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#include <iostream>
#include <utility>
#include <vector>
#include <string>
#include <math.h>
#include <climits>
#include <cassert>
#include <chrono>
// #include "graph.h"
using namespace std;
using namespace chrono;
int I, N = 0;
struct Node {
vector<int> board;
string change;
int zero;
int currentDepth;
int remainingDepth;
Node() : board(), change(), zero(), currentDepth(), remainingDepth() {}
void update_zero() {
for (this->zero = 0; this->zero < this->board.size(); this->zero++) {
if (this->board[this->zero] == 0) return;
}
}
void update_remainingDepth() {
this->remainingDepth = this->manhattan_dist();
}
bool solved() {
return this->remainingDepth == 0;
}
int depth() {
return this->currentDepth + this->remainingDepth;
}
bool equals_any_in(vector<Node*>& arr) {
for (int i = 0; i < arr.size(); i++) {
if (*arr[i] == *this) {
return true;
}
}
return false;
}
void increment(int new_zero) {
swap(this->board[new_zero], this->board[this->zero]);
this->zero = new_zero;
this->currentDepth++;
this->update_remainingDepth();
}
private:
pair<int, int> to_2D(int i) {
return { i / N, i % N };
}
int manhattan_dist() {
int total = 0;
for (int i = 0; i < this->board.size(); i++) {
if (this->board[i] == 0) continue;
auto curr = to_2D(i);
auto goal = to_2D(this->board[i] - 1 + (this->board[i] > I));
total += abs(curr.first - goal.first) + abs(curr.second - goal.second);
}
return total;
}
public:
Node& operator=(const Node& other) {
if (this != &other) {
this->change = other.change;
this->board = other.board;
this->zero = other.zero;
this->currentDepth = other.currentDepth;
this->remainingDepth = other.remainingDepth;
}
return *this;
}
friend bool operator==(const Node& left, const Node& right) {
return left.board == right.board;
}
};
#define SOLVED -1
#define SKIP_J_IF(condition) if (condition) { delete j; continue; }
int dfs(vector<Node*>& path, int maxDepth) {
Node* i = path.back();
if (i->solved()) return SOLVED;
if (i->depth() > maxDepth) return i->depth();
int min = INT_MAX;
for (int dir = 0; dir < 4; dir++) {
Node* j = new Node(*i);
int new_zero = 0;
switch (dir) {
case 0: // left
SKIP_J_IF(j->zero % N == 0);
new_zero = j->zero - 1;
j->change = "right";
break;
case 1: // right
SKIP_J_IF(j->zero % N == N - 1);
new_zero = j->zero + 1;
j->change = "left";
break;
case 2: // up
SKIP_J_IF(j->zero / N == 0);
new_zero = j->zero - N;
j->change = "down";
break;
case 3: // down
SKIP_J_IF(j->zero / N == N - 1);
new_zero = j->zero + N;
j->change = "up";
break;
}
j->increment(new_zero);
// Don't go back a step
SKIP_J_IF(j->equals_any_in(path));
path.push_back(j);
int val = dfs(path, maxDepth);
if (val == SOLVED) return SOLVED;
if (val < min) min = val;
path.pop_back();
delete j;
}
return min;
}
bool solvable(Node* root) {
vector<int> &board = root->board;
int inversions = 0;
for (int i = 0; i < board.size(); i++) {
if (board[i] == 0) continue;
for (int j = i; j < board.size(); j++) {
if (board[j] == 0) continue;
inversions += board[i] > board[j];
}
}
// n is even, an n-by-n board is solvable
// iff the number of inversions + the row of the blank square is odd
if (board.size() % 2 == 0) {
inversions += root->zero / N;
return (inversions % 2) == ((I / N) % 2);
}
// when n is odd, an n-by-n board is solvable
// iff its number of inversions is even
else {
return inversions % 2 == 0;
}
}
int main(int argc, char* argv[]) {
/* Input */
cin >> N >> I;
if (I == -1) { I = N; }
N++;
Node* root = new Node;
int temp;
for (int i = 0; i < N; i++) {
cin >> temp;
root->board.push_back(temp);
}
N = sqrt(N + 1);
/* Prepare */
root->update_zero();
if (!solvable(root)) {
std::cout << -1 << std::endl;
delete root;
return 0;
}
root->update_remainingDepth();
vector<Node*> path;
path.push_back(root);
/* IDA* */
auto startTime = system_clock::now();
int bound = 3;
while(bound != SOLVED) {
bound = dfs(path, bound);
}
auto endTime = system_clock::now();
/* Output */
cout << (path.size() - 1) << endl;
for (int i = 1; i < path.size(); i++) {
cout << path[i]->change << endl;
delete path[i];
}
delete root;
if (argc > 1) {
auto millis = duration_cast<std::chrono::milliseconds>(endTime - startTime).count();
std::cout << "Took: " << millis / 1000.0 << "s" << std::endl;
}
}
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