Алгоритм бинарного поиска

#include <iostream>
#include <vector>
#include <random>
#include <cmath>
#include <iomanip>
#include <algorithm>
using namespace std;
void show(const vector<int>& box) {
    if (box.empty()) puts("Empty box!");
    else {
        const auto width = static_cast<streamsize>(log10(box.back())) + 2;
        auto n = 0;
        for (auto x : box) {
            cout << setw(width) << x;
            if (0 == ++n % 10) puts("");
        }
        puts("");
    }
}
vector<int> make_random_array(const size_t length) {
    uniform_int_distribution<> uid(1, static_cast<int>(length << 1));
    mt19937 gen{ random_device()() };
    auto rand = [&](int& x) { x = uid(gen); };
    vector<int> box(length);
    for (auto& x : box) x = uid(gen);
    puts("Create and view an array");
    show(box);
    sort(box.begin(), box.end());
    puts("View the sorted array");
    show(box);
    return box;
}
// Алгоритм бинарного поиска
auto bin_search(const int key, vector<int>& box) {
    auto low = box.begin();
    auto high = box.end() - 1;
    while (low <= high) {
        auto pos = distance(low, high) >> 1;
        auto mid = low + pos;
        if (*mid < key) low = mid + 1;
        else if (*mid > key) high = mid - 1;
        else return mid;
    }
    return box.end();
}
int main() {
    cout << "Length: ";
    size_t length;
    cin >> length;
    auto box = make_random_array(length);
    auto pos = box.end();
    while (true) {
        cout << "Enter some number: ";
        int key;
        cin >> key;
        pos = bin_search(key, box);
        if (pos != box.end()) {
            const auto index = distance(box.begin(), pos);
            cout << "The specified number is in cells with an index: " << index << '\n';
        } else {
           puts("Number not found!");
        }
    }
}