CS100 Lecture 20

Iterators and Algorithms

Contents

• Iterators
• Algorithms

Iterators

A generalized "pointer" used for accessing elements in different containers.

Every container has its iterator, whose type is Container::iterator.

e.g. std::vector<int>::iterator, std::forward_list<std::string>::iterator

• auto comes to our rescue!

Iterators

For any container object c,

• c.begin() returns the iterator to the first element of c.
• c.end() returns the iterator to the position following the last element of c ("off-the-end", "past-the-end").

Iterators

A pair of iterators (b, e) is often used to indicate a range [b, e).

Such ranges are left-inclusive. Benefits:

• e - b is the length (size) of the range, i.e. the number of elements. There is no extra +1 or -1 in this expression.
• If b == e, the range is empty. In other words, to check whether the range is empty, we only need to do an equality test, which is easily supported by all kinds of iterators.

Iterators

Basic operations, supported by almost all kinds of iterators:

• *it: returns a reference to the element that it refers to.
• it->mem: equivalent to (*it).mem.
• ++it, it++: moves it one step forward, so that it refers to the "next" element.
  • ++it returns a reference to it, while it++ returns a copy of it before incrementation.
• it1 == it2: checks whether it1 and it2 refer to the same position in the container.
• it1 != it2: equivalent to !(it1 == it2).

These are supported by the iterators of all sequence containers, as well as std::string.

Iterators

Use the basic operations to traverse a sequence container:

void swapcase(std::string &str) {
  for (auto it = str.begin(); it != str.end(); ++it) {
    if (std::islower(*it))
      *it = std::toupper(*it);
    else if (std::isupper(*it))
      *it = std::tolower(*it);
  }
}
void print(const std::vector<int> &vec) {
  for (auto it = vec.begin(); it != vec.end(); ++it)
    std::cout << *it << ' ';
}

Iterators

Built-in pointers are also iterators: They are the iterator for built-in arrays.

For an array Type a[N]:

• The "begin" iterator is a.
• The "end" (off-the-end) iterator is a + N.

The standard library functions std::begin(c) and std::end(c) (defined in <iterator> and many other header files):

• return c.begin() and c.end() if c is a container;
• return c and c + N if c is an array of length N.

Range-for demystified

The range-based for loop

for (@declaration : container)
  @loop_body

is equivalent to

{
  auto b = std::begin(container);
  auto e = std::end(container);
  for (; b != e; ++b) {
    @declaration = *b;
    @loop_body
  }
}

Iterators: dereferenceable

Like pointers, an iterator can be dereferenced (*it) only when it refers to an existing element. ("dereferenceable")

• *v.end() is undefined behavior.
• ++it is undefined behavior if it is not dereferenceable. In other words, moving an iterator out of the range [begin, off_the_end] is undefined behavior.

Iterators: invalidation

Type *storage = new Type[n];
Type *iter = storage;
delete[] storage;
// Now `iter` does not refer to any existing element.

Some operations on some containers will invalidate some iterators:

• make these iterators not refer to any existing element.

For example:

• push_back(x) on a std::vector may cause the reallocation of storage. All iterators obtained previously are invalidated.
• pop_back() on a std::vector will invalidate the iterators that points to the deleted element.

Never use invalidated iterators or references!

void foo(std::vector<int> &vec) {
  auto it = vec.begin();
  while (some_condition(vec))
    vec.push_back(*it++); // Undefined behavior.
}

After several calls to push_back, vec may reallocate a larger chunk of memory to store its elements. This will invalidate all pointers, references and iterators that point to somewhere in the previous memory block.

More operations on iterators

The iterators of containers that support *it, it->mem, ++it, it++, it1 == it2 and it1 != it2 are ForwardIterators.

BidirectionalIterator: a ForwardIterator that can be moved in both directions

• supports --it and it--.

RandomAccessIterator: a BidirectionalIterator that can be moved to any position in constant time.

• supports it + n, n + it, it - n, it += n, it -= n for an integer n.
• supports it[n], equivalent to *(it + n).
• supports it1 - it2, returns the distance of two iterators.
• supports <, <=, >, >=.

More operations on iterators

The iterators of containers that support *it, it->mem, ++it, it++, it1 == it2 and it1 != it2 are ForwardIterators.

BidirectionalIterator: a ForwardIterator that can be moved in both directions

• supports --it and it--.

RandomAccessIterator: a BidirectionalIterator that can be moved to any position in constant time.

• supports it + n, n + it, it - n, it += n, it -= n, it[n], it1 - it2, <, <=, >, >=.
• std::string::iterator and std::vector<T>::iterator are in this category.

