+
+use std::cmp;
+use std::ops;
+
+// In the course of the next few parts, we are going to build a data-structure for
+// computations with *bug* numbers. We would like to not have an upper bound
+// to how large these numbers can get, with the memory of the machine being the
+// only limit.
+//
+// We start by deciding how to represent such big numbers. One possibility here is
+// to use a vector of "small" numbers, which we will then consider the "digits"
+// of the big number. This is like "1337" being a vector of 4 small numbers (1, 3, 3, 7),
+// except that we will use `u64` as type of our base numbers. Now we just have to decide
+// the order in which we store numbers. I decided that we will store the least significant
+// digit first. This means that "1337" would actually become (7, 3, 3, 1).<br/>
+// Finally, we declare that there must not be any trailing zeros (corresponding to
+// useless leading zeros in our usual way of writing numbers). This is to ensure that
+// the same number can only be stored in one way.
+
+// To write this down in Rust, we use a `struct`, which is a lot like structs in C:
+// Just a collection of a bunch of named fields. Every field can be private to the current module
+// (which is the default), or public (which would be indicated by a `pub` in front of the name).
+// For the sake of the tutorial, we make `dat` public - otherwise, the next parts of this
+// course could not work on `BigInt`s. Of course, in a real program, one would make the field
+// private to ensure that the invariant (no trailing zeros) is maintained.
+pub struct BigInt {
+ pub data: Vec<u64>,
+}
+
+// Now that we fixed the data representation, we can start implementing methods on it.
+impl BigInt {
+ // Let's start with a constructor, creating a `BigInt` from an ordinary integer.
+ // To create an instance of a struct, we write its name followed by a list of
+ // fields and initial values assigned to them.
+ pub fn new(x: u64) -> Self {
+ if x == 0 {
+ BigInt { data: vec![] }
+ } else {
+ BigInt { data: vec![x] }
+ }
+ }
+
+ // It can often be useful to encode the invariant of a data-structure in code, so here
+ // is a check that detects useless trailing zeros.
+ pub fn test_invariant(&self) -> bool {
+ if self.data.len() == 0 {
+ true
+ } else {
+ self.data[self.data.len() - 1] != 0
+ }
+ }
+
+ // We can convert any vector of digits into a number, by removing trailing zeros. The `mut`
+ // declaration for `v` here is just like the one in `let mut ...`, it says that we will locally
+ // change the vector `v`. In this case, we need to make that annotation to be able to call `pop`
+ // on `v`.
+ pub fn from_vec(mut v: Vec<u64>) -> Self {
+ while v.len() > 0 && v[v.len()-1] == 0 {
+ v.pop();
+ }
+ BigInt { data: v }
+ }
+}
+
+// If you have a close look at the type of `BigInt::from_vec`, you will notice that it
+// consumes the vector `v`. The caller hence loses access. There is however something
+// we can do if we don't want that to happen: We can explicitly `clone` the vector,
+// which means that a full (or *deep*) copy will be performed. Technically,
+// `clone` takes a borrowed vector, and returns a fully owned one.
+fn clone_demo() {
+ let v = vec![0,1 << 16];
+ let b1 = BigInt::from_vec(v.clone());
+ let b2 = BigInt::from_vec(v);
+}
+
+// To be clonable is a property of a type, and as such, naturally expressed with a trait.
+// In fact, Rust already comes with a trait `Clone` for exactly this purpose. We can hence
+// make our `BigInt` clonable as well.
+impl Clone for BigInt {
+ fn clone(&self) -> Self {
+ BigInt { data: self.data.clone() }
+ }
+}
+// Making a type clonable is such a common exercise that Rust can even help you doing it:
+// If you add `#[derive(Clone)]' right in front of the definition of `BigInt`, Rust will
+// generate an implementation of `clone` that simply clones all the fields. Try it!
+//
+// To put this in perspective, `clone` in Rust corresponds to what people usually manually do in
+// the copy constructor of a C++ class: It creates new, independent instance containing the
+// same values. Contrary to that, if you pass something to a function normally (like the
+// second call to `from_vec` in `clone_demo`), only a *shallow* copy is created: The fields
+// are copied, but pointers are simply duplicated. This corresponds to the default copy
+// constructor in C++. Rust assumes that after such a copy, the old value is useless
+// (as the new one uses the same pointers), and hence considers the data semantically
+// moved to the copy. That's another explanation of why Rust does not let you access
+// a vector anymore after you passed ownership to some function.
+
+// With `BigInt` being about numbers, we should be able to write a version of `vec_min`
+// that computes the minimum of a list of `BigInt`. We start by writing `min` for
+// `BigInt`. Now our assumption of having no trailing zeros comes in handy!
+impl BigInt {
+ fn min(self, other: Self) -> Self {
+ // Just to be sure, we first check that both operands actually satisfy our invariant.
+ // `debug_assert!` is a macro that checks that its argument (must be of type `bool`)
+ // is `true`, and panics otherwise. It gets removed in release builds, which you do with
+ // `cargo build --release`.
+ //
+ // If you carefully check the type of `BigInt::test_invariant`, you may be surprised that
+ // we can call the function this way. Doesn't it take `self` in borrowed form? Indeed,
+ // the explicit way to do that would be to call `(&other).test_invariant()`. However, the
+ // `self` argument of a method is treated specially by Rust, and borrowing happens automatically here.
+ debug_assert!(self.test_invariant() && other.test_invariant());
+ // If the lengths of the two numbers differ, we already know which is larger.
+ if self.data.len() < other.data.len() {
+ self
+ } else if self.data.len() > other.data.len() {
+ other
+ } else {
+ // **Exercise**: Fill in this code.
+ panic!("Not yet implemented.");
+ }
+ }
+}
+
+fn vec_min(v: &Vec<BigInt>) -> Option<BigInt> {
+ let mut min: Option<BigInt> = None;
+ for e in v {
+ // In the loop, `e` now has type `&i32`, so we have to dereference it.
+ min = Some(match min {
+ None => e.clone(),
+ Some(n) => e.clone().min(n)
+ });
+ }
+ min
+}
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