loop and string length issues

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 #include <iostream>
#include <string>
#include <vector>

using std::cout;
using std::cin;
using std::endl;
using std::string;
using std::vector;
static bool truth = true;

void looping(vector<string> plates, int numPlates);

int main(int argc, const char * argv[])
{
    int numPlates;
    string input;
    cout << "How many plates are there? ";
    cin >> numPlates;
    cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    vector<string> plates(numPlates);
    for (int i = 0; i < numPlates; i++)
    {
        cout << "Enter plate " << i+1 << ": ";
        getline(cin, input);
        plates[i] = input;
    }
    
    looping(plates, numPlates);
    
    if (truth == false)
    {
        cout << "The door cannot be opened!" << endl;
    }
    else
    {
        cout << "The door can be opened!" << endl;
    }
    
    return 0;
}

void looping(vector<string> plates, int numPlates)
{
    for (int i = 0; i < numPlates; i++)
    {
        for (int j = 0; j < numPlates; j++)
        {
            int last = plates[i].length() - 1;
            cout << plates[i].length() << endl;
            if (i == j)
            {
                // do nothing
            }
            else if (plates[i].at(last) == plates[j].at(0))
            {
                string temp = plates[i+1];
                plates[i+1] = plates[j];
                plates[j] = temp;
            }
        }
    }
    for (int i = 0; i < numPlates - 1; i++)
    {
        int last = plates[i].length() - 1;
        //issues crop up
        cout << plates[i].length() << endl;
        /*
        if (plates[i].at(last) != plates[i+1].at(0))
            {
               truth = false;
            }
         */
    }
}


This function tries to sort a bunch of different strings to see if you can match the first and last letter in a chain. Towards the end I seem to be having some issues with the .length function not working with the first plate[0] it seems to try to always say the length is 0. I can't see where it's getting changed to that length? I don't think I modify it anywhere. I'm also struggling with the loop to organize it. I think I could just make loop thats kind of a reverse of the first one I made to organize it in the other direction.
One thing is that you should make your vector a reference in the looping function:

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void looping( vector< string >& plates, int numPlates )
    {
    ...
    }


Otherwise, you are calling by value and not changing the actual vector in main.
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