Which category is the built-in pointer in?

More operations on iterators

The iterators of containers that support *it, it->mem, ++it, it++, it1 == it2 and it1 != it2 are ForwardIterators.

BidirectionalIterator: a ForwardIterator that can be moved in both directions

• supports --it and it--.

RandomAccessIterator: a BidirectionalIterator that can be moved to any position in constant time.

• supports it + n, n + it, it - n, it += n, it -= n, it[n], it1 - it2, <, <=, >, >=.
• std::string::iterator and std::vector<T>::iterator are in this category.

Which category is the built-in pointer in? - RandomAccessIterator.

Initialization from iterator range

std::string, std::vector, as well as other standard library containers, support the initialization from an iterator range:

std::vector<char> v = {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'};
std::vector v2(v.begin() + 2, v.end() - 3);  // {'c', 'd', 'e', 'f'}
std::string s(v.begin(), v.end()); // "abcdefghi"

Algorithms

Algorithms

Full list of standard library algorithms can be found here.

No one can remember all of them, but some are quite commonly used.

Algorithms: interfaces

Parameters: The STL algorithms accept pairs of iterators to represent "ranges":

int a[N], b[N]; std::vector<int> v;
std::sort(a, a + N);
std::sort(v.begin(), v.end());
std::copy(a, a + N, b); // copies elements in [a, a+N) to [b, b+N)
std::sort(v.begin(), v.begin() + 10); // Only the first 10 elements are sorted.

Since C++20, std::ranges::xxx can be used, which has more modern interfaces

std::ranges::sort(a);
std::ranges::copy(a, b);

Algorithms: interfaces

Parameters: The algorithms suffixed _n use a beginning iterator begin and an integer n to represent a range [begin, begin + n).

Example: Use STL algorithms to rewrite the constructors of Dynarray:

Dynarray::Dynarray(const int *begin, const int *end)
    : m_storage{new int[end - begin]}, m_length(end - begin) {
  std::copy(begin, end, m_storage);
}
Dynarray::Dynarray(const Dynarray &other)
    : m_storage{new int[other.size()]}, m_length{other.size()} {
  std::copy_n(other.m_storage, other.size(), m_storage);
}
Dynarray::Dynarray(std::size_t n, int x = 0)
    : m_storage{new int[n]}, m_length{n} {
  std::fill_n(m_storage, m_length, x);
}

Algorithms: interfaces

Return values: "Position" is typically represented by an iterator. For example:

std::vector<int> v = someValues();
auto pos = std::find(v.begin(), v.end(), 42);
assert(*pos == 42);
auto maxPos = std::max_element(v.begin(), v.end());

• pos is an iterator pointing to the first occurrence of 42 in v.
• maxPos is an iterator pointing to the max element in v.

"Not found" / "No such element" is often indicated by returning end.

if (std::find(v.begin(), v.end(), something) != v.end()) {
  // ...
}

if: new syntax in C++17

"Not found" / "No such element" is often indicated by returning end.

if (std::find(v.begin(), v.end(), something) != v.end()) { /* (*) */ }

If we want to use the returned iterator in (*):

if (auto pos = std::find(v.begin(), v.end(), something); pos != v.end())
  std::cout << *pos << '\n';

The new syntax of if in C++17: if (init_expr; condition).

• init_expr is just like the first part of the for statement.
• The scope of the variable declared in init_expr is within this if statement (containing the else clause, if present).

Algorithms: requirements

An algorithm may have requirements on

• the iterator categories of the passed-in iterators, and
• the type of elements that the iterators point to.

Typically, std::sort requires RandomAccessIterators, while std::copy allows any InputIterators.

Typically, all algorithms that need to compare elements rely only upon operator< and operator== of the elements.

• You don't have to define all the six comparison operators of X in order to sort a vector<X>. sort only requires operator<.

Algorithms

Since we pass iterators instead of containers to algorithms, the standard library algorithms never modify the length of the containers.

• STL algorithms never insert or delete elements in the containers (unless the iterator passed to them is some special iterator adapter).

For example: std::copy only copies elements, instead of inserting elements.

std::vector<int> a = someValues();
std::vector<int> b(a.size());
std::vector<int> c{};
std::copy(a.begin(), a.end(), b.begin()); // OK
std::copy(a.begin(), a.end(), c.begin()); // Undefined behavior!

