# Handle permutations with duplicates at compile time

I created a simple library that handles permutation sequences with duplicates at compile time in C++14.

## Overview

I published an open-source library called komoperm, which handles permutation sequences with repetition.

It can calculate an index of a sequence of integers or enumerations or generate a sequence corresponding to the given index.

#include "komoperm/komoperm.hpp"

enum Hoge {
A, B, C,
};

int main() {
constexpr komoperm::Permutations<Hoge, A, A, A, B, B, C> p;

static_assert(p.Size() == 60,
"The number os possible permutations is 60");

static_assert(p.Index({B, A, B, C, A, A}) < 60,
"{B, A, B, C, A, A} is a permutation of {A, A, A, B, B, C}");

static_assert(p.Index(p.Get(10)) == 10,
"Get() generates the 10th permutation");
}

A set of permutation sequences komoperm::Permutations have two template parameters: typename T and sequence values Vals.... The values Vals... don’t have to be sorted. Moreover, the same values don’t need to be in consecutive positions.

The komoperm calculates all expressions at compile time and works fast even at runtime, thanks to template calculation. The memory consumption at compile time is relatively small because they don’t use template recursions.

It uses only C++14 features1 In the following section, I would like to show how to realize these features.

## Implementation

The most challenging point in komoperm is not the generation of sequences but the creation of a helpful type PermutationImpl.

Input:
Permutations<T, Vals...>

Output:
PermutationsImpl<
T,
N, // sizeof...(Vals)
M, // The number of the most frequent value in Vals...
ItemCount<
Val,  // A value
N2,   // How many remaining symbols are to be placed
C    　// How many Val is to be placed
>,
ItemCount<
// ...
>
...
>

A type PermutationImpl contains each Val and its counts C as template parameters. By using this type, we can quickly realize permutation operations. In the above code example, values except for Val, N2And C are easily obtained by Vals.... Therefore, we focus on how we could make a type that has <Val, N2, C>... template parameters.

In komoperm:

1. Get unique values in Vals...
2. Sort Vals...
3. Count the number of Val for each Val
4. Expand result of 3.

Note that komoperm doesn’t use template recursion, so it doesn’t need massive memory at compile time.

1., 2., and 3. are not so difficult. This code and this code realize these features without recursions.

The toughest part is No.4. From 1-3, we have the following three arrays.

• An array that contains unique Vals
• The number of Vals in i, i+1,i+2,…
• The number of Vals

For example, consider a sequence A, A, A, B, B, C. The above sequences are as follows.

• {A, B, C}
• {6, 3, 1}
• {3, 2, 1}

Now, we would like to create a new type whose template parameters are ordered like <A, 6, 3>, <B, 3, 2>, <C, 1, 1>. One may think that is not easy, but we can realize it by index substitutions and template parameter pack expansions.

template <typename T, T... Vals, std::size_t... Indices>
struct MakePermutationsImpl<ValueSet<T, Vals...>,
std::index_sequence<Indices...>> {
private:
static constexpr auto Impl() noexcept {
constexpr auto kValue = MakeItemCountsImplCalc<T, Vals...>();
using type = PermutationsImpl<
T, sizeof...(Vals), std::max({kValue.counts[Indices]...}),
ItemCount<T, kValue.values[Indices], kValue.remains[Indices],
kValue.counts[Indices]>...>;
return type{};
}

public:
using type = decltype(Impl());
};

The point is L1 and 9-10. The parameter pack expansion ItemCount<values[Indices], remain[Indices], counts[Indices]>... generates the desired type sequence using an index parameter pack Indices..., t.

## Conclusion

In this article, I showed basic techniques for permutation sequence with repetition. I’ll be happy if you find the difficulty of c++ templates.

#### notes

1. For the user’s convenience, it switches implementations using C++17.