Vectors contain contiguous elements stored as an array. Accessing members of a vector or appending elements can be done in constant time, whereas locating a specific value or inserting elements into the vector takes linear time.

In simple words, vector are

To understand this we will look into the working of a vector using a simple example. Let us say that we have elements

**Dynamic Array**with more functionality.**How do Vector acts as a Dynamic Array?**To understand this we will look into the working of a vector using a simple example. Let us say that we have elements

**1,2,3,4,5,6,7,8,9,10**which we want to store in a vector.- When we initialize a vector and don't specify any size then its default
**size is 1**in which we insert the 1. - Now when we try to insert 2, we don't have any more space in a vector so that time it creates a new vector with
**size 4**and copies all the previous vector data to it and inserts 2. - Now we can insert 3 and 4 without altering the size of a vector. Now again when we try to insert 5, we don't have space so that time it creates a new vector of
**size 8**and copies all the data to it and inserts 5. - Now we can insert 6,7, and 8 to the vector. Now again when we try to insert 9, we don't have space so that time it again creates a new vector of
**size 16**and copies all the data to it and inserts 9. - Finally, it inserts 10.

So whenever a

**vector increases**its size then it is**twice the previous vector size**.**Vector Operators which are present in STL**

For code demonstration purposes let us take

**V**as a integer vector and

**iter**as an iterator.

**assign**- assign elements to a vector- Assigning 1 to first 10 location:
**V.assign(10,1)** - Copying element of another vector named data:
**V.assign( data.begin( ), data.end( ) )** **at**- returns an element at a specific location- To get number present at index i:
**V.at( i )** **back**- returns the last element of a vector- To get the last element:
**V.back()** **begin**- returns an iterator to the beginning of the vector**iter=V.begin( )**// returns the address of first element.**capacity**- returns the number of elements that the vector can hold**V.capacity( )****clear**- removes all elements from the vector**V.clear( )****empty**- True if the vector has no elements**V.empty( )****end**- returns an iterator just past the last element of a vector**iter=V.end( )**// returns address 1 greater then last element address. To get the address of the last element subtract 1 from iter.**erase**- removes the element from a vector- Removing single element:
**V.erase( iterator )** - Removing element in a range:
**V.erase( startIterator, endIterator )** **front**- returns the first element of a vector- To get the first element:
**V.front( )** **insert**- inserts elements into the vector**max_size**- returns the maximum number of elements that the vector can hold**pop_back**- removes the last element of a vector- Removes the last element:
**V.pop_back( )** **push_back**- add an element to the end of the vector- Appends the element to the vector:
**V.push_back( )** **rbegin**- returns a reverse_iterator to the end of the vector**rend**- returns a reverse_iterator to the beginning of the vector**reserve**- sets the minimum capacity of the vector- Reverse the vector:
**reverse( V.begin( ), V.end( ) )** **resize**- change the size of the vector**size**- returns the number of items in the vector**swap**- swap the contents of one vector with another vector.

Now we will be implementing these operators and learning the most of them. Let's begin by creating a vector.

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**assign()**

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- This function either gives the current vector the values from start to end or gives it a specified number of copies of value from the start position.
- This can also be used to copy an element from one vector to another as we have done in the above code.

**at()**

- This function returns a reference to the element in the vector at index
*(Index to be passed to it as Parameter )*. The at() function is safer than the [] operator, because it won't let you reference items outside the bounds of the vector.

**begin()**

- This returns a reference iterator to the first element of the vector and runs in constant time.

**end()**

- The end() function returns a reference iterator just past the end of the vector.
- If you want to get the lase element then just subtract 1 from this as this will reference the last element in the vector.

**push_back()**

- This appends (adds the value in the dynamic array in the end) the value to the end of the vector.
- Runs in constant time ie. O(1).

**pop_back()**

- This removes the last element of the vector.
- Runs in constant time as in push_back().

**insert()**

- The insert function either
- inserts
**value**before the given**index,**returning an iterator to the element inserted, - inserts
**num**copies of**value**before the given**index** - inserts the elements from
**start**to**end**before the given**index** - Note -
- Inserting elements into a vector can be relatively time-intensive since the underlying data structure for a vector is an array. In order to insert data into an array, you might need to displace a lot of the elements of that array, and this can take linear time.
- If you are planning on doing a lot of insertions into your vector and you care about speed, you might be better off using a container that has a linked list as its underlying data structure(such as List or a Deque).

**empty()**

- The returns (1) true if the vector has no elements, (0) false otherwise.

**clear()**

- This deletes all of the elements in the vector.

**Multidimensional Vectors.**

In this section, we will learn about creating multi-dimensional vectors. In multidimensional, vector we can implement dynamic two-dimensional array, a three-dimensional array, etc. For the purpose of explanation, we will be using 2 Dimensional Dynamic Array Implementation.

**Fig 2: Adjacency List ( Graph Representation )**

**To implement the above adjacency list we need to use a two-dimensional vector. Here we will implement this when we know the number of rows. Let rows are N.**

- Create a 2d vector for above like this.
- vector<int> adj[N]
- To push element in this we use the row number (that to which row we have to store a particular value ).
- Let u be the row number and v be the value to be inserted in the vector. This can be done as
- adj[u].push_back(v)

**To implement the two-dimensional vector when we don't have any idea about the number of rows or columns.**

- Create a 2d vector as this
- vector < vector <int> > data.
- Here the number of rows and columns both are dynamic.

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