Introduction: functions

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1. Question 1From earlier unitsWhat does int n{305}; int c{1}; while (n >= 10) { n = n / 10; ++c; } std::println("{}", c); write?

   3

   2

   4

   30

2. Question 2From earlier unitsIn the loop int total{0}; int k{1}; while (k <= n) { total += k; ++k; }, with $n \geq 0$, what relation holds each time the condition is evaluated?

   $\mathit{total} = 1 + 2 + \cdots + (k - 1)$

   $\mathit{total} = 1 + 2 + \cdots + k$

   $\mathit{total} = 1 + 2 + \cdots + n$

   $k \leq n$

3. Question 3From earlier unitsThe specification of division says: “given integers $a \geq 0$ and $b > 0$, obtain $q$ and $r$ with $a = b \cdot q + r$ and $0 \leq r < b$”. What is its precondition?

   $a \geq 0$ and $b > 0$.

   $a = b \cdot q + r$ and $0 \leq r < b$.

   That $q$ and $r$ be integers.

   It has none: it holds for every pair of integers.

4. Question 4From earlier unitsAfter int a{3}; int b{a}; b = 7;, what is the value of a?

   3

   7

   An indeterminate value.

5. Question 5From earlier unitsThe program of lesson 4.4 that writes the primes less than 100 has a loop that runs through the candidates and, inside it, another that tries their divisors. Which part is a computation with its own inputs and outputs, one that would be worth naming?

   Deciding whether an integer $n$ is prime: $n$ goes in, a logical value comes out.

   Reading the data and writing the result.

   The increment of the divisor.

   The variable that says whether a divisor was found.

6. Question 6A program starts in main; main calls a function g, and g calls another function h. While h is running, which calls are in progress?

   Those of main, g and h, with h on top.

   Only that of h.

   Those of main and h.

   I don’t know yet.

7. Question 7With the function int f(int x) { x = x + 1; return x; }, what does int a{3}; int b{f(a)}; std::println("{} {}", a, b); write?

   3 4

   4 4

   3 3

   It does not compile.

8. Question 8A program reads a date and must write its day of the week. Which decomposition separates the computation from the presentation?

   One function computes the day as a number from 0 to 6; another converts it into its name; main reads, calls and writes.

   A single function that computes and writes the day.

   A global variable that one function fills and another reads.

   I don’t know yet.

9. Question 9Which of the following definitions defines $n!$ for every natural number $n$?

   $0! = 1$, and $n! = n \cdot (n - 1)!$ if $n \geq 1$.

   $n! = n \cdot (n - 1)!$ for every $n$.

   $1! = 1$, and $n! = n \cdot (n - 1)!$ if $n \geq 2$.

   $0! = 1$, and $n! = (n + 1) \cdot n!$ if $n \geq 1$.

10. Question 10With int f(int n) { if (n == 0) { return 0; } return n + f(n - 1); }, what does std::println("{}", f(3)); write?

    6

    3

    0

    It does not compile: a function cannot call itself.