <file identifier>, <variable>
    CLOSEFILE <file identifier>
    

    Normally you do not know how many lines there are, so you read until the end of the file — which is what the EOF function reports.

    OPENFILE "names.txt" FOR WRITE
    WRITEFILE "names.txt", "Mei"
    WRITEFILE "names.txt", "Sam"
    WRITEFILE "names.txt", "Ana"
    CLOSEFILE "names.txt"
    
    DECLARE Line : STRING
    OPENFILE "names.txt" FOR READ
    WHILE NOT EOF("names.txt") DO
        READFILE "names.txt", Line
        OUTPUT Line
    ENDWHILE
    CLOSEFILE "names.txt"
    

    EOF("names.txt") is TRUE once every line has been read, so WHILE NOT EOF(...) means while there is still something to read.

    Counting while reading

    OPENFILE "marks.txt" FOR WRITE
    WRITEFILE "marks.txt", 40
    WRITEFILE "marks.txt", 65
    WRITEFILE "marks.txt", 88
    CLOSEFILE "marks.txt"
    
    DECLARE Mark, Count, Total : INTEGER
    Count ← 0
    Total ← 0
    OPENFILE "marks.txt" FOR READ
    WHILE NOT EOF("marks.txt") DO
        READFILE "marks.txt", Mark
        Count ← Count + 1
        Total ← Total + Mark
    ENDWHILE
    CLOSEFILE "marks.txt"
    OUTPUT Count, " marks, mean ", Total / Count
    

    Common mistakes

    • A WHILE EOF(...) loop — that runs only when there is nothing left. You want NOT.
    • Reading past the end because the loop has no EOF guard.
    • Opening FOR READ a file that was never written.
  • 11 A-Level 9618: what changes
    11.1

    Layout and operators

    Cambridge publishes two pseudocode specifications, and they disagree. Everything in topics 1-10 is IGCSE 0478. A-Level 9618 changes the details below — and a student who studies both loses marks by writing one in the other's paper.

    IGCSE 0478 A-Level 9618
    THEN on its own line, indented 2 on the IF line
    constants CONSTANT Pi ← 3.142 CONSTANT Pi = 3.142
    DIV / MOD functions: DIV(10, 3) operators: 10 DIV 3
    joining strings commas in OUTPUT the & operator
    identifiers must start with a capital mixed case allowed 混合大小写
    NEXT must name its counter good practice
    ROUND, RANDOM() both published neither exists

    This is the 0478 form, and it runs here:

    DECLARE Total : REAL
    CONSTANT Rate ← 0.5
    Total ← 10
    IF MOD(7, 2) = 1
      THEN
        OUTPUT "Odd, half rate ", Total * Rate
    ENDIF
    

    The 9618 form of the same algorithm is written like this — note THEN on the IF line, = in the CONSTANT, and MOD between its two values:

    DECLARE Total : REAL
    CONSTANT Rate = 0.5
    Total ← 10
    IF 7 MOD 2 = 1 THEN
        OUTPUT "Odd, half rate " & STR(Total * Rate)
    ENDIF
    

    ⚠️ Which one is right depends only on which paper you are sitting. Neither is a mistake; each is a mistake in the other's exam. The playground on this page runs the 0478 rules, so a 9618 construct is refused with a message naming the syllabus it belongs to — which is a quick way to check your own habits.

    Common mistakes

    • Writing THEN on the IF line in an 0478 answer, because that is what a textbook or a website showed. It is the single commonest cross-syllabus slip.
    • 10 MOD 3 in 0478. There it is MOD(10, 3).
    • ROUND(3.14159, 2) in a 9618 answer. 9618 has no ROUND at all.
    Vocabulary
    EnglishChinesePinyin
    mixed case/mɪkst keɪs/混合大小写hùn hé dà xiǎo xiě
    11.2

    Parameters: BYVAL and BYREF

    0478 passes every parameter by value 传值 (topic 9). 9618 lets you choose, and says so in the header.

    • BYVAL — the procedure gets a copy. Changing it changes nothing outside. This is the default when neither word is written.
    • BYREF — the procedure works on the caller's own variable 引用, so a change is visible after the call.

    This is 9618 only. It does not run here, and it is not accepted in an 0478 answer:

    PROCEDURE Increase(BYREF Value : INTEGER)
        Value ← Value + 1
    ENDPROCEDURE
    
    DECLARE Count : INTEGER
    Count ← 5
    CALL Increase(Count)
    OUTPUT Count      // prints 6
    

    The 0478 way to get a value back

    Use a FUNCTION and assign what it returns. This is the whole of the 0478 answer, and it runs:

    FUNCTION Increased(Value : INTEGER) RETURNS INTEGER
        RETURN Value + 1
    ENDFUNCTION
    
    DECLARE Count : INTEGER
    Count ← 5
    Count ← Increased(Count)
    OUTPUT Count
    

    Common mistakes

    • Writing BYREF in an 0478 answer. The keyword is not in that syllabus.
    • Expecting a plain 9618 parameter to behave like BYREF. Without the word it is BYVAL.
    Vocabulary
    EnglishChinesePinyin
    by value/baɪ ˈvæljuː/传值chuán zhí
    own variable/əʊn ˈveərɪəbl/引用yǐn yòng
    11.3

    Records and other types

    9618 has data structures 数据结构 that 0478 does not. You will meet them only at A-Level, and none of them runs under the 0478 rules of this page.

    A record 记录 groups fields of different types under one name (9618 section 4):

    TYPE Student
        DECLARE Name : STRING
        DECLARE Mark : INTEGER
    ENDTYPE
    
    DECLARE Candidate : Student
    Candidate.Name ← "Mei"
    Candidate.Mark ← 91
    OUTPUT Candidate.Name, " scored ", Candidate.Mark
    

    An enumerated type 枚举类型 lists the only values a variable may take:

    TYPE Vehicle = (Car, Bus, Taxi)
    DECLARE MyRide : Vehicle
    MyRide ← Taxi
    

    9618 also adds a DATE data type, random-access files (OPENFILE … FOR RANDOM), pointers, and classes with CLASS … ENDCLASS for its object-oriented paper.

    ⚠️ 0478 has five data types and arrays, and nothing else (topic 2). A 0478 answer that declares a record is answering a different syllabus.

    Common mistakes

    • Using a record in an 0478 answer. Use parallel arrays instead — one array per field, sharing an index.
    • Thinking TYPE means the same as DECLARE. TYPE defines a new type; DECLARE creates a variable of an existing one.
    Vocabulary
    EnglishChinesePinyin
    data structures/ˈdeɪtə ˈstrʌktʃəz/数据结构shù jù jié gòu
    record/ˈrekɔːd/记录jì lù
    enumerated type/ɪˈnjuːməreɪtɪd taɪp/枚举类型méi jǔ lèi xíng

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