Justify why one loop structure may be better suited to solve a problem than the others

Cambridge A‑Level Computer Science (9618) – Topic 11.2 Constructs: Loop Structures

Learning Objective (AO1 + AO2 + AO3)

Explain, analyse and justify why one loop structure (for, while or do…while) is the most appropriate choice for a given problem. Use clear pseudocode, state pre‑ and post‑conditions, and discuss algorithmic efficiency where relevant.

Syllabus Mapping

• 11.2 Constructs – iteration (loop) structures.
• 9.1 Algorithm design – step‑wise refinement, flow‑chart ↔ pseudocode.
• 9.2 Analysis – pre‑conditions, post‑conditions, time‑complexity.

1. Overview of the Three Loop Constructs

for (initialisation; test; update) {
    // body
}

while (test) {
    // body
}

do {
    // body
} while (test);

2. Choosing the Right Loop – Decision Guide

1. Known, fixed number of repetitions
   • Prefer a for loop.
   • Pre‑condition: the loop counter satisfies the test before the first iteration.
   • Complexity: O(n), where n is the bound.

   Example – Print the first n Fibonacci numbers

   for (int i = 1; i <= n; i++) {
       // calculate and display Fibonacci(i)
   }
   

2. Indeterminate repetitions, condition‑driven
   • Prefer a while loop.
   • Pre‑condition expressed directly in the test; the body may never execute.
   • Complexity: depends on how many times the test evaluates true (≤ n).

   Example – Read values until sentinel -1 is entered

   int value = readNext();
   while (value != -1) {
       // process value
       value = readNext();
   }
   

3. At least one execution required
   • Prefer a do…while loop.
   • Post‑condition tested after the first pass, guaranteeing one execution.
   • Complexity: same as a while loop plus the guaranteed first iteration.

   Example – Simple menu‑driven program

   int choice;
   do {
       displayMenu();
       choice = getChoice();
       // handle the choice
   } while (choice != EXIT);
   

3. Pre‑condition / Post‑condition Summary

4. Nested Loops & Control Variables

• Nested loop definition: a loop placed inside the body of another loop. Useful for two‑dimensional data (matrices) or when an inner repetition depends on an outer iteration.
• Each loop must have its own control variable(s) to avoid accidental interference.
• Overall time‑complexity is the product of the individual complexities (e.g., two nested for loops → O(n²)).

Example – Multiplication table of size 

for (int i = 1; i <= n; i++) {          // outer loop – rows
    for (int j = 1; j <= n; j++) {      // inner loop – columns
        print(i * j + "\t");
    }
    println();                         // new line after each row
}

5. Common Errors Checklist (AO2/AO3)

• Off‑by‑one errors – using <= instead of < (or vice‑versa) in the test.
• Infinite loops – forgetting to update the control variable or using a condition that can never become false.
• Uninitialised or out‑of‑scope counters – declaring the loop variable outside the loop when it should be local.
• Incorrect loop type – choosing do…while when the body must not run for an empty data set.
• Array‑index out‑of‑bounds – iterating beyond array.length‑1.
• Mismatched pre‑/post‑conditions – not stating what must hold before/after the loop, leading to logical errors.

6. Detailed Justification Example – Searching a List

Problem: Find the first occurrence of target in an array list of unknown length.

int i = 0;
while (i < list.length && list[i] != target) {
    i++;
}
if (i < list.length) {
    // target found at index i
} else {
    // target not present
}

• Why while is optimal
  • The number of iterations depends on data; the loop stops as soon as the target is found or the end is reached.
  • If list.length == 0, the test fails before any body execution, preventing an out‑of‑bounds error.
  • The combined termination condition (i < list.length AND list[i] != target) is naturally expressed in the while header, keeping the algorithm readable.
  • Time‑complexity: O(k), where k ≤ n (position of the target or the array length).
• Using a for loop would obscure the early‑termination nature and require an extra break statement.
• Using a do…while loop would guarantee one execution, risking an out‑of‑bounds access when the array is empty.

7. Comparison Table – When to Use Each Loop

8. Key Points to Remember (AO1)

• Match the loop type to the problem nature:
  • Fixed count → for
  • Data‑driven condition → while
  • Mandatory first pass → do…while
• Always state the pre‑condition (what must be true before the first iteration) and the post‑condition (what is true when the loop finishes).
• Consider algorithmic efficiency – a loop with a known bound is easier to analyse and often yields a tighter complexity bound.
• Watch for off‑by‑one errors, infinite loops, and the scope of control variables.
• When nesting loops, keep each control variable distinct; overall complexity multiplies (e.g., two nested for loops → O(n²)).

9. Suggested Diagram (for visual learners)