#include "worldmap.h"
#include <algorithm>
#include <iostream>
#include <functional>
#include <utility>
#include <cmath>
std::vector<int> spanning_tree(std::vector<std::vector<int>>& adj_list, std::vector<std::vector<int>>& adj_matrix) {
std::function<bool(int, int)> dfs;
std::vector<int> visited(adj_list.size(), 0), path;
dfs = [&](int u, int p) {
if (visited[u]) return false;
visited[u] = 1;
path.push_back(u);
for (int v: adj_list[u])
if (dfs(v, u)) path.push_back(u);
return true;
}; dfs(1, 0);
for (int i=1; i<path.size(); i++) {
adj_matrix[path[i-1]][path[i]] = adj_matrix[path[i]][path[i-1]] = 0;
}
std::vector<std::vector<int>> new_adj_list(adj_list.size());
for (int i=1; i<adj_matrix.size(); i++)
for (int j=1; j<adj_matrix.size(); j++)
if (adj_matrix[i][j])
new_adj_list[i].push_back(j);
adj_list = new_adj_list;
return path;
}
std::vector<std::vector<int>> create_map(int N, int M, std::vector<int> A, std::vector<int> B) {
std::vector<std::vector<int>> adj_list(N+1);
std::vector<std::vector<int>> adj_matrix(adj_list.size(), std::vector<int>(adj_list.size(), 0));
for (int i=0; i<M; i++) {
adj_list[A[i]].push_back(B[i]);
adj_list[B[i]].push_back(A[i]);
adj_matrix[A[i]][B[i]] = adj_matrix[B[i]][A[i]] = 1;
}
std::vector<int> partial = spanning_tree(adj_list, adj_matrix);
// Diagonalization - Insert a new edge and take advantage of that edge
int K = partial.size();
std::vector<std::vector<int>> ans(K, std::vector<int>(K, 0));
for (int i=0; i<K; i++) {
ans[0][i] = partial[i];
}
for (int i=1; i<K; i++) {
// Merge node
int index = -1;
for (int j=1; j<K-1 && index == -1; j++) {
if (ans[i-1][j-1] == ans[i-1][j+1]) {
ans[i][j] = ans[i-1][j-1];
index = j;
}
}
for (int j=index+1; j<K; j++) {
for (int x=1; x<=N; x++) {
if (adj_matrix[ans[i-1][j]][x] && adj_matrix[x][ans[i][j-1]]) {
ans[i][j] = x;
adj_matrix[ans[i-1][j]][x] = 0;
adj_matrix[x][ans[i-1][j]] = 0;
adj_matrix[ans[i][j-1]][x] = 0;
adj_matrix[x][ans[i][j-1]] = 0;
break;
}
}
if (ans[i][j] == 0) {
ans[i][j] = ans[i-1][std::min(j+1, K-1)];
}
}
for (int j=index-1; j>=0; j--) {
for (int x=1; x<=N; x++) {
if (adj_matrix[ans[i-1][j]][x] && adj_matrix[x][ans[i][j+1]]) {
ans[i][j] = x;
adj_matrix[ans[i-1][j]][x] = 0;
adj_matrix[x][ans[i-1][j]] = 0;
adj_matrix[ans[i][j+1]][x] = 0;
adj_matrix[x][ans[i][j+1]] = 0;
break;
}
}
if (ans[i][j] == 0) {
ans[i][j] = ans[i-1][std::max(j-1, 0)];
}
}
}
return ans;
}
