feat: solving magic sequence problem with backtracking (#1533)

* Create magic_sequence.cpp * update code formatter * updating DIRECTORY.md * Update magic_sequence.cpp * Delete settings.json * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update magic_sequence.cpp * Revert "Delete settings.json" This reverts commit 64b08dee6d. * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * clang-format and clang-tidy fixes for 2263f033 * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update magic_sequence.cpp * Update magic_sequence.cpp * Update magic_sequence.cpp * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update magic_sequence.cpp * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * clang-format and clang-tidy fixes for f889fb4f * Update backtracking/magic_sequence.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update magic_sequence.cpp * fix: Apply suggestions from code review Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: David Leal <halfpacho@gmail.com>
2026-04-01 17:52:40 +08:00 · 2021-07-17 12:06:19 +02:00
parent 7bab516e59
commit ae8685fb6a
2 changed files with 136 additions and 0 deletions
--- a/backtracking/magic_sequence.cpp
+++ b/backtracking/magic_sequence.cpp
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+/*
+ * @brief [Magic sequence](https://www.csplib.org/Problems/prob019/)
+ * implementation
+ *
+ * @details Solve the magic sequence problem with backtracking
+ *
+ * "A magic sequence of length $n$ is a sequence of integers $x_0
+ * \ldots x_{n-1}$ between $0$ and $n-1$, such that for all $i$
+ * in $0$ to $n-1$, the number $i$ occurs exactly $x_i$ times in
+ * the sequence. For instance, $6,2,1,0,0,0,1,0,0,0$ is a magic
+ * sequence since $0$ occurs $6$ times in it, $1$ occurs twice, etc."
+ * Quote taken from the [CSPLib](https://www.csplib.org/Problems/prob019/)
+ * website
+ *
+ * @author [Jxtopher](https://github.com/Jxtopher)
+ */
+
+#include <algorithm>  /// for std::count
+#include <cassert>    /// for assert
+#include <iostream>   /// for IO operations
+#include <list>       /// for std::list
+#include <numeric>    /// for std::accumulate
+#include <vector>     /// for std::vector
+
+/**
+ * @namespace backtracking
+ * @brief Backtracking algorithms
+ */
+namespace backtracking {
+/**
+ * @namespace magic_sequence
+ * @brief Functions for the [Magic
+ * sequence](https://www.csplib.org/Problems/prob019/) implementation
+ */
+namespace magic_sequence {
+using sequence_t =
+    std::vector<unsigned int>;  ///< Definition of the sequence type
+/**
+ * @brief Print the magic sequence
+ * @param s working memory for the sequence
+ */
+void print(const sequence_t& s) {
+    for (const auto& item : s) std::cout << item << " ";
+    std::cout << std::endl;
+}
+
+/**
+ * @brief Check if the sequence is magic
+ * @param s working memory for the sequence
+ * @returns true if it's a magic sequence
+ * @returns false if it's NOT a magic sequence
+ */
+bool is_magic(const sequence_t& s) {
+    for (unsigned int i = 0; i < s.size(); i++) {
+        if (std::count(s.cbegin(), s.cend(), i) != s[i]) {
+            return false;
+        }
+    }
+    return true;
+}
+
+/**
+ * @brief Sub-solutions filtering
+ * @param s working memory for the sequence
+ * @param depth current depth in tree
+ * @returns true if the sub-solution is valid
+ * @returns false if the sub-solution is NOT valid
+ */
+bool filtering(const sequence_t& s, unsigned int depth) {
+    return std::accumulate(s.cbegin(), s.cbegin() + depth,
+                           static_cast<unsigned int>(0)) <= s.size();
+}
+
+/**
+ * @brief Solve the Magic Sequence problem
+ * @param s working memory for the sequence
+ * @param ret list of the valid magic sequences
+ * @param depth current depth in the tree
+ */
+void solve(sequence_t* s, std::list<sequence_t>* ret, unsigned int depth = 0) {
+    if (depth == s->size()) {
+        if (is_magic(*s)) {
+            ret->push_back(*s);
+        }
+    } else {
+        for (unsigned int i = 0; i < s->size(); i++) {
+            (*s)[depth] = i;
+            if (filtering(*s, depth + 1)) {
+                solve(s, ret, depth + 1);
+            }
+        }
+    }
+}
+
+}  // namespace magic_sequence
+}  // namespace backtracking
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // test a valid magic sequence
+    backtracking::magic_sequence::sequence_t s_magic = {6, 2, 1, 0, 0,
+                                                        0, 1, 0, 0, 0};
+    assert(backtracking::magic_sequence::is_magic(s_magic));
+
+    // test a non-valid magic sequence
+    backtracking::magic_sequence::sequence_t s_not_magic = {5, 2, 1, 0, 0,
+                                                            0, 1, 0, 0, 0};
+    assert(!backtracking::magic_sequence::is_magic(s_not_magic));
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+
+    // solve magic sequences of size 2 to 11 and print the solutions
+    for (unsigned int i = 2; i < 12; i++) {
+        std::cout << "Solution for n = " << i << std::endl;
+        // valid magic sequence list
+        std::list<backtracking::magic_sequence::sequence_t> list_of_solutions;
+        // initialization of a sequence
+        backtracking::magic_sequence::sequence_t s1(i, i);
+        // launch of solving the problem
+        backtracking::magic_sequence::solve(&s1, &list_of_solutions);
+        // print solutions
+        for (const auto& item : list_of_solutions) {
+            backtracking::magic_sequence::print(item);
+        }
+    }
+}