make exercise more clear

[rust-101.git] / solutions / src / bigint.rs

diff --git a/solutions/src/bigint.rs b/solutions/src/bigint.rs
index e9dfdf0b9edfe9a3a627e7971e98eb2697ebeb5d..5869ba89401076c8998bb7414dae31e71a3d738c 100644 (file)
--- a/solutions/src/bigint.rs
+++ b/solutions/src/bigint.rs
@@ -2,29 +2,54 @@ use std::ops;
 use std::cmp;
 use std::fmt;
 
 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) {
 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)

     }
 }
 
     }
 }
 

+// Subtract with carry, returning the difference and the carry
+fn overflowing_sub(a: u64, b: u64, carry: bool) -> (u64, bool) {
+    let diff = u64::wrapping_sub(a, b);
+    let carry_n = if carry { 1 } else { 0 };
+    if diff <= a { // the first diff did not wrap
+        let diff_total = u64::wrapping_sub(diff, carry_n);
+        let had_wrap = diff_total > diff;
+        (diff_total, had_wrap)
+    } else { // the first diff did wrap
+        // it is impossible for this to wrap again, as we are just substracting 0 or 1
+        (diff - carry_n, true)
+    }
+}

 
 impl BigInt {
     /// Construct a BigInt from a "small" one.
 
 impl BigInt {
     /// Construct a BigInt from a "small" one.


@@ -44,50 +69,33 @@ impl BigInt {
         }
     }
 
         }
     }
 

-    /// Construct a BigInt from a vector of 64-bit "digits", with the last significant digit being first
+    /// Construct a BigInt from a vector of 64-bit "digits", with the last significant digit being first. Solution to 05.1.

     pub fn from_vec(mut v: Vec<u64>) -> Self {
     pub fn from_vec(mut v: Vec<u64>) -> Self {

-        // remove trailing zeroes
+        // remove trailing zeros

         while v.len() > 0 && v[v.len()-1] == 0 {
             v.pop();
         }
         BigInt { data: v }
     }
 
         while v.len() > 0 && v[v.len()-1] == 0 {
             v.pop();
         }
         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;
-                }
+    /// Increments the number by 1.
+    pub fn inc1(&mut self) {
+        let mut idx = 0;
+        // This loop adds "(1 << idx)". If there is no more carry, we leave.
+        while idx < self.data.len() {
+            let cur = self.data[idx];
+            let sum = u64::wrapping_add(cur, 1);
+            self.data[idx] = sum;
+            if sum >= cur {
+                // No overflow, we are done.
+                return;
+            } else {
+                // We need to go on.
+                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[..]
+        // If we came here, there is a last carry to add
+        self.data.push(1);

     }
 
     /// Increments the number by "by".
     }
 
     /// Increments the number by "by".


@@ -129,34 +137,66 @@ impl Clone for BigInt {
     }
 }
 
     }
 }
 

-

 impl PartialEq for BigInt {
     fn eq(&self, other: &BigInt) -> bool {
         debug_assert!(self.test_invariant() && other.test_invariant());
 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 {
+    // This is essentially the solution to 06.1.
+    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();
+            while idx > 0 {
+                idx = idx-1;
+                if self.data[idx] < other.data[idx] {
+                    return self;
+                } else if self.data[idx] > other.data[idx] {
+                    return other;
+                }
+            }
+            // the two are equal
+            return self;
+        }

     }
 }
 
 impl fmt::Debug for BigInt {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
     }
 }
 
 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 {
     }
 }
 
 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 max_len = cmp::max(self.data.len(), rhs.data.len());
+        let mut result_vec:Vec<u64> = Vec::with_capacity(max_len);

         let mut carry:bool = false; // the carry bit
         let mut carry:bool = false; // the carry bit

-        for (i, val) in self.data().into_iter().enumerate() {
+        for i in 0..max_len {

             // compute next digit and carry
             // 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);
+            let lhs_val = if i < self.data.len() { self.data[i] } else { 0 };
+            let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
+            let (sum, new_carry) = overflowing_add(lhs_val, rhs_val, carry);

             // store them
             result_vec.push(sum);
             carry = new_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, one od the two digits
+        // is the last of its number and hence not 0.
+        BigInt { data: result_vec }

     }
 }
 
     }
 }
 


@@ -184,10 +224,81 @@ impl ops::Add<BigInt> for BigInt {
     }
 }
 
     }
 }
 

+impl<'a, 'b> ops::Sub<&'a BigInt> for &'b BigInt {
+    type Output = BigInt;
+    fn sub(self, rhs: &'a BigInt) -> Self::Output {
+        let max_len = cmp::max(self.data.len(), rhs.data.len());
+        let mut result_vec:Vec<u64> = Vec::with_capacity(max_len);
+        let mut carry:bool = false; // the carry bit
+        for i in 0..max_len {
+            // compute next digit and carry
+            let lhs_val = if i < self.data.len() { self.data[i] } else { 0 };
+            let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
+            let (sum, new_carry) = overflowing_sub(lhs_val, rhs_val, carry);
+            // store them
+            result_vec.push(sum);
+            carry = new_carry;
+        }
+        if carry {
+            panic!("Wrapping subtraction of BigInt");
+        }
+        // We may have trailing zeroes, so get rid of them
+        BigInt::from_vec(result_vec)
+    }
+}
+
+impl<'a> ops::Sub<BigInt> for &'a BigInt {
+    type Output = BigInt;
+    #[inline]
+    fn sub(self, rhs: BigInt) -> Self::Output {
+        self - &rhs
+    }
+}
+
+impl<'a> ops::Sub<&'a BigInt> for BigInt {
+    type Output = BigInt;
+    #[inline]
+    fn sub(self, rhs: &'a BigInt) -> Self::Output {
+        &self - rhs
+    }
+}
+
+impl ops::Sub<BigInt> for BigInt {
+    type Output = BigInt;
+    #[inline]
+    fn sub(self, rhs: BigInt) -> Self::Output {
+        &self - &rhs
+    }
+}
+

