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CS253 Algorithms

First published computer algorithm, by Ada Lovelace

Definition

In Computer Science, algorithm means “how to do something”.
In C++, algorithm refers to templatized functions from the <algorithm> header file.
There are many algorithms in <algorithm>. We will focus on a few:
count() copy_if()

count_if() replace()

find() transform()

find_if() sort()

copy() unique()

Arguments

Algorithms generally take their input from half-open iterator ranges, which always (?) come first.
For output, algorithms take a single iterator, which says where the output starts.
A second iterator indicating the end of the output is not required, since the length of the output is determined by the size of the input, possibly filtered in some way, as in copy_if().
Additional arguments may specify a value to look for, a predicate to select items, etc.

count()

vector v = {1, 1,2, 1,2,3, 1,2,3,4};
cout << count(v.begin(), v.end(), 2) << '\n'
     << count(v.begin(), v.end(), 3.0) << '\n';

3
2

count() counts how many times a thing is found. 🤯
The first two arguments form a half-open interval, which is exactly what .begin() and .end() give, since .end() “points” one past the last element.
Each element in the interval is compared to the third argument, which does not have to be the same type as the items in the range.
The interval can be two iterators into any sort of container. As long as the first iterator can be incremented, and compared to the second iterator, and assuming that the first iterator will eventually become equal to the second, it’s ok.
Pointers are iterators, so pointers into C arrays, C strings, or the heap are ok.

count_if()

bool small(int n) {
    return n < 5;
}

int main() {
    multiset ms = {3,1,4,1,5,9,2,6,5,3,5,8,9,7,9};
    cout << count_if(ms.begin(), ms.end(), small) << '\n'
         << count_if(ms.begin(), ms.end(),
                     [](int n){return n>7;}) << '\n';
}

6
4

count_if() is like count(), except it takes a predicate (a function that returns a bool) instead of a target value.

find()

The find() algorithm searches a half-open range for a value.
If it finds the value, it returns:
- not an index to the value found ✘
- not a pointer to the value found ✘
- an iterator that “points” to the value found. ✔️
- What type of iterator? The same type that you gave it to indicate the range.
If it can’t find the value, it returns:
- not a 0 or −1 ✘
- not a null pointer ✘
- not a pointer ✘
- the second iterator given; the end of the half-open interval. ✔️
OK, technically, if you give find() raw pointers, then it does return the same type, namely, a pointer.

find()

vector primes{ 2,  3,  5,  7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
              43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };

auto it = find(primes.begin(), primes.end(), 13);
if (it == primes.end())
    cout << "not found\n";
else
    cout << "Found "<< *it << " at " << it-primes.begin() << '\n';

Found 13 at 5

An algorithm; not a method! Some containers have a .find() method, which is preferred, if it exists.

find()

vector primes{ 2,  3,  5,  7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
              43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };

int *start = &primes[3], *end = &primes[20];

cout << "Search the interval [" << *start << ',' << *end << ")\n"
     << "It includes " << *start << ", but not " << *end << '\n';

int *p = find(start, end, 13);
cout << "Found " << *p << " at " << p-&primes[0] << '\n';

p = find(start, end, 89);
cout << "Nope " << *p << " at " << p-&primes[0] << '\n';

Search the interval [7,73)
It includes 7, but not 73
Found 13 at 5
Nope 73 at 20

find_if()

bool pred(int n) {
    return n > 50;                  // Should find 53
}

int main() {
    set primes{ 2,  3,  5,  7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
               43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };
    if (auto it = find_if(primes.begin(), primes.end(), pred); it == primes.end())
        cout << "Failure\n";
    else
        cout << "Found " << *it << '\n';
}

Found 53

Note the C++17 if statement with if (init; condition)
find_if() is like find(), except that it takes a predicate instead of target value.

copy()

string str = "bonehead";
set alpha = {'P', 'D', 'Q'};
copy(alpha.begin(), alpha.end(), str.begin());
cout << str << '\n';

DPQehead

string alpha = "abcdefghijklmnopqrstuvwxyz";
string initials = "JRA";
copy(initials.begin(), initials.begin()+2, alpha.begin()+20);
cout << alpha << '\n';

abcdefghijklmnopqrstJRwxyz

The iterator arguments don’t just have to be .begin() and .end().

copy_if()

copy_if() is like copy(), except that it doesn’t copy everything.
Instead it takes a predicate that determines whether or not to copy a given element.
- A predicate is a function that returns bool.
copy_if() takes three iterators and a predicate:
copy_if(source-begin, source-end, dest-begin, predicate)

Why isn’t there a dest-end ?

