use std::cmp;
use std::fmt;
+pub trait Minimum {
+ /// Return the smaller of the two
+ fn min<'a>(&'a self, other: &'a Self) -> &'a Self;
+}
+
+/// Return a pointer to the minimal value of `v`.
+pub fn vec_min<T: Minimum>(v: &Vec<T>) -> Option<&T> {
+ let mut min = None;
+ for e in v {
+ min = Some(match min {
+ None => e,
+ Some(n) => e.min(n)
+ });
+ }
+ min
+}
+
pub struct BigInt {
data: Vec<u64>, // least significant digits first. The last block will *not* be 0.
}
// Add with carry, returning the sum and the carry
fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
- match u64::checked_add(a, b) {
- Some(sum) if !carry => (sum, false),
- Some(sum) => { // we have to increment the sum by 1, where it may overflow again
- match u64::checked_add(sum, 1) {
- Some(total_sum) => (total_sum, false),
- None => (0, true) // we overflowed incrementing by 1, so we are just "at the edge"
- }
- },
- None => {
- // Get the remainder, i.e., the wrapping sum. This cannot overflow again by adding just 1, so it is safe
- // to add the carry here.
- let rem = u64::wrapping_add(a, b) + if carry { 1 } else { 0 };
- (rem, true)
- }
+ let sum = u64::wrapping_add(a, b);
+ let carry_n = if carry { 1 } else { 0 };
+ if sum >= a { // the first sum did not overflow
+ let sum_total = u64::wrapping_add(sum, carry_n);
+ let had_overflow = sum_total < sum;
+ (sum_total, had_overflow)
+ } else { // the first sum did overflow
+ // it is impossible for this to overflow again, as we are just adding 0 or 1
+ (sum + carry_n, true)
}
}
-
impl BigInt {
/// Construct a BigInt from a "small" one.
pub fn new(x: u64) -> Self {
BigInt { data: v }
}
- /// Return the smaller of the two numbers
- pub fn min(self, other: Self) -> Self {
- debug_assert!(self.test_invariant() && other.test_invariant());
- if self.data.len() < other.data.len() {
- self
- } else if self.data.len() > other.data.len() {
- other
- } else {
- // compare back-to-front, i.e., most significant digit first
- let mut idx = self.data.len()-1;
- while idx > 0 {
- if self.data[idx] < other.data[idx] {
- return self;
- } else if self.data[idx] > other.data[idx] {
- return other;
- }
- else {
- idx = idx-1;
- }
- }
- // the two are equal
- return self;
- }
- }
-
- /// Returns a view on the raw digits representing the number.
- ///
- /// ```
- /// use solutions::bigint::BigInt;
- /// let b = BigInt::new(13);
- /// let d = b.data();
- /// assert_eq!(d, [13]);
- /// ```
- pub fn data(&self) -> &[u64] {
- &self.data[..]
- }
-
/// Increments the number by "by".
pub fn inc(&mut self, mut by: u64) {
let mut idx = 0;
}
}
-
impl PartialEq for BigInt {
fn eq(&self, other: &BigInt) -> bool {
debug_assert!(self.test_invariant() && other.test_invariant());
- self.data() == other.data()
+ self.data == other.data
+ }
+}
+
+impl Minimum for BigInt {
+ fn min<'a>(&'a self, other: &'a Self) -> &'a Self {
+ debug_assert!(self.test_invariant() && other.test_invariant());
+ if self.data.len() < other.data.len() {
+ self
+ } else if self.data.len() > other.data.len() {
+ other
+ } else {
+ // compare back-to-front, i.e., most significant digit first
+ let mut idx = self.data.len()-1;
+ while idx > 0 {
+ if self.data[idx] < other.data[idx] {
+ return self;
+ } else if self.data[idx] > other.data[idx] {
+ return other;
+ }
+ else {
+ idx = idx-1;
+ }
+ }
+ // the two are equal
+ return self;
+ }
}
}
impl fmt::Debug for BigInt {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
- self.data().fmt(f)
+ self.data.fmt(f)
}
}
impl<'a, 'b> ops::Add<&'a BigInt> for &'b BigInt {
type Output = BigInt;
fn add(self, rhs: &'a BigInt) -> Self::Output {
- let mut result_vec:Vec<u64> = Vec::with_capacity(cmp::max(self.data().len(), rhs.data().len()));
+ let mut result_vec:Vec<u64> = Vec::with_capacity(cmp::max(self.data.len(), rhs.data.len()));
let mut carry:bool = false; // the carry bit
- for (i, val) in self.data().into_iter().enumerate() {
+ for (i, val) in (&self.data).into_iter().enumerate() {
// compute next digit and carry
- let rhs_val = if i < rhs.data().len() { rhs.data()[i] } else { 0 };
+ let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
let (sum, new_carry) = overflowing_add(*val, rhs_val, carry);
// store them
result_vec.push(sum);
carry = new_carry;
}
- BigInt::from_vec(result_vec)
+ if carry {
+ result_vec.push(1);
+ }
+ // We know that the invariant holds: overflowing_add would only return (0, false) if
+ // the arguments are (0, 0, false), but we know that in the last iteration, `val` is the
+ // last digit of `self` and hence not 0.
