2D Arrays & Matrix Grid Iteration

A Two-Dimensional (2D) Array represents data arranged in a grid of rows and columns (a matrix). Like 1D arrays, all elements in a 2D array must be of the same data type.

1. Declaration in Cambridge Pseudocode

DECLARE <Identifier> : ARRAY[<RowStart>:<RowEnd>, <ColStart>:<ColEnd>] OF <DataType>

Example:

DECLARE ChessBoard : ARRAY[1:8, 1:8] OF CHAR
DECLARE StudentMarks : ARRAY[1:30, 1:4] OF INTEGER  // 30 students, 4 subjects

Row-Major Indexing:

Cambridge pseudocode follows the standard mathematical convention where the first index represents the row and the second index represents the column:

2. Iterating Across 2D Grids

Traversing every cell in a 2D array requires nested FOR loops:

• The outer loop iterates through the rows.
• The inner loop iterates through the columns for each row:

FOR r <- 1 TO 30
    TotalScore <- 0
    FOR c <- 1 TO 4
        TotalScore <- TotalScore + StudentMarks[r, c]
    NEXT c
    OUTPUT "Student ", r, " Total: ", TotalScore
NEXT r

Worked non-square traversal

For two rows [2,4,6] and [10,20,30], row totals are 12 and 60. Set Total to zero at the start of EACH row, then add its three columns. If Total is reset only once, the second result becomes 72. In ARRAY[1:2,1:3], swapping the indices can also attempt a nonexistent third row.

Before solving, draw the two-by-three table, label both index ranges and trace the reset. Then use data different from this worked example.