forked from lengyueyang/LeetCode
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sliding-puzzle.cpp
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/
sliding-puzzle.cpp
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// Time: O((m * n) * (m * n)!)
// Space: O((m * n) * (m * n)!)
// A* Search Algorithm
class Solution {
public:
int slidingPuzzle(vector<vector<int>>& board) {
const auto& R = board.size(), &C = board[0].size();
vector<int> begin, end;
unordered_map<int, pair<int, int>> expected;
int zero_idx = 0;
for (int i = 0; i < R; ++i) {
for (int j = 0; j < C; ++j) {
auto val = (C * i + j + 1) % (R * C);
expected[val] = {i, j};
if (board[i][j] == 0) {
zero_idx = begin.size();
}
begin.emplace_back(board[i][j]);
end.emplace_back(val);
}
}
int min_steps = heuristic_estimate(begin, R, C, expected);
unordered_set<vector<int>, Hash<vector<int>>> lookup;
vector<pair<int, vector<int>>> closer{make_pair(zero_idx, begin)}, detour;
while (true) {
if (closer.empty()) {
if (detour.empty()) {
return -1;
}
min_steps += 2;
swap(closer, detour);
}
int zero;
vector<int> board;
tie(zero, board) = closer.back(); closer.pop_back();
if (board == end) {
return min_steps;
}
if (!lookup.count(board)) {
lookup.emplace(board);
int r = zero / C;
int c = zero % C;
static const vector<pair<int, int>> directions{{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
for (const auto& direction : directions) {
int i = r + direction.first;
int j = c + direction.second;
if (0 <= i && i < R && 0 <= j && j < C) {
auto new_zero = C * i + j;
auto new_board = board;
swap(new_board[zero], new_board[new_zero]);
int r2, c2;
tie(r2, c2) = expected[board[new_zero]];
int r1 = zero / C;
int c1 = zero % C;
int r0 = new_zero / C;
int c0 = new_zero % C;
bool is_closer = dot({r1 - r0, c1 - c0}, {r2 - r0, c2 - c0}) > 0;
is_closer ? closer.emplace_back(new_zero, new_board) : detour.emplace_back(new_zero, new_board);
}
}
}
}
return min_steps;
}
private:
int heuristic_estimate(const vector<int>& board, int R, int C, const unordered_map<int, pair<int, int>>& expected) {
int result = 0;
for (int i = 0; i < R; ++i) {
for (int j = 0; j < C; ++j) {
const auto& val = board[C * i + j];
if (val == 0) {
continue;
}
int r, c;
tie(r, c) = expected.at(val);
result += abs(r - i) + abs(c - j);
}
}
return result;
}
inline int dot(const pair<int, int>& a, const pair<int, int>& b) {
return a.first * b.first + a.second * b.second;
}
template<typename ContType>
struct Hash {
size_t operator()(const ContType& v) const {
size_t seed = 0;
for (const auto& i : v) {
seed ^= std::hash<typename ContType::value_type>{}(i) + 0x9e3779b9 + (seed<<6) + (seed>>2);
}
return seed;
}
};
};
// Time: O((m * n) * (m * n)! * log((m * n)!))
// Space: O((m * n) * (m * n)!)
// A* Search Algorithm
class Solution2 {
public:
int slidingPuzzle(vector<vector<int>>& board) {
const auto& R = board.size(), &C = board[0].size();
vector<int> begin, end;
unordered_map<int, pair<int, int>> expected;
int zero_idx = 0;
for (int i = 0; i < R; ++i) {
for (int j = 0; j < C; ++j) {
auto val = (C * i + j + 1) % (R * C);
expected[val] = {i, j};
if (board[i][j] == 0) {
zero_idx = begin.size();
}
begin.emplace_back(board[i][j]);
end.emplace_back(val);
}
}
vector<int> end_wrong(end);
swap(end_wrong[end_wrong.size() - 2], end_wrong[end_wrong.size() - 3]);
using P = tuple<int, int, int, vector<int>>;
priority_queue<P, vector<P>, greater<P>> min_heap;
min_heap.emplace(make_tuple(0, 0, zero_idx, begin));
unordered_map<vector<int>, int, Hash<vector<int>>> lookup;
lookup[begin] = 0;
while (!min_heap.empty()) {
int f, g, zero;
vector<int> board;
tie(f, g, zero, board) = min_heap.top(); min_heap.pop();
if (board == end) {
return g;
}
if (board == end_wrong) {
return -1;
}
if (f > lookup[board]) {
continue;
}
int r = zero / C;
int c = zero % C;
static const vector<pair<int, int>> directions{{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
for (const auto& direction : directions) {
int i = r + direction.first;
int j = c + direction.second;
if (0 <= i && i < R && 0 <= j && j < C) {
auto new_zero = C * i + j;
auto new_board = board;
swap(new_board[zero], new_board[new_zero]);
f = g + 1 + heuristic_estimate(new_board, R, C, expected);
if (!lookup.count(new_board) || f < lookup[new_board])
lookup[new_board] = f;
min_heap.emplace(make_tuple(f, g + 1, new_zero, new_board));
}
}
}
}
return -1;
}
private:
int heuristic_estimate(const vector<int>& board, int R, int C, const unordered_map<int, pair<int, int>>& expected) {
int result = 0;
for (int i = 0; i < R; ++i) {
for (int j = 0; j < C; ++j) {
const auto& val = board[C * i + j];
if (val == 0) {
continue;
}
int r, c;
tie(r, c) = expected.at(val);
result += abs(r - i) + abs(c - j);
}
}
return result;
}
template<typename ContType>
struct Hash {
size_t operator()(const ContType& v) const {
size_t seed = 0;
for (const auto& i : v) {
seed ^= std::hash<typename ContType::value_type>{}(i) + 0x9e3779b9 + (seed<<6) + (seed>>2);
}
return seed;
}
};
};