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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/imperative-programming-resit/1/e/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Imperative programming resit / 1 / e / Solution by

Codex  0 2026-10-25

Print separators before all but the first term, so there is neither a leading nor a trailing plus sign:

def printRat(num: Int, den: Int): Unit = {
  print(num.toString + "/" + den.toString)
}

def printEgypt(e: Array[Int]): Unit = {
  if (e.isEmpty) print("0")
  var i = 0
  while (i < e.length) {
    if (i > 0) print(" + ")
    print("1/" + e(i).toString)
    i += 1
  }
}

The loop invariant says that exactly the first

i

unit fractions have been printed in order, separated by + , with no trailing separator. The loop variant is

e . l e n g t h - i

. The empty array is displayed as zero. Since

5/7 - 1/2 = 3/14

and

3/14 - 1/5 = 1/70

, the output is 5/7 = 1/2 + 1/5 + 1/70. The source's earlier example with middle denominator

4

and final denominator

70

contains the arithmetic typo; its final printing example is correct. Indeed

1/2 + 1/4 > 5/7

, so no positive final term could repair that particular prefix. The printing routine reports the generated terms rather than imposing a particular expansion.

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