合并排序算法中的 C++“以未捕获的 std::out_of_range 类型异常终止：向量”错误

我有一个 C++ 代码，它应该使用合并排序算法对一个包含 800,000 多个单词的文件进行排序，每个单词在一个新行上。

我做了什么 ？

首先，我尝试实现以下合并排序算法并尝试在一小部分输入上对其进行测试。我无法弄清楚我在哪里得到了向量的索引越界错误。如果有人能帮我解决这个问题，我将不胜感激

#include <fstream>
#include <iostream>
#include <vector>

using namespace std;


vector<string> merge(const vector<string>& first,
                     const vector<string>& second) {
    // Write your code to merge vectors first and
    // second onto result.

    vector<string> output;
    int i = 0;
    int j = 0 ;
    int size_first = sizeof(first);
    int size_second = sizeof(second);

    while(i < size_first || j < size_second){
        if (i < size_first && j < size_second){
            if (first.at(i) < second.at(j)){
                output.push_back(first.at(i));
                i++;
            }
            else{
                output.push_back(second.at(i));
                j++;
            }
        }
        else if (i < size_first){
            output.push_back(first.at(i));
            i++;
        }
        else{
            output.push_back(second.at(j));
            j++;
        }

    }
    return output;
}

void mergeSort(vector<string>& words) {
    if (words.size() <= 1)
    {
        return;
    }
    int n = words.size();
    int middle = n/2;

    vector<string> first_half(middle);
    for (int i = 0; i < middle; ++i) {
        first_half[i] = words[i];
    }

    vector<string> second_half(n - middle);
    for (int i = middle; i < n; ++i) {
        second_half[i - middle] = words[i];
    }

    words = merge(first_half, second_half);
}

void sort(vector<string>& words) {

    // Invoke mergeSort  here.
    mergeSort(words);
}

int main(){

    vector<string> names;
    names.push_back("Smith");
    names.push_back("Abinash");
    names.push_back("Ciara");
    names.push_back("Reeta");

    sort(names);

    return 0;

}