+ BigInt { data: result_vec }
}
}
// * [Part 03](part03.html)
// * [Part 04](part04.html) (WIP)
// * (to be continued)
-#![allow(dead_code, unused_imports, unused_variables)]
+#![allow(dead_code, unused_imports, unused_variables, unused_mut)]
mod part00;
mod part01;
mod part02;
mod part04;
mod part05;
mod part06;
+mod part07;
// To actually run the code of some part (after filling in the blanks, if necessary), simply edit the `main`
// function.
// Rust-101, Part 05: Copy, Clone
// ==============================
+
+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
+}
-// Rust-101, Part 06: Abstract Datastructure, Testing
-// ==================================================
+// Rust-101, Part 06: Lifetimes, Testing
+// =====================================
use std::cmp;
use std::ops;
+use std::fmt;
+use part05::BigInt;
-pub struct BigInt {
- data: Vec<u64>, // least significant digits first. The last block will *not* be 0.
-}
-impl BigInt {
- pub fn new(x: u64) -> Self {
- if x == 0 {
- BigInt { data: vec![] }
- } else {
- BigInt { data: vec![x] }
- }
+impl PartialEq for BigInt {
+ fn eq(&self, other: &BigInt) -> bool {
+ debug_assert!(self.test_invariant() && other.test_invariant());
+ self.data == other.data
}
}
-/// Add with carry, returning the sum and the carry
-fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
- match u64::checked_add(a, b) {
- Some(sum) if !carry => (sum, false),
- Some(sum) => { // we have to increment the sum by 1, where it may overflow again
- match u64::checked_add(sum, 1) {
- Some(total_sum) => (total_sum, false),
- None => (0, true) // we overflowed incrementing by 1, so we are just "at the edge"
- }
- },
- None => {
- // Get the remainder, i.e., the wrapping sum. This cannot overflow again by adding just 1, so it is safe
- // to add the carry here.
- let rem = u64::wrapping_add(a, b) + if carry { 1 } else { 0 };
- (rem, true)
- }
- }
+fn call_eq() {
+ let b1 = BigInt::new(13);
+ let b2 = BigInt::new(37);
+ println!("b1 == b1: {} ; b1 == b2: {}; b1 != b2: {}", b1 == b1, b1 == b2, b1 != b2);
}
-#[test]
-fn test_overflowing_add() {
- assert_eq!(overflowing_add(10, 100, false), (110, false));
- assert_eq!(overflowing_add(10, 100, true), (111, false));
- assert_eq!(overflowing_add(1 << 63, 1 << 63, false), (0, true));
- assert_eq!(overflowing_add(1 << 63, 1 << 63, true), (1, true));
- assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
+
+impl fmt::Debug for BigInt {
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ self.data.fmt(f)
+ }
}
-impl ops::Add<BigInt> for BigInt {
- type Output = BigInt;
- fn add(self, rhs: BigInt) -> Self::Output {
- let mut result_vec:Vec<u64> = Vec::with_capacity(cmp::max(self.data.len(), rhs.data.len()));
- let mut carry:bool = false; // the carry bit
- for (i, val) in self.data.into_iter().enumerate() {
- // compute next digit and carry
- let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
- let (sum, new_carry) = overflowing_add(val, rhs_val, carry);
- // store them
- result_vec.push(sum);
- carry = new_carry;
- }
- BigInt { data: result_vec }
+
+
+impl BigInt {
+ pub fn inc(&mut self, mut by: u64) {
+ panic!("Not yet implemented.");
}
}
+#[test]
+fn test_inc() {
+ let mut b = BigInt::new(1337);
+ b.inc(1337);
+ assert!(b == BigInt::new(1337 + 1337));
+
+ b = BigInt::new(0);
+ assert_eq!(b, BigInt::from_vec(vec![0]));
+ b.inc(1 << 63);
+ assert_eq!(b, BigInt::from_vec(vec![1 << 63]));
+ b.inc(1 << 63);
+ assert_eq!(b, BigInt::from_vec(vec![0, 1]));
+ b.inc(1 << 63);
+ assert_eq!(b, BigInt::from_vec(vec![1 << 63, 1]));
+ b.inc(1 << 63);
+ assert_eq!(b, BigInt::from_vec(vec![0, 2]));
+}
--- /dev/null
+use std::cmp;
+use std::ops;
+use part05::BigInt;
+
+// Add with carry, returning the sum and the carry
+fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
+ let sum = u64::wrapping_add(a, b);
+ if sum >= a {
+ panic!("First addition did not overflow. Not implemented.");
+ } else {
+ panic!("First addition *did* overflow. Not implemented.");
+ }
+}
+
+/*#[test]*/
+fn test_overflowing_add() {
+ assert_eq!(overflowing_add(10, 100, false), (110, false));
+ assert_eq!(overflowing_add(10, 100, true), (111, false));
+ assert_eq!(overflowing_add(1 << 63, 1 << 63, false), (0, true));
+ assert_eq!(overflowing_add(1 << 63, 1 << 63, true), (1, true));
+ assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
+}
+
+impl ops::Add for BigInt {
+ type Output = BigInt;
+ fn add(self, rhs: BigInt) -> Self::Output {
+ let mut result_vec:Vec<u64> = Vec::with_capacity(cmp::max(self.data.len(), rhs.data.len()));
+ panic!("Not yet implemented.");
+ }
+}
projects / rust-101.git / commitdiff