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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/imperative-programming/4/e/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming / 4 / e / Solution by

Codex  0 2026-10-31

Scan the polynomial coefficients from highest degree downward. Omit zero terms, omit coefficient magnitude one on nonconstant terms, print - for negative terms, and print + only before a positive term after the first. A helper prints small integral magnitudes without a decimal suffix; other real numbers use Out.Real.

PROCEDURE OutMagnitude(c: REAL);
VAR n: INTEGER;
BEGIN
  IF c < MAX(INTEGER) THEN
    n := ENTIER(c);
    IF c = n THEN Out.Int(n, 0) ELSE Out.Real(c, 0) END
  ELSE
    Out.Real(c, 0)
  END
END OutMagnitude;

PROCEDURE OutPoly(p: Poly);
VAR i: INTEGER; c, magnitude: REAL; first: BOOLEAN;
BEGIN
  IF p.degree < 0 THEN Out.String("0"); RETURN END;
  first := TRUE; i := p.degree;
  WHILE i >= 0 DO
    c := p.coeff[i];
    IF c # 0.0 THEN
      IF c < 0.0 THEN Out.Char("-")
      ELSIF ~first THEN Out.Char("+")
      END;
      magnitude := ABS(c);
      IF (i = 0) OR (magnitude # 1.0) THEN
        OutMagnitude(magnitude)
      END;
      IF i > 0 THEN
        Out.Char("x");
        IF i > 1 THEN Out.Char("^"); Out.Int(i, 0) END
      END;
      first := FALSE
    END;
    DEC(i)
  END
END OutPoly;

The representation invariant ensures a nonzero polynomial prints at least one term. Constant

1

and

- 1

retain their coefficients, whereas

x

and

- x

omit magnitude one. Thus the requested example prints

x^{4} - 3 x^{2} + 7 x - 1.

(1)

Different Out.Real implementations may use decimal or scientific notation for nonintegral coefficients; either denotes the appropriate real number. The number of coefficient inspections is linear in the stored polynomial degree.

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