It isn’t needed. source-begin and source-end say how much to copy.

First attempt

Let’s ensure that we know how to use copy() before moving on to copy_if():

string foo = "I have to ration my Diet Mountain Dew!";
cout << foo << "\n";
string bar;
copy(foo.begin(), foo.end(), bar.begin());
cout << bar << "\n";

SIGSEGV: Segmentation fault

Of course, plain bar = foo; would have worked nicely.

Why did that fail?

There is no space allocated in bar. You can’t allocate space by pretending that it exists.

Second attempt

string foo = "I have to ration my Diet Mountain Dew!";
cout << foo << "\n";
string bar;
bar.resize(foo.size());
copy(foo.begin(), foo.end(), bar.begin());
cout << bar << "\n";

I have to ration my Diet Mountain Dew!
I have to ration my Diet Mountain Dew!

There—we allocated enough space in bar, via string::resize().
Fine, we’ve mastered copy(), so we’ll move on to copy_if().

Third attempt

string foo = "I have to ration my Diet Mountain Dew!";
cout << foo << "\n";
string bar;
bar.resize(foo.size());
// Don’t copy vowels:
copy_if(foo.begin(), foo.end(), bar.begin(),
        [](char c){return "aeiouAEIOU"s.find(c)==string::npos;} );

cout << bar << "\n";

I have to ration my Diet Mountain Dew!
 hv t rtn my Dt Mntn Dw!␀␀␀␀␀␀␀␀␀␀␀␀␀␀

Hooray, copy_if() worked!

Hey, what’s with those ␀ characters?

.resize() filled the string with '\0', which display as ␀ here. Your terminal may simply ignore them and so not display them. bar.size() is unchanged.

Fourth attempt

string foo = "I have to ration my Diet Mountain Dew!";
cout << foo << "\n";

string bar(foo.size(), 'X');
// Don’t copy vowels:
auto it = copy_if(foo.begin(), foo.end(), bar.begin(),
                  [](char c){return "aeiouAEIOU"s.find(c)==string::npos;} );

// Make bar the correct size:
bar.resize(it-bar.begin());
cout << bar << "\n";

I have to ration my Diet Mountain Dew!
 hv t rtn my Dt Mntn Dw!

We resized bar to the correct size.

In-place

string foo = "I have to ration my Diet Mountain Dew!";
cout << foo << "\n";

auto it = copy_if(foo.begin(), foo.end(), foo.begin(),
                  [](char c){return "aeiouyAEIOUY"s.find(c)==string::npos;} );
// Make foo the correct size:
foo.resize(it-foo.begin());
cout << foo << "\n";

I have to ration my Diet Mountain Dew!
 hv t rtn m Dt Mntn Dw!

We can copy from & to the same location.

replace()

string fact = "Warren Harding’s middle name was Gamaliel.";
replace(fact.begin(), fact.end(), ' ', '_');
cout << fact << '\n';

Warren_Harding’s_middle_name_was_Gamaliel.

string fact = "Warren Harding’s middle name was Gamaliel.";
replace_if(fact.begin(), fact.end(),
           [](char c) { return c=='o' || c=='a';}, '*');
cout << fact << '\n';

W*rren H*rding’s middle n*me w*s G*m*liel.

transform()

string name = "Joseph Robinette Biden Jr.";
string out;
transform(name.begin(), name.end(), out.begin(),
          [](char c) { return c ^ 040; });
cout << out << '\n';

SIGSEGV: Segmentation fault

Oops! Didn’t allocate any memory in out!

string name = "Joseph Robinette Biden Jr.";
string out;
out.resize(name.size());
transform(name.begin(), name.end(), out.begin(),
          [](char c) { return c ^ 040; });
cout << out << '\n';

jOSEPH␀rOBINETTE␀bIDEN␀jR␎

sort()

The sort() algorithm (from the header file <algorithm>) has two forms:

sort(begin, end );
sort(begin, end, comparison-object-or-function);
Only a single half-open interval is given.
- It’s an in-place sort.

How do I sort() from container1 to container2?

copy() to container2, sort() the data there. It’s still O(N).

Containers

Of course, some containers are intrinsically sorted.
You might specify a comparison functor for those containers.
You wouldn’t use sort() algorithm on those containers.
However, you might want to apply the sort() algorithm to an unsorted container, such as a std::array, vector, string, or even a C array.
list has a sort() method.

Default comparison

string s = "Kokopelli";
sort(s.begin(), s.end());
cout << s << '\n';

Keiklloop

Explicit comparison

string s = "Kokopelli";
sort(s.begin(), s.end(), less<char>);
cout << s << '\n';

c.cc:2: error: expected primary-expression before ')' token

Why doesn’t that work?

