Arrays, Strings And Data Handling: Two-Dimensional Arrays: Table-Based Problems (Copy)

Two-Dimensional Arrays: Table-Based Problems

What A Two-Dimensional Array Is

• A two-dimensional array (2D array) stores data in:
  • Rows
  • Columns
• Used to represent:
  • Tables
  • Grids
  • Matrices
  • Timetables
  • Scoreboards
• Each element accessed using two indices:
  • Row index
  • Column index

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Core Structure Of A Two-Dimensional Array

Feature	Description
Data type	Same type for all elements
Dimensions	Rows × Columns
Access	array[row][column]
Storage	Logical table form
Processing	Usually nested loops

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Declaring A Two-Dimensional Array

General Declaration Format

DECLARE arrayName : ARRAY[rowStart..rowEnd, colStart..colEnd] OF dataType

Example: Integer Table (5 Rows × 3 Columns)

DECLARE marks : ARRAY[1..5, 1..3] OF INTEGER

• Meaning
  • 5 students
  • 3 subjects per student

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Example: String Table

DECLARE names : ARRAY[1..4, 1..2] OF STRING

• Example use
  • Column 1 → First name
  • Column 2 → Last name

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Visualising A Two-Dimensional Array (Exam Skill)

Example Table: marks

Row (Student)	Col 1	Col 2	Col 3
1	65	72	80
2	55	60	70
3	90	88	92
4	40	50	45
5	78	85	80

• marks[3,2] = 88
• marks[5,1] = 78

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Assigning Values To A 2D Array

Manual Assignment (Small Tables)

marks[1,1] ← 65
marks[1,2] ← 72
marks[1,3] ← 80

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Assignment Using Nested Loops (MOST COMMON)

FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    INPUT marks[row, col]
  NEXT col
NEXT row

• Examiner focus
  • Correct nesting order
  • Correct loop limits

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Accessing And Outputting A 2D Array

Output Entire Table

FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    OUTPUT marks[row, col]
  NEXT col
NEXT row

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Output Row By Row (Readable Format)

FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    OUTPUT marks[row, col], " "
  NEXT col
  OUTPUT NEWLINE
NEXT row

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Table-Based Problems: Common Exam Scenarios

Scenario 1: Total Marks Per Row (Row Processing)

FOR row ← 1 TO 5
  total ← 0
  FOR col ← 1 TO 3
    total ← total + marks[row, col]
  NEXT col
  OUTPUT total
NEXT row

• Key idea
  • Reset accumulator inside outer loop

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Scenario 2: Total Marks Per Column (Column Processing)

FOR col ← 1 TO 3
  total ← 0
  FOR row ← 1 TO 5
    total ← total + marks[row, col]
  NEXT row
  OUTPUT total
NEXT col

• Common mistake
  • Swapping row/column order incorrectly

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Scenario 3: Finding Maximum Value In Entire Table

max ← marks[1,1]
FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    IF marks[row, col] > max THEN
      max ← marks[row, col]
    ENDIF
  NEXT col
NEXT row

• Correct initialisation avoids logic errors

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Scenario 4: Counting Values That Meet A Condition

• Example: Count marks ≥ 50

count ← 0
FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    IF marks[row, col] >= 50 THEN
      count ← count + 1
    ENDIF
  NEXT col
NEXT row

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Table-Based Problem Patterns (Exam-Focused)

Task	Outer Loop	Inner Loop
Row totals	Rows	Columns
Column totals	Columns	Rows
Full table scan	Rows	Columns
Search	Rows	Columns
Modify values	Rows	Columns

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Searching In A Two-Dimensional Array

Linear Search In Table

found ← FALSE
row ← 1

WHILE row <= 5 AND found = FALSE DO
  col ← 1
  WHILE col <= 3 AND found = FALSE DO
    IF marks[row, col] = target THEN
      found ← TRUE
    ELSE
      col ← col + 1
    ENDIF
  ENDWHILE
  row ← row + 1
ENDWHILE

• Examiner focus
  • Bounds protection
  • Flag logic

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Updating Values In A Table

Example: Increase All Marks By 5

FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    marks[row, col] ← marks[row, col] + 5
  NEXT col
NEXT row

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Example: Replace Negative Values With Zero

FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    IF marks[row, col] < 0 THEN
      marks[row, col] ← 0
    ENDIF
  NEXT col
NEXT row

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Common Logic Errors In Table-Based Problems

Error 1: Not Resetting Accumulator

total ← 0
FOR row ← 1 TO 5
  FOR col ← 1 TO 3
    total ← total + marks[row, col]
  NEXT col
  OUTPUT total
NEXT row

• Error
  • Totals accumulate incorrectly
• Fix
  • Reset total inside outer loop

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Error 2: Loop Bounds Mismatch

• Declared [1..5,1..3]
• Looping:

FOR row ← 1 TO 6

• Causes out-of-range access

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Error 3: Swapped Indices

marks[col, row]

• Logical error
• Leads to incorrect values

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Dry-Run Technique For 2D Arrays

Step-by-Step Method

• Draw table on paper
• Label rows and columns
• Fill values as inputs occur
• Track changes per loop iteration
• Verify which loop controls rows/columns

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Safe 2D Array Template (Copy-Paste)

DECLARE table : ARRAY[1..r, 1..c] OF INTEGER

FOR row ← 1 TO r
  FOR col ← 1 TO c
    INPUT table[row, col]
  NEXT col
NEXT row

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Examiner Checklist For Full Marks

• Correct 2D declaration syntax
• Correct use of two indices
• Proper nested loop structure
• Correct accumulator placement
• No out-of-range access
• Clear row vs column logic

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

One-Line Rules To Memorise

• Tables need nested loops
• Outer loop = major grouping
• Inner loop = detailed processing
• Reset totals correctly
• Row/column order matters