Create magic_sequence.cpp

backtracking/magic_sequence.cpp

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+/*
+ * @brief [Magic sequence](https://www.csplib.org/Problems/prob019/)
+ *
+ * @details
+ *
+ * @author [Jxtopher](https://github.com/jxtopher)
+ */
+
+#include <algorithm>
+#include <cassert>
+#include <iostream>
+#include <list>
+#include <numeric>
+#include <vector>
+
+namespace backtracking {
+namespace magic_sequence {
+    using sequence_t = std::vector<unsigned int>;
+
+    void print(const sequence_t& s) {
+        for(auto item : s) std::cout << item << " ";
+        std::cout << std::endl;
+    }
+
+    // Check if it's 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;
+    }
+
+    // Filtering of sub-solutions
+    // true if the sub-solution is valid otherwise false
+    bool filtering(const sequence_t& s, unsigned int depth) {
+        return std::accumulate(s.cbegin(), s.cbegin() + depth, static_cast<unsigned int>(0)) <=
+               s.size();
+    }
+
+    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
+
+using namespace backtracking::magic_sequence;
+
+static void test() {
+    sequence_t s_magic = {6, 2, 1, 0, 0, 0, 1, 0, 0, 0};
+    assert(is_magic(s_magic));
+
+    sequence_t s_not_magic = {5, 2, 1, 0, 0, 0, 1, 0, 0, 0};
+    assert(!is_magic(s_not_magic));
+}
+
+int main() {
+    test();
+
+    for(unsigned int i = 2; i < 12; i++) {
+        std::cout << "Solution for n = " << i << std::endl;
+        std::list<sequence_t> r1;
+        sequence_t s1(i, i);
+        solve(s1, r1);
+        for(auto item : r1) print(item);
+    }
+}