# Vectors

Vectors are one of many ways of keeping a collection of values “under one roof.” We can give one name to a collection of values and then access each value by a position. We can also add more values or remove values.

(The “traditional” way of representing a collection of values is the “array.” We won’t be looking at arrays this quarter because they’re much more difficult to use than vectors and, for our purposes, they aren’t any more powerful.)

## Vector usage

When you create a vector, you have to decide what (single) kind of value it will hold. This type is specified in a funny way (using a “template” which we’ll learn about later).

Here is how you create a vector full of integers:

``````vector<int> myvec;
``````

(Don’t forget `#include <vector>` at the top of your files when you use vectors).

``````vector<double> vals;
``````

It’s not possible to have a vector full of doubles and ints, for example (“heterogeneous” containers are not possible in C++).

You can put elements in your vector with several methods. Most common is `push_back`:

``````vector<double> vals;
vals.push_back(5.3);
vals.push_back(0.66);
``````

You can retrieve the size of a vector with the `size` function:

``````cout << vals.size() << endl;
``````

And you can get to an element in the vector with `[i]` where `i` is some position (“index”):

``````cout << vals << endl;
``````

Note that positions for vectors start at 0, so `` refers to the second element (the value 0.66).

Using the `size` function and the `[]` syntax, we can print the contents of a vector using a simple `for()` loop:

``````for(int i = 0; i < vals.size(); i++)
{
cout << vals[i] << endl;
}
``````

TODO: back(), pop_back()

## Example 1 – simple vector

``````#include <iostream>
#include <vector>  // this is necessary to use vectors
using namespace std;

int main()
{
vector<int> vals;
vals.push_back(5);
vals.push_back(6);
vals.push_back(1);

cout << "Size of vals: " << vals.size() << endl;
for(unsigned int i = 0; i < vals.size(); i++)
{
cout << "Value at index " << i
<< " is " << vals[i] << endl;
}
return 0;
}
``````

Output:

```Size of vals: 3
Value at index 0 is 5
Value at index 1 is 6
Value at index 2 is 1
```

## Example 2 – vector with initial values

You can create a vector of some specific size and give it an initial (repeated) value. This is most often used to give a vector a bunch of zeros.

``````#include <iostream>
#include <vector>
using namespace std;

int main()
{
// create a vector of size 10,
// with every element equal to 0
vector<int> vals(10, 0);
vals.push_back(5);
vals.push_back(6);
vals.push_back(1);

cout << "Size of vals: " << vals.size() << endl;
for(unsigned int i = 0; i < vals.size(); i++)
{
cout << "Value at index " << i
<< " is " << vals[i] << endl;
}
return 0;
}
``````

Output:

```Size of vals: 13
Value at index 0 is 0
Value at index 1 is 0
Value at index 2 is 0
Value at index 3 is 0
Value at index 4 is 0
Value at index 5 is 0
Value at index 6 is 0
Value at index 7 is 0
Value at index 8 is 0
Value at index 9 is 0
Value at index 10 is 5
Value at index 11 is 6
Value at index 12 is 1
```

## Example 3 – clearing a vector

The `clear()` function deletes all the values in the vector.

``````#include <iostream>
#include <vector>
using namespace std;

int main()
{
// create a vector of size 10,
// with every element equal to 0
vector<int> vals(10, 0);
vals.push_back(5);
vals.push_back(6);
vals.push_back(1);

cout << "Size of vals: " << vals.size() << endl;
for(unsigned int i = 0; i < vals.size(); i++)
{
cout << "Value at index " << i
<< " is " << vals[i] << endl;
}

vals.clear();
cout << "Size of vals: " << vals.size() << endl;

return 0;
}
``````

Output:

```Size of vals: 13
Value at index 0 is 0
Value at index 1 is 0
Value at index 2 is 0
Value at index 3 is 0
Value at index 4 is 0
Value at index 5 is 0
Value at index 6 is 0
Value at index 7 is 0
Value at index 8 is 0
Value at index 9 is 0
Value at index 10 is 5
Value at index 11 is 6
Value at index 12 is 1
Size of vals: 0
```

## Example 4 – vector of strings

You can put anything in vectors, even strings (which are themselves more-or-less vectors, too). You can put vectors inside vectors, ad nauseum.

``````#include <iostream>
#include <vector>
#include <string>
using namespace std;

int main()
{
vector<string> names;
names.push_back("Euler");
names.push_back("Descartes");
names.push_back("Turing");
names.push_back("Church");

cout << "Size of names: " << names.size() << endl;
for(unsigned int i = 0; i < names.size(); i++)
{
cout << "Name at index " << i
<< " is " << names[i] << endl;
}

return 0;
}
``````

Output:

```Size of names: 4
Name at index 0 is Euler
Name at index 1 is Descartes
Name at index 2 is Turing
Name at index 3 is Church
```

## Example 5 – using the empty() function

The `clear()` function deletes all the values in the vector. The `empty()` function tells us if a vector has no values.

``````#include <iostream>
#include <vector>
#include <string>
using namespace std;

int main()
{
vector<string> names;
names.push_back("Euler");
names.push_back("Descartes");
names.push_back("Turing");
names.push_back("Church");

names.clear();

if(names.empty())
{
cout << "Names vector is empty." << endl;
}
else
{
cout << "Names vector is not empty." << endl;
}

return 0;
}
``````

