How to add elements to set while traversing it? - c++

Question

We have a set S {1,10,100,1000,10000}. Now we input an integer x (say x = 4).
Now we have to add every element of set's product with x to the set itself. So finally
S={1,10,100,1000,10000,4,40,400,4000,40000}
[S is not limited to only 5 entries initially]
We have to visit only the initial elements in the set.
I tried an approach like:
for(auto i=s.begin();i!=s.end();i++)
{
s.insert((*i)*x);
}
This doesnt give the desired result, as the size of set keeps increasing.
Another approach I tried was to store all the multiples (*i)*x in another temporary set/vector and to merge it with s later.
But since the original dataset is huge, it worsens the time complexity.
Any optimizations ?

Answer 1

Since the std::set is ordered, and iterators are not invalidated by insertion, you can simply insert while iterating as long as you don't insert to the range that is still left to be iterated.
If we can assume all numbers to be positive, then we can iterate in reverse direction, because the result of multiplication is always going to be greater than the inputs:
for (auto it = S.rbegin(); it != S.rend(); ++it)
S.insert(*it*x);
If x is negative and set contains only positive, then order of iteration doesn't matter. If the set may contain negative numbers, this becomes more challenging.
But since the original dataset is huge, it worsens the time complexity.
Inserting N elements into std::set is O(N log N). Merging std::sets is O(N log N). The merge approach does not worsen asymptotic time complexity.
If you were to use an std::unordered_set though, the merge approach would be O(N) in average case. It's still O(N log N) in worst case however. I recommend using the merge approach with an unordered set.

Answer 2

Here you are.
#include <iostream>
#include <set>
#include <iterator>
std::set<int> & update( std::set<int> &s, int value )
{
for ( auto it = rbegin( s ); it != rend( s ); ++it )
{
s.insert( *it * value );
}
return s;
}
int main()
{
std::set<int> s = { 1, 10, 100, 1000, 10000 };
for ( const auto &value : s )
{
std::cout << value << ' ';
}
std::cout << '\n';
for ( const auto &value : update( s, 4 ) )
{
std::cout << value << ' ';
}
std::cout << '\n';
return 0;
}
The program output is
1 10 100 1000 10000
1 4 10 40 100 400 1000 4000 10000 40000
According to the C++ 20 Standard (22.2.6 Associative containers)
9 The insert and emplace members shall not affect the validity of
iterators and references to the container, and the erase members shall
invalidate only iterators and references to the erased elements.
Or a more general approach
#include <iostream>
#include <set>
#include <iterator>
std::set<int> & update( std::set<int> &s, int value )
{
auto partition = s.lower_bound( 0 );
for ( auto it = rbegin( s ); it != std::set<int>::reverse_iterator( partition ); ++it )
{
s.insert( *it * value );
}
for ( auto it = begin( s ); it != partition; ++it )
{
s.insert( *it * value );
}
return s;
}
int main()
{
std::set<int> s = { -10000, -1000, -100, -10, -1, 1, 10, 100, 1000, 10000 };
for ( const auto &value : s )
{
std::cout << value << ' ';
}
std::cout << '\n';
for ( const auto &value : update( s, 4 ) )
{
std::cout << value << ' ';
}
std::cout << '\n';
return 0;
}
The program output is
-10000 -1000 -100 -10 -1 1 10 100 1000 10000
-40000 -10000 -4000 -1000 -400 -100 -40 -10 -4 -1 1 4 10 40 100 400 1000 4000 10000 40000

Answer 3

As mentioned in the comments, it's simplest to use a temporary set. With C++17, you can use std::set::merge with the temporary set casted to an rvalue:
#include <algorithm>
std::set<int> s2;
std::transform(s1.cbegin(), s1.cend(), std::inserter(s2, s2.end()),
[](int orig){ return 4*orig; });
s1.merge(std::move(s2));
Otherwise, note that iterators into the set aren't invalidated while inserting. Take this together with the fact that the set is ordered and in case of the scenario you described (scaling an existing value is larger than the original value, but less or equal than the next existing one), you can do it in a loop like this:
for (auto it = s1.begin(); it != s1.end(); ++it)
it = s.insert(*it*4).first;
For fewer restrictions, you can use this more verbose loop:
for (std::set<int>::iterator it1 = s.begin(), it2; it1 != s.end();
it1 = std::next(it1) == it2 ? std::next(it1, 2) : it2)
it2 = s.insert(*it1*4).first;