competitive-programming-library
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other/Sudoku.hpp
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- Last update: 2024-06-19 15:49:33+09:00
- Include:
#include "other/Sudoku.hpp"
Depends on
basic/template.hpp
Code
#pragma once
#include "../basic/template.hpp"
class Sudoku {
static void determine(int i, int j, int x,
std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& target) {
target[i][j] = x;
rep(k, 9) flag[i][k][x - 1] = flag[k][j][x - 1] = false;
rep(k, 3) rep(l, 3) flag[i / 3 * 3 + k][j / 3 * 3 + l][x - 1] = false;
rep(k, 9) flag[i][j][k] = false;
flag[i][j][x - 1] = true;
}
static bool completed(const std::array<std::array<int, 9>, 9>& ans) {
rep(i, 9) rep(j, 9) if (!ans[i][j]) return false;
return true;
}
static bool solvable(const std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
const std::array<std::array<int, 9>, 9>& ans) {
rep(i, 9) {
rep(j, 9) {
if (!ans[i][j]) {
bool ok = false;
rep(k, 9) ok |= flag[i][j][k];
if (!ok) return false;
}
}
}
return true;
}
static void logic(std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& ans) {
while (true) {
bool updated = false;
rep(i, 9) rep(j, 9) {
int cand = 0, cnt = 0;
rep(k, 9) {
if (!ans[i][j] && flag[i][j][k]) {
cand = k + 1, cnt++;
if (cnt > 1) break;
}
}
if (cnt == 1) determine(i, j, cand, flag, ans), updated = true;
}
rep(i, 9) {
rep(j, 9) {
int cand = -1;
rep(k, 9) {
if (ans[i][k] == j + 1) {
cand = -1;
break;
}
if (flag[i][k][j]) {
if (cand != -1) {
cand = -1;
break;
}
cand = k;
}
}
if (cand != -1) determine(i, cand, j + 1, flag, ans), updated = true;
cand = -1;
rep(k, 9) {
if (ans[k][i] == j + 1) {
cand = -1;
break;
}
if (flag[k][i][j]) {
if (cand != -1) {
cand = -1;
break;
}
cand = k;
}
}
if (cand != -1) determine(cand, i, j + 1, flag, ans), updated = true;
}
}
rep(i, 3) {
rep(j, 3) {
rep(k, 9) {
IP cand = {-1, -1};
bool ng = false;
rep(l, 3) {
rep(m, 3) {
if (ans[i * 3 + l][j * 3 + m] == k + 1) {
cand = IP{-1, -1};
ng = true;
break;
}
if (flag[i * 3 + l][j * 3 + m][k]) {
if (cand != IP{-1, -1}) {
cand = IP{-1, -1};
ng = true;
break;
}
cand = IP{l, m};
}
}
if (ng) break;
}
if (!ng && cand != IP{-1, -1})
determine(i * 3 + cand.first, j * 3 + cand.second, k + 1, flag, ans),
updated = true;
}
}
}
if (!updated) break;
}
}
static bool solve(std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& ans) {
logic(flag, ans);
auto nflag = flag;
auto nans = ans;
rep(i, 9) {
rep(j, 9) {
if (!nans[i][j]) {
rep(k, 9) {
if (nflag[i][j][k]) {
determine(i, j, k + 1, nflag, nans);
if (!solvable(nflag, nans) || !solve(nflag, nans)) {
flag[i][j][k] = false;
nflag = flag, nans = ans;
}
}
}
}
}
}
if (completed(nans)) {
flag = nflag, ans = nans;
return true;
}
return false;
}
public:
static std::array<std::array<int, 9>, 9> solve(const std::array<std::array<int, 9>, 9>& prob) {
std::array<std::array<std::array<bool, 9>, 9>, 9> flag;
auto ans = prob;
rep(i, 9) rep(j, 9) rep(k, 9) flag[i][j][k] = true;
rep(i, 9) rep(j, 9) if (prob[i][j]) determine(i, j, prob[i][j], flag, ans);
solve(flag, ans);
return ans;
}
};#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()
using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#else
#ifndef __clang__
return __builtin_popcount(x);
#endif
#endif
x = (x & 0x55555555) + (x >> 1 & 0x55555555);
x = (x & 0x33333333) + (x >> 2 & 0x33333333);
x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
return [f = std::forward<F>(f)](auto&&... args) {
return f(f, std::forward<decltype(args)>(args)...);
};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
return ost << x.first << " " << x.second;
}
template <class Container,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
-> decltype(typename Container::iterator(), std::cin)& {
Container tmp;
while (true) {
typename Container::value_type t;
ist >> t;
tmp.emplace_back(t);
if (getchar() == '\n') break;
}
cont = Container(std::move(tmp));
return ist;
}
template <class Container, class Stream,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
-> decltype(typename Container::iterator(), ost)& {
for (auto it = cont.begin(); it != cont.end(); it++) {
if (it != cont.begin()) ost << ' ';
ost << *it;
}
return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
lint res = 0;
for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
while (b) {
lint c = a;
a = b;
b = c % b;
}
return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
if (n == 1) return false;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
T res(1);
while (true) {
if (b & 1) res *= a;
