Data update

Task/Permutations-Derangements/C++/permutations-derangements.cpp

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+#include <cstdint>
+#include <iomanip>
+#include <iostream>
+#include <numeric>
+#include <vector>
+
+typedef std::pair<std::vector<std::vector<int32_t>>, int32_t> list_or_count;
+
+uint64_t factorial(const int32_t& n) {
+	uint64_t result = 1;
+	for ( int32_t i = 2; i <= n; ++i ) {
+		result *= i;
+	}
+	return result;
+}
+
+uint64_t subfactorial(const int32_t& n) {
+	if ( n >= 0 && n <= 2 ) {
+		return ( n == 1 ) ? 0 : 1;
+	}
+	return ( n - 1 ) * ( subfactorial(n - 1) + subfactorial(n - 2) );
+}
+
+list_or_count derangements(const int32_t& n, const bool& count_only) {
+	std::vector<int32_t> sequence(n, 0);
+	std::iota(sequence.begin() ,sequence.end(), 1);
+	std::vector<int32_t> original(sequence);
+	uint64_t permutation_count = factorial(n);
+
+	std::vector<std::vector<int32_t>> list;
+	int32_t count = ( n == 0 ) ? 1 : 0;
+
+	while ( --permutation_count > 0 ) {
+		int32_t j = n - 2;
+		while ( sequence[j] > sequence[j + 1] ) {
+			j--;
+		}
+		int32_t k = n - 1;
+		while ( sequence[j] > sequence[k] ) {
+			k--;
+		}
+		std::swap(sequence[j], sequence[k]);
+
+		int32_t r = n - 1;
+		int32_t s = j + 1;
+		while ( r > s ) {
+			std::swap(sequence[r], sequence[s]);
+			r--;
+			s++;
+		}
+
+		j = 0;
+		while ( j < n && sequence[j] != original[j] ) {
+			j++;
+		}
+		if ( j == n ) {
+			if ( count_only ) {
+				count++;
+			} else {
+				std::vector<int32_t> copy_sequence(sequence);
+				list.emplace_back(copy_sequence);
+			}
+		}
+	}
+	return list_or_count(list, count);
+}
+
+int main() {
+	std::cout << "Derangements for n = 4" << std::endl;
+	list_or_count list_count = derangements(4, false);
+	for ( std::vector<int32_t> list : list_count.first ) {
+		std::cout << "[";
+		for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
+			std::cout << list[i] << ", ";
+		}
+		std::cout << list.back() << "]" << std::endl;
+	}
+	std::cout << std::endl;
+
+	std::cout << "n   derangements      !n" << std::endl;
+	std::cout << "------------------------" << std::endl;
+	for ( int32_t n = 0; n < 10; ++n ) {
+		int32_t count = derangements(n, true).second;
+		std::cout << n << ":  " << std::setw(9) << count << "  " << std::setw(9) << subfactorial(n) << std::endl;
+	}
+	std::cout << std::endl;
+
+	std::cout << "!20 = " << subfactorial(20) << std::endl;
+}