 #[cfg(test)]
 mod tests {
 #[cfg(test)]
 mod tests {

-    use super::overflowing_add;
-    use super::BigInt;
+    use std::u64;
+    use super::{overflowing_add,overflowing_sub,BigInt,Minimum,vec_min};
+
+    #[test]
+    fn test_min() {
+        let b1 = BigInt::new(1);
+        let b2 = BigInt::new(42);
+        let b3 = BigInt::from_vec(vec![0, 1]);
+
+        assert_eq!(b1.min(&b2), &b1);
+        assert_eq!(b2.min(&b1), &b1);
+        assert_eq!(b3.min(&b2), &b2);
+        assert_eq!(b2.min(&b3), &b2);
+    }
+
+    #[test]
+    fn test_vec_min() {
+    let b1 = BigInt::new(1);
+        let b2 = BigInt::new(42);
+        let b3 = BigInt::from_vec(vec![0, 1]);
+
+        assert_eq!(vec_min(&vec![b2.clone(), b1.clone(), b3.clone()]), Some(&b1));
+        assert_eq!(vec_min(&vec![b2.clone(), b3.clone()]), Some(&b2));
+        assert_eq!(vec_min(&vec![b3.clone()]), Some(&b3));
+        assert_eq!(vec_min::<BigInt>(&vec![]), None);
+    }

 
     #[test]
     fn test_overflowing_add() {
 
     #[test]
     fn test_overflowing_add() {


@@ -198,6 +309,72 @@ mod tests {
         assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
     }
 
         assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
     }
 

+    #[test]
+    fn test_overflowing_sub() {
+        assert_eq!(overflowing_sub(100, 10, false), (90, false));
+        assert_eq!(overflowing_sub(100, 10, true), (89, false));
+        assert_eq!(overflowing_sub(10, 1 << 63, false), ((1 << 63) + 10, true));
+        assert_eq!(overflowing_sub(10, 1 << 63, true), ((1 << 63) + 9, true));
+        assert_eq!(overflowing_sub(42, 42 , true), (u64::max_value(), true));
+    }
+
+    #[test]
+    fn test_add() {
+        let b1 = BigInt::new(1 << 32);
+        let b2 = BigInt::from_vec(vec![0, 1]);
+        let b3 = BigInt::from_vec(vec![0, 0, 1]);
+        let b4 = BigInt::new(1 << 63);
+
+        assert_eq!(&b1 + &b2, BigInt::from_vec(vec![1 << 32, 1]));
+        assert_eq!(&b2 + &b1, BigInt::from_vec(vec![1 << 32, 1]));
+        assert_eq!(&b2 + &b3, BigInt::from_vec(vec![0, 1, 1]));
+        assert_eq!(&b2 + &b3 + &b4 + &b4, BigInt::from_vec(vec![0, 2, 1]));
+        assert_eq!(&b2 + &b4 + &b3 + &b4, BigInt::from_vec(vec![0, 2, 1]));
+        assert_eq!(&b4 + &b2 + &b3 + &b4, BigInt::from_vec(vec![0, 2, 1]));
+    }
+
+    #[test]
+    fn test_sub() {
+        let b1 = BigInt::new(1 << 32);
+        let b2 = BigInt::from_vec(vec![0, 1]);
+        let b3 = BigInt::from_vec(vec![0, 0, 1]);
+        let b4 = BigInt::new(1 << 63);
+
+        assert_eq!(&b2 - &b1, BigInt::from_vec(vec![u64::max_value() - (1 << 32) + 1]));
+        assert_eq!(&b3 - &b2, BigInt::from_vec(vec![0, u64::max_value(), 0]));
+        assert_eq!(&b2 - &b4 - &b4, BigInt::new(0));
+        assert_eq!(&b3 - &b2 - &b4 - &b4, BigInt::from_vec(vec![0, u64::max_value() - 1]));
+        assert_eq!(&b3 - &b4 - &b2 - &b4, BigInt::from_vec(vec![0, u64::max_value() - 1]));
+        assert_eq!(&b3 - &b4 - &b4 - &b2, BigInt::from_vec(vec![0, u64::max_value() - 1]));
+    }
+
+    #[test]
+    #[should_panic(expected = "Wrapping subtraction of BigInt")]
+    fn test_sub_panic1() {
+        let _ = BigInt::new(1) - BigInt::new(5);
+    }
+
+    #[test]
+    #[should_panic(expected = "Wrapping subtraction of BigInt")]
+    fn test_sub_panic2() {
+        let _ = BigInt::from_vec(vec![5,8,3,33,1<<13,46,1<<49, 1, 583,1<<60,2533]) - BigInt::from_vec(vec![5,8,3,33,1<<13,46,1<<49, 5, 583,1<<60,2533]);
+    }
+
+    #[test]
+    fn test_inc1() {
+        let mut b = BigInt::new(0);
+        b.inc1();
+        assert_eq!(b, BigInt::new(1));
+        b.inc1();
+        assert_eq!(b, BigInt::new(2));
+
+        b = BigInt::new(u64::MAX);
+        b.inc1();
+        assert_eq!(b, BigInt::from_vec(vec![0, 1]));
+        b.inc1();
+        assert_eq!(b, BigInt::from_vec(vec![1, 1]));
+    }
+

     #[test]
     fn test_power_of_2() {
         assert_eq!(BigInt::power_of_2(0), BigInt::new(1));
     #[test]
     fn test_power_of_2() {
         assert_eq!(BigInt::power_of_2(0), BigInt::new(1));