b >>= 1;
if (!b) break;
a *= a;
}
return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
a %= m;
lint res(1);
while (b) {
if (b & 1) res *= a, res %= m;
a *= a, a %= m, b >>= 1;
}
return res;
}
LP extGcd(lint a, lint b) noexcept {
if (b == 0) return {1, 0};
LP s = extGcd(b, a % b);
std::swap(s.first, s.second);
s.second -= a / b * s.first;
return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
auto p = extGcd(m1, m2);
lint g = gcd(m1, m2), l = m1 / g * m2;
lint tmp = (b2 - b1) / g * p.first % (m2 / g);
lint r = (b1 + m1 * tmp + l) % l;
return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
rep(i, a.size()) {
rep(j, b.size()) {
chmax(dp[i + 1][j], dp[i][j]);
chmax(dp[i][j + 1], dp[i][j]);
if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
}
chmax(dp[i + 1][b.size()], dp[i][b.size()]);
}
rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
auto tmp = vec;
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
std::vector<T> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
std::vector<typename InputIter::value_type> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter,
std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
if (lhs.first.first / M < rhs.first.first / M) return true;
if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
return false;
});
int before = -1, cnt = 0;
bool f = false;
for (InputIter i = l; i != r; i++) {
if (before != i->first.first / M) {
if (f) std::reverse(i - cnt, i);
f ^= true, before = i->first.first / M, cnt = 1;
} else
cnt++;
}
if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
std::vector<T> res;
for (T i : vec) {
for (T j : res) {
chmin(i, i ^ j);
}
if (i) res.emplace_back(i);
}
return res;
}
#line 3 "other/Sudoku.hpp"
class Sudoku {
static void determine(int i, int j, int x,
std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& target) {
target[i][j] = x;
rep(k, 9) flag[i][k][x - 1] = flag[k][j][x - 1] = false;
rep(k, 3) rep(l, 3) flag[i / 3 * 3 + k][j / 3 * 3 + l][x - 1] = false;
rep(k, 9) flag[i][j][k] = false;
flag[i][j][x - 1] = true;
}
static bool completed(const std::array<std::array<int, 9>, 9>& ans) {
rep(i, 9) rep(j, 9) if (!ans[i][j]) return false;
return true;
}
static bool solvable(const std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
const std::array<std::array<int, 9>, 9>& ans) {
rep(i, 9) {
rep(j, 9) {
if (!ans[i][j]) {
bool ok = false;
rep(k, 9) ok |= flag[i][j][k];
if (!ok) return false;
}
}
}
return true;
}
static void logic(std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& ans) {
while (true) {
bool updated = false;
rep(i, 9) rep(j, 9) {
int cand = 0, cnt = 0;
rep(k, 9) {
if (!ans[i][j] && flag[i][j][k]) {
cand = k + 1, cnt++;
if (cnt > 1) break;
}
}
if (cnt == 1) determine(i, j, cand, flag, ans), updated = true;
}
rep(i, 9) {
rep(j, 9) {
int cand = -1;
rep(k, 9) {
if (ans[i][k] == j + 1) {
cand = -1;
break;
}
if (flag[i][k][j]) {
if (cand != -1) {
cand = -1;
break;
}
cand = k;
}
}
if (cand != -1) determine(i, cand, j + 1, flag, ans), updated = true;
cand = -1;
rep(k, 9) {
if (ans[k][i] == j + 1) {
cand = -1;
break;
}
if (flag[k][i][j]) {
if (cand != -1) {
cand = -1;
break;
}
cand = k;
}
}
if (cand != -1) determine(cand, i, j + 1, flag, ans), updated = true;
}
}
rep(i, 3) {
rep(j, 3) {
rep(k, 9) {
IP cand = {-1, -1};
bool ng = false;
rep(l, 3) {
rep(m, 3) {
if (ans[i * 3 + l][j * 3 + m] == k + 1) {
cand = IP{-1, -1};
ng = true;
break;
}
if (flag[i * 3 + l][j * 3 + m][k]) {
if (cand != IP{-1, -1}) {
cand = IP{-1, -1};
ng = true;
break;
}
cand = IP{l, m};
}
}
if (ng) break;
}
if (!ng && cand != IP{-1, -1})
determine(i * 3 + cand.first, j * 3 + cand.second, k + 1, flag, ans),
updated = true;
}
}
}
if (!updated) break;
}
}
static bool solve(std::array<std::array<std::array<bool, 9>, 9>, 9>& flag,
std::array<std::array<int, 9>, 9>& ans) {
logic(flag, ans);
auto nflag = flag;
auto nans = ans;
rep(i, 9) {
rep(j, 9) {
if (!nans[i][j]) {
rep(k, 9) {
if (nflag[i][j][k]) {
determine(i, j, k + 1, nflag, nans);
if (!solvable(nflag, nans) || !solve(nflag, nans)) {
flag[i][j][k] = false;
nflag = flag, nans = ans;
}
}
}
}
}
}
if (completed(nans)) {
flag = nflag, ans = nans;
return true;
}
return false;
}
public:
static std::array<std::array<int, 9>, 9> solve(const std::array<std::array<int, 9>, 9>& prob) {
std::array<std::array<std::array<bool, 9>, 9>, 9> flag;
auto ans = prob;
rep(i, 9) rep(j, 9) rep(k, 9) flag[i][j][k] = true;
rep(i, 9) rep(j, 9) if (prob[i][j]) determine(i, j, prob[i][j], flag, ans);
solve(flag, ans);
return ans;
}
};