Output:

```Names vector is empty.
```

## Example 6 – sorting

Vectors can sort themselves (using the “quick sort” technique).

``````#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;

int main()
{
vector<string> names;
names.push_back("Euler");
names.push_back("Descartes");
names.push_back("Turing");
names.push_back("Church");

sort(names.begin(), names.end());

for(unsigned int i = 0; i < names.size(); i++)
{
cout << "Name at index " << i
<< " is " << names[i] << endl;
}

return 0;
}
``````

Output:

```Name at index 0 is Church
Name at index 1 is Descartes
Name at index 2 is Euler
Name at index 3 is Turing
```

## Example 7 – random shuffling

The reverse of sorting is shuffling; sometimes useful to randomize the order of our data for experiments.

``````#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <ctime>
#include <cstdlib>
using namespace std;

int main()
{
// initialize the random number generator "seed"
// to the current time (in seconds); this way,
// the seed is different each time we run the program
srand(time(NULL));

vector<string> names;
names.push_back("Euler");
names.push_back("Descartes");
names.push_back("Turing");
names.push_back("Church");
names.push_back("Curry");
names.push_back("Gauss");
names.push_back("Riemann");
names.push_back("McCarthy");
names.push_back("Hopper");
names.push_back("Lovelace");

sort(names.begin(), names.end());

cout << "--Sorted names:" << endl;
for(unsigned int i = 0; i < names.size(); i++)
{
cout << names[i] << endl;
}
cout << endl;

random_shuffle(names.begin(), names.end());

cout << "--Randomly shuffled names:" << endl;
for(unsigned int i = 0; i < names.size(); i++)
{
cout << names[i] << endl;
}

return 0;
}
``````

Output:

```--Sorted names:
Church
Curry
Descartes
Euler
Gauss
Hopper
Lovelace
McCarthy
Riemann
Turing

--Randomly shuffled names:
Curry
Hopper
Turing
Descartes
Gauss
Lovelace
McCarthy
Church
Euler
Riemann
```

## Example 8 – passing a vector to a function

When you pass a vector to the function, the whole package is copied and given to the function; so if you change the vector in the function, the rest of the world is not affected. Also note that while you have to provide a function the size of the array when you use arrays and functions together, the vector already knows how big it is, so we don’t need a “size” parameter.

``````#include <iostream>
#include <vector>
using namespace std;

int sum(vector<int> vals)
{
int sum = 0;
for(unsigned int i = 0; i < vals.size(); i++)
{
sum += vals[i];
}
return sum;
}

int main()
{
vector<int> xs;

for(int i = 0; i < 1000; i++)
{
xs.push_back(i + 1);
}

cout << "Sum of integers 1 to 1000: " << sum(xs) << endl;

return 0;
}
``````

Output:

```Sum of integers 1 to 1000: 500500
```

## Example 11 – returning a vector from a function

Vectors can be returned from functions, in the usual way:

``````#include <iostream>
#include <vector>
using namespace std;

vector<double> repeatThree(vector<double> vals)
{
vector<double> repeatedVals;

for(unsigned int i = 0; i < vals.size(); i++)
{
repeatedVals.push_back(vals[i]);
repeatedVals.push_back(vals[i]);
repeatedVals.push_back(vals[i]);
}

return repeatedVals;
}

int main()
{
vector<double> vals;
vals.push_back(1.4);
vals.push_back(2.3);
vals.push_back(5.3);
vals.push_back(6.2);

vector<double> newVals = repeatThree(vals);

for(unsigned int i = 0; i < newVals.size(); i++)
{
cout << newVals[i] << endl;
}

return 0;
}
``````

## Example 12 – passing a vector by reference to a function

If we want the function to be able to modify the vector given in a parameter, or we simply want to avoid the cost of copying a large vector, we can use “call-by-reference” in the parameter:

``````#include <iostream>
#include <vector>
using namespace std;

void repeatThree(vector<double> &vals)
{
vector<double> repeatedVals;

for(unsigned int i = 0; i < vals.size(); i++)
{
repeatedVals.push_back(vals[i]);
repeatedVals.push_back(vals[i]);
repeatedVals.push_back(vals[i]);
}

vals = repeatedVals;
}

int main()
{
vector<double> vals;
vals.push_back(1.4);
vals.push_back(2.3);
vals.push_back(5.3);
vals.push_back(6.2);

repeatThree(vals);

for(unsigned int i = 0; i < vals.size(); i++)
{
cout << vals[i] << endl;
}

return 0;
}
``````

## Strings are (just like) vectors

Interestingly enough, strings are just vectors of `char` values (more or less). We can use the same vector functions on strings (mostly). For example, we can ask a string its size (`mystring.size()`), reverse it (`mystring.reverse()`), etc.

## Using 2D vectors

Since a vector can store any single type of value, and vectors themselves are types of values, you can put vectors inside a vector:

``````// creates a 10x10 matrix with all 0's inside
vector<vector<int> > matrix(10, vector<int>(10, 0));

// set row 3, column 2:
matrix = 55;
``````

Note that the extra space in the first line of code: `> >` is necessary, otherwise the compiler thinks you are writing `>>` like in `cin >> x`.

## Storing 2D structures in 1D structures

If you want to keep a “2D matrix” in a 1D structure, you have to use a simple calculation to figure out where row i, column j exists inside the 1D structure. If we essentially lay out the matrix with each row appended to the prior, then we get the following calculation: `[i][j]` is the same as `[i * cols + j]` (assuming `i` and `j` start counting at 0).

``````// 10x10 "matrix" as a 1D vector, full of 0's
vector<int> matrix(100, 0);

// set row 3, column 2:
matrix[2 * 10 + 1] = 55;
``````