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Sandor Dargo
Sandor Dargo

Posted on • Originally published at sandordargo.com

The big STL Algorithms tutorial: heap operations

In this next part of the big STL algorithm tutorial, we are going to talk about heap operations:

  • is_heap
  • is_heap_until
  • make_heap
  • push_heap
  • pop_heap
  • sort_heap

The first question we have to answer - before we'd start discussing the above functions one by one - is what we mean by a heap.

It's worth mentioning this because the most often a C++ developer meets the word heap is about static and dynamic memory allocations. It's about the heap vs the stack.

Not this time. In this case, we talk about data structures, in particular, max-heaps:

  • binary trees where all levels of the tree (except the last one) are fully filled. On the last level, they are filled from left to right.
  • the key stored in each node is either greater than or equal to the keys in the node's children,

We got used to the fact that standard C++ algorithms work on all the different kinds of containers. It's not the case for heap operations. They work on containers that are supporting random access iterators, such as std::vector or std::deque.

If you pass a list, your code will not compile and you'll get some horribly long error messages. Go and try yourself.

Now it's time to get the details.

is_heap

is_heap in its simplest form takes two parameters and returns a boolean. If the input range is a max heap, it returns true, otherwise false.

The two input parameters are denoting the beginning and the end of the range to check.

As we got used to it, there are two optional parameters. At the last position, you might pass in a binary predicate, a comparator that would return true if the first argument is smaller than the second one.

Since C++17, you can pass in an optional execution policy before all the other parameters.

#include <algorithm>
#include <iostream>
#include <vector>

int main()
{
    std::vector<int> orderedNumbers { 1, 2, 3, 4, 5 };

    std::vector<int> numbersInHeapOrder { 5, 4, 3, 1, 2 };

    std::cout << std::boolalpha;
    std::cout << "orderedNumbers.is_heap()?: " 
              << std::is_heap(orderedNumbers.begin(), orderedNumbers.end())
              << '\n';
    std::cout << "numbersInHeapOrder.is_heap()?: " 
              << std::is_heap(numbersInHeapOrder.begin(), numbersInHeapOrder.end())
              << '\n';
}
/*
orderedNumbers.is_heap()?: false
numbersInHeapOrder.is_heap()?: true
*/
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is_heap_until

is_heap_until finds the longest range that is a max heap starting from the first input parameter that denotes the beginning of the range to check up until the second input that signifies the last element to check.

The return value will be a pointer that points at the end of the longest map heap found.

As usual, you have the possibility to pass in a custom comparator and since C++17 an execution policy.

#include <algorithm>
#include <iostream>
#include <vector>

int main()
{
    std::vector<int> numbers { 5, 4, 3, 1, 2, 6 };

    std::cout << std::boolalpha;
    std::cout << "numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';
    std::cout << "numbers until the last but one position "
              << "are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end()-1)
              << '\n';
    std::cout << "the first element not part of the largest heap: " 
              << *(std::is_heap_until(numbers.begin(), numbers.end()))
              << '\n';
}
/*
numbers are organized as a max heap?: false
numbers until the last but one position are organized as a max heap?: true
the first element not part of the largest heap: 6
*/
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make_heap

While the previous two presented functions were non-intrusive, they don't change the passed in container, make_heap does.

You pass in a range of elements in any order and you'll get it back with the data organized into a max heap.

You can also pass in your custom comparator as a third parameter.

Unlike in other cases, there is no option to pass in an execution policy. If you think about it, it makes sense. It'd be pretty hard to construct a heap in parallel.

The function is void, meaning that it doesn't return anything.

#include <algorithm>
#include <iostream>
#include <vector>

int main()
{
    std::vector<int> numbers { 1, 2, 3, 4, 5 };

    std::cout << std::boolalpha;
    std::cout << "numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';
    for(const auto n : numbers) {
      std::cout << n << ' ';
    }
    std::cout << '\n';

    std::make_heap(numbers.begin(), numbers.end());

    std::cout << "what about now?: " 
              << std::is_heap(numbers.begin(), numbers.end()-1)
              << '\n';
    for(const auto n : numbers) {
      std::cout << n << ' ';
    }
    std::cout << '\n';
}
/*
numbers are organized as a max heap?: false
1 2 3 4 5 
what about now?: true
5 4 3 1 2 
*/
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Just as a side note, there is no make_heap_copy, or similar function that would leave the original input unchanged and build the heap somewhere else.

But you can make your copy first and then turn it into a heap.

push_heap

From time to time, there are functions in the standard library and in the <algorithm> header that doesn't exactly work the way you'd expect based on its name.

Or at least, not how I'd expect.

I thought that push_heap would insert an element into a range that is already organized into a heap.

Not exactly.

It takes a range denoted by its beginning and end and an optional comparator.

It assumes that all the elements, but the last one are organized into a max heap and takes that missing last element and inserts it into a heap.

So it doesn't take care of adding an element to the container. Before calling push_heap, is_heap on the full container would potentially return false, but is_heap(v.begin(), v.end()-1) is required to return true. After calling push_heap, even is_heap(v.begin(), v.end()) must return true.

