How Does a Vector Internally Works in C++?
Last Updated :
15 Nov, 2024
In C++, a vector is a dynamic array that can resize itself when more elements are added or deleted. So, one may ask that how a vector internally works to achieve its dynamic resizing capability while maintaining similar efficiency to static arrays in operations?
For vector to work as a resizable dynamic array, it has to implement the following features:
- Random Access using Index: Quick access to elements using index, with O(1) time complexity.
- Dynamic Resizing: The size should automatically change according to elements inserted or deleted without any user interference.
- Fast Insertion and Deletion at the End: Insertion and deletion of the elements at the end of the vector must provide O(1) time complexity.
- Homogeneous Elements: All the elements must be of same type.
Implementation of Features
Let's discuss how the above features can be implemented in the vector:
- Random Access Using Index: To provide random access to the elements using index, all the elements of the vector should be stored continuously in the memory. It is possible by allocating a block of memory in the heap using new operator.
- Dynamic Resizing: For dynamic resizing, the whole block of vector memory has to be reallocated to the larger size using new operator when the vector becomes full.
- Homogeneous Elements: The block returned by the new operator already allocate the memory of given number of elements of same type.
- Fast Insertion and Deletion at the End: If the vector already has enough space, there is no issues with providing O(1) insertion at the end. But if the vector is full, a reallocation is needed.
Internal Working of Vector
Let's understand the internal working by taking the basic use of the vector step-by-step as a reference:
Creating a Vector
When an empty vector is created, a memory block of a default size is allocated in the head. The size of this memory block is called capacity of the vector.
Inserting Elements
When an element is inserted, it is copied to the allocated memory and the number of stored elements. We can keep inserting element like this till the size is equal to the capacity, which means that the vector is full. To insert more elements, a reallocation needed to be done.
Reallocation
In reallocation, we encounter an issue. You see, reallocating a memory block doesn't extent it in place, instead, it copies the whole block to the new block of larger size, which will take O(n). So, if a reallocation is done at each insertion or deletion, it will increase the time complexity by a factor of O(n).
To provide the fast insertion and deletion at the end while maintaining the vector's dynamic resizing capability, the exponential growth policy is used for reallocation. According to this policy,
Initially, a memory block of fixed size allocated for vector. Whenever the vector becomes full and needs resizing, instead of increasing the size of the memory block by just one element, it is doubled in size.
One may argue here that the complexity of reallocation is still not changed and remains O(n), but the number of times reallocation is needed is reduced exponentially leading to amortized complexity of inserting element at the end to be O(1). Refer to the article Amortized Analysis Introduction for mathematical proof.
Deleting Elements
Deleting elements does not trigger any reallocation. The object deleted will be destroyed but the memory would still belong to the vector.
Example: Suppose a vector starts with an initial size of 1:
- Insert 1st element: Size = 1, Capacity = 1 (no reallocation needed).
- Insert 2nd element: Size = 2, Capacity = 2 (reallocation needed, copy 1 element).
- Insert 3rd element: Size = 3, Capacity = 4 (reallocation needed, copy 2 elements).
- Insert 4th element: Size = 4, Capacity = 4 (no reallocation needed).
- Insert 5th element: Size = 5, Capacity = 8 (reallocation needed, copy 4 elements).
We can actually verify this copying in a C++ program using a vector of a custom data type that signals whenever its object is copied.
C++
#include <bits/stdc++.h>
using namespace std;
// Custom data type to track copying
class C {
public:
int a;
C(int x = 0): a(x){}
// Copy Constructor
C(const C& other) : a(other.a) {
cout << "Copying C(" << a << ")\n";
}
};
// Main function to demonstrate the behavior
int main() {
vector<C> v;
// Pushing 8 elements
for (int i = 0; i < 8; i++) {
v.emplace_back(i + 1);
}
return 0;
}
OutputCopying C(1)
Copying C(1)
Copying C(2)
Copying C(1)
Copying C(2)
Copying C(3)
Copying C(4)
As we can see, the elements are copied exactly 8 times which was predicted above. This proves that the vector internally uses the exponential growth.
Note:vector emplace_back() is used to avoid the extra copies of elements.
Summary
From this article, we can summarize the working of the vector as:
- Initially, a vector is allocated default amount of memory.
- When the vector becomes full, reallocation is done.
- Reallocation follows exponential growth by doubling the size of the memory block ensuring fewer reallocations for efficiency.
- While insertion and deletion at the end are not strictly O(1), they achieve an amortized time complexity of O(1).
- Deleting elements destroys the object but does not trigger memory reallocation.
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