/* Upwards Collatz Build a collatz series starting from the low end (1,2,4) and make it as long as you can. Verify its number of steps through the normal Collatz. The Collatz conjecture (aka Ulam conjecture or the Syracuse problem) is formulated as: 1. Take any natural number 2. If it's even, half it, otherwise triple it and add one 3. Repeat step 2. until you reach 4, 2, 1 sequenceh 4. You will ALWAYS reach 1, eventually. You can find it in sololearn : https://www.sololearn.com/learn/6768/ */ /* The code produce a graph for reverse collatz sequence. After the sequence 1->2->4->8->16 we have two options 5 and 32. The code finds the next element from each node. So you will have the sequence like 1->2->4->8->16->5 or 1->2->4->8->16->32 then from there it will be like 1->2->4->8->16->5->10 and 1->2->4->8->16->32->64 1->2->4->8->16->5->10->3 and 1->2->4->8->16->5->10->20 1->2->4->8->16->32->64->128 and so on */ #include #include #include #include using namespace std; using UL = unsigned long long; using V = vector

; auto rev_collatz = [](UL mxl)->pair { VV vv{{1}}; while(vv.size() < mxl) { V v; auto&& last {vv.back()}; transform(last.begin(), last.end(), back_inserter(v), [&](UL num) { UL odd {(num - 1) / 3}; // check for 1, if found skip it // else the sequence will get stuck // in 1->2->4->1 sequence if(((num % 6) == 4) && odd != 1) v.emplace_back(odd); return num << 1; }); vv.emplace_back(v); } return {mxl,vv}; }; int main() { auto print = [=](auto&& col_seq) { auto&&[mxl, levels] = col_seq; cout << "reverse_collatz(" << mxl <<") = ["; for_each(levels.begin(), levels.end(), [](auto&& lvl) { cout << '['; for(auto e : lvl) cout << e << ','; cout << "], "; }); cout << "]\n\n"; }; // the numbers represent the levels in the graph for(auto n : {1, 2, 3, 4, 5, 6, 9, 11, 15, 20, 25, 30, 35}) print(rev_collatz(n)); }

Reverse_Collatz_graph.cpp