Permutations/Rank of a permutation: Difference between revisions
Permutations/Rank of a permutation (view source)
Revision as of 19:33, 27 August 2023
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22: [ 0, 1, 3, 2 ] = 22
23: [ 0, 1, 2, 3 ] = 23
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=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <cstdint>
#include <iostream>
#include <random>
#include <vector>
void print_vector(const std::vector<int32_t>& list) {
std::cout << "[";
for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
std::cout << list[i] << ", ";
}
std::cout << list.back() << "]";
}
uint64_t factorial(const int32_t& n) {
uint64_t factorial = 1;
for ( int32_t i = 2; i <= n; ++i ) {
factorial *= i;
}
return factorial;
}
uint64_t rank1(const int32_t& n, std::vector<int32_t>& vec, std::vector<int32_t>& inverse) {
if ( n < 2 ) {
return 0;
}
const int32_t last = vec[n - 1];
std::swap(vec[n - 1], vec[inverse[n - 1]]);
std::swap(inverse[last], inverse[n - 1]);
return last + n * rank1(n - 1, vec, inverse);
}
void unrank1(const int64_t& rank, const int32_t& n, std::vector<int32_t>& vec) {
if ( n < 1 ) {
return;
}
const int64_t quotient = rank / n;
const int64_t remainder = rank % n;
std::swap(vec[remainder], vec[n - 1]);
unrank1(quotient, n - 1, vec);
}
int64_t rank(const int32_t& n, std::vector<int32_t>& vec) {
std::vector<int32_t> copy_vec(n, 0);
std::vector<int32_t> inverse(n, 0);
for ( int32_t i = 0; i < n; ++i ) {
copy_vec[i] = vec[i];
inverse[vec[i]] = i;
}
return rank1(n, copy_vec, inverse);
}
void permutation(const int64_t& rank, const int32_t& n, std::vector<int32_t>& vec) {
std::iota(vec.begin(), vec.end(), 0);
unrank1(rank, n, vec);
}
int main() {
int32_t test_size = 3;
std::vector<int32_t> test_vector(test_size, 0);
for ( uint64_t count = 0; count < factorial(test_size); ++count ) {
permutation(count, test_size, test_vector);
std::cout << count << " -> ";
print_vector(test_vector);
std::cout << " -> " << rank(3, test_vector) << std::endl;
}
std::cout << std::endl;
test_size = 12; // test_size can be increased up to a maximum of 20
test_vector.resize(test_size);
std::random_device random;
std::mt19937 generator(random());
std::uniform_real_distribution<double> distribution(0.0F, 1.0F);
for ( int32_t count = 0; count < 4; ++count ) {
const uint64_t rand = distribution(generator) * factorial(test_size);
permutation(rand, test_size, test_vector);
std::cout << rand << " -> ";
print_vector(test_vector);
std::cout << " -> " << rank(test_size, test_vector) << std::endl;
}
}
</syntaxhighlight>
{{ out }}
<pre>
0 -> [1, 2, 0] -> 0
1 -> [2, 0, 1] -> 1
2 -> [1, 0, 2] -> 2
3 -> [2, 1, 0] -> 3
4 -> [0, 2, 1] -> 4
5 -> [0, 1, 2] -> 5
247958875 -> [9, 1, 10, 5, 2, 0, 4, 11, 8, 6, 3, 7] -> 247958875
115652888 -> [10, 9, 4, 1, 3, 6, 5, 7, 0, 11, 2, 8] -> 115652888
353180282 -> [7, 5, 4, 1, 3, 10, 6, 0, 9, 8, 11, 2] -> 353180282
275422075 -> [2, 4, 10, 1, 3, 5, 8, 11, 6, 0, 9, 7] -> 275422075
</pre>
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