Some common algorithms (<algorithm>)

Non-modifying sequence operations:

• count(begin, end, x), find(begin, end, x), find_end(begin, end, x), find_first_of(begin, end, x), search(begin, end, pattern_begin, pattern_end)

Modifying sequence operations:

• copy(begin, end, dest), fill(begin, end, x), reverse(begin, end), ...
• unique(begin, end): drop duplicate elements.
  • requires the elements in the range [begin, end) to be sorted (in ascending order by default).
  • It does not remove any elements! Instead, it moves all the duplicated elements to the end of the sequence, and returns an iterator pos, so that [begin, pos) has no duplicate elements.

Some common algorithms (<algorithm>)

Example: unique

std::vector v{1, 1, 2, 2, 2, 3, 5};
auto pos = std::unique(v.begin(), v.end());
// Now [v.begin(), pos) contains {1, 2, 3, 5}.
// [pos, v.end()) has the values {1, 2, 2}, but the exact order is not known.
v.erase(pos, v.end()); // Typical use with the container's `erase` operation
// Now v becomes {1, 2, 3, 5}.

unique does not remove the duplicate elements! To remove them, use the container's erase operation.

Some common algorithms (<algorithm>)

Partitioning, sorting and merging algorithms:

• partition, is_partitioned, stable_partition
• sort, is_sorted, stable_sort
• nth_element
• merge, inplace_merge

Binary search on sorted ranges:

• lower_bound, upper_bound, binary_search, equal_range

Heap algorithms:

• is_heap, make_heap, push_heap, pop_heap, sort_heap

Learn the underlying algorithms and data structures of these functions in CS101!

Some common algorithms

Min/Max and comparison algorithms: (<algorithm>)

• min_element(begin, end), max_element(begin, end), minmax_element(begin, end)
• equal(begin1, end1, begin2), equal(begin1, end1, begin2, end2)
• lexicographical_compare(begin1, end1, begin2, end2)

Numeric operations: (<numeric>)

• accumulate(begin, end, initValue): Sum of elements in [begin, end), with initial value initValue.
  • accumulate(v.begin(), v.end(), 0) returns the sum of elements in v.
• inner_product(begin1, end1, begin2, initValue): Inner product of two vectors , added with the initial value initValue.

Predicates

Consider the Point2d class:

struct Point2d {
  double x, y;
};
std::vector<Point2d> points = someValues();

Suppose we want to sort points in ascending order of the x coordinate.

• std::sort requires operator< in order to compare the elements,
• but it is not recommended to overload operator< here! (What if we want to sort some Point2ds in another way?)

(C++20 modern way: std::ranges::sort(points, {}, &Point2d::x);)

Predicates

std::sort has another version that accepts another argument cmp:

bool cmp_by_x(const Point2d &lhs, const Point2d &rhs) {
  return lhs.x < rhs.x;
}
std::sort(points.begin(), points.end(), cmp_by_x);

sort(begin, end, cmp)

• cmp is a Callable object. When called, it accepts two arguments whose type is the same as the element type, and returns bool.
• std::sort will use cmp(x, y) instead of x < y to compare elements.
• After sorting, cmp(v[i], v[i + 1]) is true for every i [0, v.size()-1).

Predicates

To sort numbers in reverse (descending) order:

bool greater_than(int a, int b) { return a > b; }
std::sort(v.begin(), v.end(), greater_than);

To sort them in ascending order of absolute values:

bool abs_less(int a, int b) { return std::abs(a) < std::abs(b); } // <cmath>
std::sort(v.begin(), v.end(), abs_less);

Predicates

Many algorithms accept a Callable object. For example, find_if(begin, end, pred) finds the first element in [begin, end) such that pred(element) is true.

bool less_than_10(int x) {
  return x < 10;
}
std::vector<int> v = someValues();
auto pos = std::find_if(v.begin(), v.end(), less_than_10);

for_each(begin, end, operation) performs operation(element) for each element in the range [begin, end).

void print_int(int x) { std::cout << x << ' '; }
std::for_each(v.begin(), v.end(), print_int);

Predicates

Many algorithms accept a Callable object. For example, find_if(begin, end, pred) finds the first element in [begin, end) such that pred(element) is true.

What if we want to find the first element less than k, where k is determined at run-time?

Predicates

What if we want to find the first element less than k, where k is determined at run-time?

struct LessThan {
  int k_;
  LessThan(int k) : k_{k} {}
  bool operator()(int x) const {
    return x < k_;
  }
};
auto pos = std::find_if(v.begin(), v.end(), LessThan(k));

• LessThan(k) constructs an object of type LessThan, with the member k_ initialized to k.
• This object has an operator() overloaded: the function-call operator.
  • LessThan(k)(x) is equivalent to LessThan(k).operator()(x), which is x < k.

