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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/imperative-programming-resit/3/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming (resit) / 3 / a / Solution by

Codex  0 2026-10-31

Return the exclusive endpoint of the maximal initial run:

PROCEDURE Run(a, b: INTEGER): INTEGER;
VAR c: INTEGER;
BEGIN
  IF a = b THEN RETURN b END;
  c := a+1;
  WHILE c < b DO
    IF u[c-1] > u[c] THEN RETURN c END;
    c := c+1
  END;
  RETURN c
END Run;

The loop invariant is

a < c \leq b

and

u [a .. c)

is nondecreasing. An unsuccessful adjacent-order test extends the run by one; a strict descent at

c

prevents any extension across it. If

c = b

, the whole segment is a run. The loop variant is

b - c

u [a .. Run (a, b)) is the maximal initial run .

(1)

For a run of length

s > 0

, the running time is

Θ (s)

, including at most one failed extension test; an empty segment takes

Θ (1)

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