#include "worldmap.h"
#include <algorithm>
#include <iostream>
#include <functional>
#include <utility>
#include <cmath>
#include <cassert>
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) {
// if (M == 0) {
// for (int i=1; i<=N; i++) {
// for (int j=i+1; j<=N; j++) {
// A.push_back(i);
// B.push_back(j);
// }
// }
// M = A.size();
// }
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 = 3*N;
std::vector<std::vector<int>> ans(K, std::vector<int>(K, 0));
for (int i=0; i<K; i++) ans[0][i] = partial[i%partial.size()];
int last_copy = 0;
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=0; j<K && index == -1; j++) {
for (int x=N; x>=1; x--) {
if (adj_matrix[ans[i-1][j]][x]) {
ans[i][j] = x;
index = j;
adj_matrix[ans[i-1][j]][x] = 0;
adj_matrix[x][ans[i-1][j]] = 0;
break;
}
}
}
if (index == -1) {
for (int j=0; j<K; j++) {
ans[i][j] = ans[last_copy][j];
}
last_copy = std::max(last_copy, 0);
continue;
}
last_copy = i;
for (int j=index+1; j<K; j++) {
for (int x=N; x>=1; 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)];
ans[i][j] = ans[i-1][j-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)];
ans[i][j] = ans[i-1][j+1];
}
}
}
// // Write a checker to debug.
// std::cout << "Final size: " << N << '\t' << M << '\n';
// for (int i=0; i<ans.size(); i++) {
// for (int j=0; j<ans.size(); j++) {
// std::cout << ans[i][j] << ' ';
// }
// std::cout << '\n';
// }
// int validate[N+5][N+5];
// memset(validate, 0, sizeof(validate));
// for (int i=0; i<K; i++) {
// for (int j=0; j<K; j++) {
// if (i-1 >= 0) {
// if (std::min(ans[i][j], ans[i-1][j]) == 3
// && std::max(ans[i][j], ans[i-1][j]) == 7) {
// std::cout << i << '\t' << j << '\n';
// }
// validate[ans[i][j]][ans[i-1][j]] = 1;
// validate[ans[i-1][j]][ans[i][j]] = 1;
// }
// if (j-1 >= 0) {
// if (std::min(ans[i][j], ans[i][j-1]) == 3
// && std::max(ans[i][j], ans[i][j-1]) == 7) {
// std::cout << i << '\t' << j << '\n';
// }
// validate[ans[i][j]][ans[i][j-1]] = 1;
// validate[ans[i][j-1]][ans[i][j]] = 1;
// }
// }
// }
// for (int i=0; i<M; i++) {
// validate[A[i]][B[i]]--;
// validate[B[i]][A[i]]--;
// }
// bool flag = false;
// for (int i=1; i<=N; i++)
// for (int j=i+1; j<=N; j++)
// if (validate[i][j] != 0) {
// std::cout << i << '\t' << j << '\t' << validate[i][j] << '\n';
// flag = true;
// }
// if (flag) exit(-1);
return ans;
}
