To declare and initialize a vector in C++, you can use curly braces ({}) or the std::vector constructor.

Here are some examples:

#include <iostream>
#include <vector>

int main() {
    // Initialize vector with default values
    std::vector<int> v1;              // empty vector

    // Initialize vector with a given number of elements
    std::vector<int> v2(5);           // vector of 5 elements, initialized to 0
    std::vector<int> v3(5, 10);       // vector of 5 elements, initialized to 10

    // Initialize vector with an initializer list
    std::vector<int> v4 = {1, 2, 3};  // vector of 3 elements, initialized to 1, 2, and 3
    std::vector<int> v5{1, 2, 3};     // vector of 3 elements, initialized to 1, 2, and 3

    // Initialize vector from another vector
    std::vector<int> v6(v4);          // copy of v4

    // Output the vectors
    std::cout << "v1: ";
    for (int i : v1) std::cout << i << " ";
    std::cout << std::endl;

    std::cout << "v2: ";
    for (int i : v2) std::cout << i << " ";
    std::cout << std::endl;

    std::cout << "v3: ";
    for (int i : v3) std::cout << i << " ";
    std::cout << std::endl;

    std::cout << "v4: ";
    for (int i : v4) std::cout << i << " ";
    std::cout << std::endl;

    std::cout << "v5: ";
    for (int i : v5) std::cout << i << " ";
    std::cout << std::endl;

    std::cout << "v6: ";
    for (int i : v6) std::cout << i << " ";
    std::cout << std::endl;

    return 0;
}

Output:

v1:
v2: 0 0 0 0 0
v3: 10 10 10 10 10
v4: 1 2 3
v5: 1 2 3
v6: 1 2 3

In the above example, v1 is an empty vector, v2 is a vector of 5 elements initialized to 0, v3 is a vector of 5 elements initialized to 10, v4 and v5 are vectors of 3 elements initialized to 1, 2, and 3, and v6 is a copy of v4. Note that the for loops are using range-based for loops to iterate over the elements of the vectors.