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hamiltonian.cpp
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hamiltonian.cpp
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#include <iostream>
#include <vector>
#include <array>
#include <deque>
#include <iterator>
#include <algorithm>
#include <cstdlib>
#include <ctime>
#include <thread>
#include <future>
using std::cout;
using std::endl;
struct Entry {
int weight;
std::pair<int, int> coords;
};
struct Node {
int val;
Node* next1 = nullptr;
Node* next2 = nullptr;
};
std::vector<Entry> owal;
const int chessNo = 11;
void printOwal(const std::vector<Entry>& owal) {
for (auto&& e : owal) {
cout << "w:" << e.weight << " at (" << e.coords.first << "," << e.coords.second << ")" << endl;
}
}
void printCom(const std::vector<int>& a) {
for (auto&& e: a) {
cout << e << " ";
}
cout << endl;
}
void printCount(const std::array<int, chessNo>& a) {
cout << "Count: ";
for (auto&& e : a)
cout << e << " ";
cout << endl;
}
std::array<Node, chessNo> genCycle(const std::vector<int>& com) {
std::array<Node, chessNo> nodes;
for (int i = 1; i <= chessNo; i++) {
nodes[i - 1].val = i;
}
for (int i = 0; i < owal.size(); i++) {
if (com[i]) {
if (nodes[owal[i].coords.first - 1].next1 == nullptr) {
nodes[owal[i].coords.first - 1].next1 = &nodes[owal[i].coords.second - 1];
} else {
nodes[owal[i].coords.first - 1].next2 = &nodes[owal[i].coords.second - 1];
}
if (nodes[owal[i].coords.second - 1].next1 == nullptr) {
nodes[owal[i].coords.second - 1].next1 = &nodes[owal[i].coords.first - 1];
} else {
nodes[owal[i].coords.second - 1].next2 = &nodes[owal[i].coords.first - 1];
}
}
}
return nodes;
}
std::array<int, chessNo> genPath(const std::array<Node, chessNo>& nodes) {
std::array<int, chessNo> path;
const Node* n = &nodes[chessNo - 1];
path[0] = n->val;
int old1 = n->val;
n = n->next1;
path[1] = n->val;
int old2 = n->val;
for (int i = 2; i <= chessNo; i++) {
old2 = n->val;
if (old1 == n->next1->val)
n = n->next2;
else
n = n->next1;
path[i] = n->val;
old1 = old2;
}
return path;
};
bool checkCycle(const std::array<int, chessNo>& cycle) {
bool valid_first = true;
bool valid_second = true;
// check if continuous cycle
if (std::find(cycle.begin()+1, cycle.end(), chessNo) != cycle.end()) {
return false;
}
// ONE DIRECTION
const int half = (chessNo - 1) / 2;
for (int i = 1, n = 0; i < chessNo; i++) {
if (cycle[(i) % chessNo] <= half)
n++;
else n--;
if (n < 0) {
valid_first = false;
break;
}
}
if (!valid_first) {
for (int i = 1, n = 0; i < chessNo; i++) {
if (cycle[(chessNo - i) % chessNo] <= half)
n++;
else n--;
if (n < 0) {
valid_second = false;
break;
}
}
}
return valid_first || valid_second;
}
void printNodes(const std::array<Node, chessNo> nodes) {
cout << "Cycle: ";
const Node* n = &nodes[chessNo - 1];
cout << n->val << " ";
int old1 = n->val;
n = n->next1;
cout << n->val << " ";
int old2 = n->val;
for (int i = 0; i < chessNo - 2; i++) {
old2 = n->val;
if (old1 == n->next1->val)
n = n->next2;
else
n = n->next1;
cout << n->val << " ";
old1 = old2;
}
cout << endl;
}
void printPath(const std::array<int, chessNo> p) {
cout << "Cycle: ";
for (auto&& e : p) {
cout << e << " ";
}
cout << endl;
}
bool checkCombination(const std::vector<int>& com) {
std::array<int, chessNo> count{};
for (int i = 0; i < owal.size(); i++) {
if (com[i]) {
count[owal[i].coords.first - 1]++;
count[owal[i].coords.second - 1]++;
}
}
// printCount(count);
for (int i = 0; i < chessNo; i++) {
if (count[i] != 2) break;
else if (i == chessNo - 1) {
std::array<Node, chessNo> nodes = genCycle(com);
// printCom(com);
// printCount(count);
std::array<int, chessNo> path = genPath(nodes);
// printPath(path);
if (checkCycle(path)) {
cout << "FOUND." << endl;
printPath(path);
printCom(com);
int w = 0;
for (int j = 0; j < owal.size(); j++) {
if (com[j]) {
w += owal[j].weight;
}
}
cout << "Total weight: " << w << endl;
return true;
}
}
}
return false;
}
int main() {
std::srand(std::time(nullptr));
/** Setup OWAL */
for (int i = 1, temp = 0; i <= chessNo; i++) {
for (int j = i + 1; j <= chessNo; j++) {
cout << "(" << i << "," << j << ")";
// cin >> temp;
temp = 1+std::rand()%50;
owal.push_back({temp, {i, j}});
}
}
sort(owal.begin(), owal.end(), [](const Entry& a, const Entry& b) {
return a.weight < b.weight;
});
printOwal(owal);
/** Setup k-combination */
std::vector<int> com = {};
for (int i = 0; i < chessNo; i++)
com.push_back(1);
for (int i = 0; i < owal.size() - chessNo; i++)
com.push_back(0);
std::next_permutation(com.begin(), com.end());
std::vector<int> original_com = com;
/** for each k-combination, O(n) per cycle */
int cnt = 0;
do {
prev_permutation(com.begin(), com.end());
if (++cnt % 10000000 == 0) cout << cnt << endl;
if (checkCombination(com)) break;
} while (com != original_com);
}