Two-Dimensional Arrays, Nested Loops and String Processing

Two-dimensional arrays. A table of marks — students in rows, tests in columns — is stored as an array of arrays. In IB pseudocode MARKS[R][C] names the element in row R and column C, and both indices start at 0, so a 3 × 4 table has rows 0–2 and columns 0–3. The row index always comes first; MARKS[1][2] is row 1, column 2. The most common exam error is running a loop to 3 instead of 2 and stepping outside the array. Keep the dimensions as named constants (ROWS, COLS) and loop from 0 to ROWS − 1.

Nested loops. Visiting every element needs a loop inside a loop. The outer loop chooses a row, the inner loop walks along it; the inner loop's counter restarts every time the outer loop advances. For 3 rows and 4 columns the inner body runs 3 × 4 = 12 times, and when both dimensions grow to n the work grows as n², which is why nested loops are the usual source of O(n²) algorithms. Which loop is outside determines what you can accumulate: rows outside gives a total per student, columns outside gives a total per test. The classic bug is placing TOTAL = 0 before both loops instead of inside the outer loop, so that totals accumulate across every row. Other nested-loop patterns to recognise: finding the largest element and its position (two variables updated together), counting how many elements satisfy a condition, and checking whether every row sums to the same value.

Strings as sequences. A string is a sequence of characters that can be indexed like an array. The operations examiners expect: length; extracting one character; joining (concatenation); comparing two strings, which works character by character using the character codes, so uppercase letters sort before lowercase and "10" sorts before "9"; converting between a character and its code; and searching for a substring. Standard algorithms built from these: counting vowels (a loop and a condition), reversing a string (build a new string from the last character backwards), checking a palindrome (compare position I with position LENGTH − 1 − I until they meet), and validating a password (loop once, set flags for length, digit, uppercase, then decide). Every string algorithm is a loop from 0 to LENGTH − 1 plus a condition, and the trace table has one row per character.

Collections versus arrays. The IB collection has no index: you reset it, then loop with hasNext and getNext until the end. It grows as items are added, which arrays cannot, but you cannot jump to the fifth item directly. Choose an array when position matters or when the size is known; choose a collection when the number of items is unknown and you only ever process them in order.