Question

Is it possible to sort a list based off one item?

For instance, if I have

1,3,2,4,5,6,7 ... 1000000

And I know that 3 is the second element, is it possible to efficiently sort 3 into it’s correct position between 2 and 4 without re-sorting the entire list?

EDIT: I should also note that, in this scenario, it is assumed that the rest of the list is already sorted; it is simply the 3 that is now out of place.

Answer 1

You could simply find that unordered object (O(n)), take the object out (O(1)), find the correct position (O(n)), then insert it again (O(1)).

Assuming C++11,

#include <list>
#include <algorithm>
#include <iostream>

int main() {
    std::list<int> values {1, 2, 3, 9, 4, 5, 6, 7, 12, 14};

    auto it = std::is_sorted_until(values.begin(), values.end());
    auto val = *--it;
    // ^ find that object.

    auto next = values.erase(it);
    // ^ remove it.

    auto ins = std::lower_bound(next, values.end(), val);
    // ^ find where to put it back.

    values.insert(ins, val);
    // ^ insert it.

    for (auto value : values) {
        std::cout << value << std::endl;
    }
}

Before C++11 you need to implement std::is_sorted_until yourself.