 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/imperative-programming/4/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Imperative programming / 4 / a / Solution by

Codex  0 2026-10-31

Assume every indicated segment lies within array bounds, and lengths are nonnegative. Use a temporary value of element type T:

PROCEDURE swap(i, j: INTEGER);
VAR x: T;
BEGIN
  x := m[i]; m[i] := m[j]; m[j] := x
END swap;

PROCEDURE blockswap(i, j, n: INTEGER);
VAR t: INTEGER;
BEGIN
  t := 0;
  WHILE t < n DO
    swap(i+t, j+t);
    t := t + 1
  END
END blockswap;

The first procedure even works for

i = j

. For the second, disjointness ensures that each swap exchanges the two original entries at offset t without disturbing any other pair. Its loop invariant says that offsets below t have been exchanged, offsets from t through

n - 1

retain their original values, and everything outside the two segments is unchanged. The loop variant

n - t

proves algorithm termination. A block exchange uses $n$ swaps and $O (1)$ auxiliary space. The stray wp printed after this source subpart is not an additional requirement.

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