Function objects

Modern way:

struct LessThan {
  int k_; // No constructor is needed, and k_ is public.
  bool operator()(int x) const { return x < k_; }
};
auto pos = std::find_if(v.begin(), v.end(), LessThan{k}); // {} instead of ()

A function object (aka "functor") is an object fo with operator() overloaded.

• fo(arg1, arg2, ...) is equivalent to fo.operator()(arg1, arg2, ...). Any number of arguments is allowed.

Function objects

Exercise: use a function object to compare integers by their absolute values.

struct AbsCmp {
  bool operator()(int a, int b) const {
    return std::abs(a) < std::abs(b);
  }
};
std::sort(v.begin(), v.end(), AbsCmp{});

Lambda expressions

Defining a function or a function object is not good enough:

• These functions or function objects are almost used only once, but
• too many lines of code is needed, and
• you have to add names to the global scope.

Is there a way to define an unnamed, immediate callable object?

Lambda expressions

To sort by comparing absolute values:

std::sort(v.begin(), v.end(),
          [](int a, int b) -> bool { return std::abs(a) < std::abs(b); });

To sort in reverse order:

std::sort(v.begin(), v.end(),
          [](int a, int b) -> bool { return a > b; });

To find the first element less than k:

auto pos = std::find_if(v.begin(), v.end(),
                        [k](int x) -> bool { return x < k; });

Lambda expressions

The return type can be omitted and deduced by the compiler.

std::sort(v.begin(), v.end(),
          [](int a, int b) { return std::abs(a) < std::abs(b); });

std::sort(v.begin(), v.end(), [](int a, int b) { return a > b; });

auto pos = std::find_if(v.begin(), v.end(), [k](int x) { return x < k; });

Lambda expressions

A lambda expression has the following syntax:

[capture_list](params) -> return_type { function_body }

The compiler will generate a function object according to it.

int k = 42;
auto f = [k](int x) -> bool { return x < k; };
bool b1 = f(10); // true
bool b2 = f(100); // false

Lambda expressions

[capture_list](params) -> return_type { function_body }

It is allowed to write complex statements in function_body, just as in a function.

struct Point2d { double x, y; };
std::vector<Point2d> points = somePoints();
// prints the l2-norm of every point
std::for_each(points.begin(), points.end(),
              [](const Point2d &p) {
                auto norm = std::sqrt(p.x * p.x + p.y * p.y);
                std::cout << norm << std::endl;
              });

Lambda expressions: capture

To capture more variables:

auto pos = std::find_if(v.begin(), v.end(),
                    [lower, upper](int x) { return lower <= x && x <= upper;});

To capture by reference (so that copy is avoided)

std::string str = someString();
std::vector<std::string> wordList;
// finds the first string that is lexicographically greater than `str`,
// but shorter than `str`.
auto pos = std::find_if(wordList.begin(), wordList.end(),
     [&str](const std::string &s) { return s > str && s.size() < str.size();});

Here &str indicates that str is captured by referece. & here is not the address-of operator!

More on lambda expressions

• C++ Primer Section 10.3
• Effective Modern C++ Chapter 6 (Item 31-34)

Note that C++ Primer (5th edition) is based on C++11 and Effective Modern C++ is based on C++14. Lambda expressions are evolving at a very fast pace in modern C++, with many new things added and many limitations removed.

More fancy ways of writing lambda expressions are not covered in CS100.

Back to algorithms

So many things in the algorithm library! How can we remember them?

• Remember the conventions:
  • No insertion/deletion of elements
  • Iterator range [begin, end)
  • Functions named with the suffix _n uses [begin, begin + n)
  • Pass functions, function objects, and lambdas for customized operations
  • Functions named with the suffix _if requires a boolean predicate
• Remember the common ones: copy, find, for_each, sort, ...
• Look them up in cppreference before use.

Summary

Iterators

• A generalized "pointer" used for accessing elements in different containers.
• Iterator range: a left-inclusive interval [b, e).
• c.begin(), c.end()
• Basic operations: *it, it->mem, ++it, it++, it1 == it2, it1 != it2.
• Range-based for loops are in fact traversal using iterators.
• More operations: BidirectionalIterator supports it-- and --it. RandomAccessIterator supports all pointer arithmetics.
• Initialization of standard library containers from an iterator range.

Summary

Algorithms

• Normal functions accept iterator range [b, e). Functions with _n accept an iterator and an integer, representing the range [begin, begin + n).
• Position is represented by an iterator.
• STL algorithms never insert or delete elements in the containers.
• Some algorithms accept a predicate argument, which is a callable object. It can be a function, a pointer to function, an object of some type that has an overloaded operator(), or a lambda.
• Lambda: [capture_list][params] -> return_type { function_body }