What does sort() want for the third argument?

It wants something that the function call operator () works on: a function or functor object.

What kind of thing is less<char>?

It’s a type. Not an object—a type.
However, less<char>() is an object of that type.

Can you pass a type as a function argument?

No. An object of that type, sure, but not a type.

Explicit comparison

string s = "Kokopelli";
sort(s.begin(), s.end(), less<char>());
cout << s << '\n';

Keiklloop

less<char> is a type.
less<char>() is a temporary object of that type.
- The () invoke the ctor—not operator().

Reverse sort

string s = "Kokopelli";
sort(s.begin(), s.end(), greater<char>());
cout << s << '\n';

poollkieK

Comparison function

bool lt(char a, char b) {
    return a < b;
}

int main() {
    string s = "Kokopelli";
    sort(s.begin(), s.end(), lt);
    cout << s << '\n';
}

Keiklloop

λ-function

string s = "Kokopelli";
sort(s.begin(), s.end(),
     [](char a, char b){return a<b;});
cout << s << '\n';
sort(s.begin(), s.end(),
     [](char a, char b){return a>b;});
cout << s << '\n';

Keiklloop
poollkieK

Case folding

bool lt(char a, char b) {
    return toupper(a) < toupper(b);
}

int main() {
    string s = "Kokopelli";
    sort(s.begin(), s.end(), lt);
    cout << s << '\n';
}

eiKklloop

Unique

If you want to avoid duplicates, then use unique().

bool lt(char a, char b) {
    return toupper(a) < toupper(b);
}

int main() {
    string s = "Kokopelli";
    sort(s.begin(), s.end(), lt);
    auto it = unique(s.begin(), s.end());
    s.resize(it-s.begin());
    cout << s << '\n';
}

eiKklop

unique() requires that its input is in order already. That way, it can run in O(n) time, as opposed to O(n²) time.

Unique

Case-independent uniqueness doesn’t come free:

bool lt(char a, char b) {
    return toupper(a) < toupper(b);
}

bool eq(char a, char b) {
    return toupper(a) == toupper(b);
}

int main() {
    string s = "Kokopelli";
    sort(s.begin(), s.end(), lt);
    auto it = unique(s.begin(), s.end(), eq);
    s.resize(it-s.begin());
    cout << s << '\n';
}

eiKlop

Unfortunately, we’ve duplicated the calls to toupper().

Unique and DRY

Duplication of code is a bad thing, but avoiding it sometimes has a cost.

bool lt(char a, char b) {
    return toupper(a) < toupper(b);
}

bool eq(char a, char b) {
    return !(lt(a,b) || lt(b,a));
}

int main() {
    string s = "Kokopelli";
    sort(s.begin(), s.end(), lt);
    auto it = unique(s.begin(), s.end(), eq);
    s.resize(it-s.begin());
    cout << s << '\n';
}

eiKlop

Generality

It’s not just about strings:

int a[] = {333, 22, 4444, 1};
sort(begin(a), end(a));
for (auto val : a)
    cout << val << '\n';

vector<double> v = {1.2, 0.1, 6.7, 4.555};
sort(v.begin(), v.end(), greater<double>());
for (auto val : v)
    cout << val << '\n';

6.7
4.555
1.2
0.1

Why didn’t I say a.begin()?

Because a is a C array. It’s not an object—no methods!
BTW, just plain a would have worked as well as begin(a).

Attitude

These algorithms may strike you as simplistic. “I could write that!”.
You could write a for loop as a while loop, but that would just confuse everybody. A for loop has semantic value.
Sure, you could write your own code. But would it be correct? Even the corner cases, like searching an empty range?
Using standard algorithms conveys meaning. Educated C++ programmers recognize the standard algorithms. Even though “female parent” would suffice, we all use the term “mother”.
Compilers might recognize algorithms and replace them with special machine code. copy() for chars might get replaced with ultra-fast looping instructions to copy memory 16 bytes at a time.

CS253: Software Development with C++

Spring 2021

Algorithms

CS253 Algorithms

Definition

Arguments

count()

count_if()

find()

find()

find()

find_if()

copy()

copy_if()

First attempt

Second attempt

Third attempt

Fourth attempt

In-place

replace()

transform()

sort()

Containers

Default comparison

Explicit comparison

Explicit comparison

Reverse sort

Comparison function

λ-function

Case folding

Unique

Unique

Unique and DRY

Generality

Attitude