#include <algorithm>
#include <iostream>
#include <vector>

int main()
{
    std::vector<int> numbers { 5, 4, 3, 1, 2, }; 

    std::cout << std::boolalpha;
    std::cout << "numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';

    numbers.push_back(42);

    std::cout << std::boolalpha;
    std::cout << "after adding 42, numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';
    std::cout << "numbers are organized as a max heap "
              << "until the last but one element?: " 
              << std::is_heap(numbers.begin(), numbers.end()-1)
              << '\n';
    for(const auto n : numbers) {
      std::cout << n << ' ';
    }
    std::cout << '\n';

    std::push_heap(numbers.begin(), numbers.end());

    std::cout << "what about now, are all numbers in a heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';
    for(const auto n : numbers) {
      std::cout << n << ' ';
    }
    std::cout << '\n';
}
/*
numbers are organized as a max heap?: true
after adding 42, numbers are organized as a max heap?: false
numbers are organized as a max heap until the last but one element?: true
5 4 3 1 2 42 
what about now, are all numbers in a heap?: true
42 4 5 1 2 3 
*/
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pop_heap

Just like push_heap, pop_heap will make sure that the range between the first and the last but one element is organized as a heap. But before it makes the corresponding changes, it swaps the first and the last element of the passed in range.

The input parameters are the same as for push_heap, so it takes two iterators denoting the first and last elements of the range you work with and it also accepts an optional comparator.

#include <algorithm>
#include <iostream>
#include <vector>

int main()
{
    std::vector<int> numbers { 9, 8, 3, 1, 2, 6}; 

    std::cout << std::boolalpha;
    std::cout << "numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';

    std::pop_heap(numbers.begin(), numbers.end());

    std::cout << std::boolalpha;
    std::cout << "after calling pop_heap, numbers are organized as a max heap?: " 
              << std::is_heap(numbers.begin(), numbers.end())
              << '\n';
    std::cout << "numbers are organized as a max heap "
              << "until the last but one element?: " 
              << std::is_heap(numbers.begin(), numbers.end()-1)
              << '\n';
    for(const auto n : numbers) {
      std::cout << n << ' ';
    }
    std::cout << '\n';
}
/*
numbers are organized as a max heap?: false
after calling pop_heap, numbers are organized as a max heap?: false
numbers are organized as a max heap until the last but one element?: true
8 6 3 1 2 9 
*/

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sort_heap

This is our last algorithm for today, with sort_heap we leave the realms of heaps. Just like the passed in container.

Call sort_heap on a range, and you'll get back your container where the elements are sorted in ascending order, so the input range loses its max heap property.

If you wonder about why std::sort_heap exists when we std::sort, I don't have a clear answer for you. Since C++11, std::sort will always work within the complexity of O(n*logn), while for std::sort_heap we also have 2*n*logn comparisons, which is the same order of magnitude.

My test were showing std::sort consistently faster by a factor 3-4.

At the same time, I found someone saying in terms of memory requirements std::sort has a requirement for O(logn) memory on the stack while std::sort_heap only for O(1) meaning that in the microcontroller world std::sort_heap is preferable to avoid stack overflow.

Otherwise it seems not a lot of usecases for std::sort_heap. Nevertheless here is an example on how to use it:

#include <algorithm>
#include <iostream>
#include <vector>

int main() {
  std::vector<int> numbers{1, 2, 3, 4, 5};
  std::make_heap(numbers.begin(), numbers.end());
  for(const auto n : numbers) {
    std::cout << n << ' ';
  }
  std::cout << '\n';

  std::sort_heap(numbers.begin(), numbers.end());
  for(const auto n : numbers) {
    std::cout << n << ' ';
  }
  std::cout << '\n';
}
/*
5 4 3 1 2 
1 2 3 4 5 
*/
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Conclusion

This time, we learned about heap algorithms that work not on the heap memory but on "heaply organized" data structures. I hope you found it interesting.

Next time we'll discuss minimum/maximum operations.

Stay tuned!

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Discussion (7)

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Pierre Gradot

Or at least, not how I'd expect.

At least, there are 2 people in this case... std::push_heap and std::pop_heap have a weird signature. Maybe the purpose was to have similar signatures. I don't really get the point here.

std::sort_heap is somehow the counterpart of std::make_heap but I also find it weird.

I guess I don't have the appropriate background to understand these functions' signatures and names ^^

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Sandor Dargo Author

I guess I don't have the appropriate background to understand these functions' signatures and names ^^

I have no idea who has such a background :D

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pgradot profile image
Pierre Gradot

Let's find the authors of the proposal for these functions XD

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Sandor Dargo Author

What do you want to do with them? :D

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pgradot profile image
Pierre Gradot

Ask them "but why ????"

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Sandor Dargo Author

I was afraid of something more drastic :D

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pgradot profile image
Pierre Gradot

Don't worry I'm a nice guy 😇