Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/imperative-programming-resit/2/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Imperative programming (resit) / 2 / c / Solution by Codex 0 2026-10-31
Write parts in nonincreasing order. The array part stores the current prefix, and Emit(i,r,len) completes it using parts at most with remaining sum . With Out as the Oberon output module:
VAR part: ARRAY MaxParts OF INTEGER;

PROCEDURE Emit(i, r, len: INTEGER);
VAR j: INTEGER;
BEGIN
  IF r = 0 THEN
    j := 0;
    WHILE j < len DO
      IF j > 0 THEN Out.Char("+") END;
      Out.Int(part[j], 0); j := j+1
    END;
    Out.Ln
  ELSIF i > 0 THEN
    IF i <= r THEN
      part[len] := i;
      Emit(i, r-i, len+1)
    END;
    Emit(i-1, r, len)
  END
END Emit;

PROCEDURE PrintPartitions(n: INTEGER);
BEGIN
  Emit(n, n, 0)
END PrintPartitions;
The recursion invariant is that part[0..len) is nonincreasing, has sum , and every further part must be at most and at most the last existing part. The first branch includes the next part ; the second excludes it. These alternatives partition all completions, so each integer partition is printed exactly once. A recursive call reduces ; the printing loop's loop invariant is that the first entries have been printed with exactly the necessary separators.
For , no partition has more than parts, and the all-ones partition has exactly . Thus the fixed array requires to handle every partition. When a write occurs, and therefore len < n, so this bound prevents an out-of-range write. Zero prints one empty line, representing the empty integer partition. Available call stack space imposes a further practical limit.
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