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7x7-skyscrapers.cpp
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7x7-skyscrapers.cpp
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#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <map>
#include <vector>
#include <iostream>
using namespace std;
const int N = 7;
const int SIDES = 4;
const int MASK = (1 << N) - 1;
const int s[SIDES * N] = {0,1,2,3,4,5,6,6,13,20,27,34,41,48,48,47,46,45,44,43,42,42,35,28,21,14,7,0};
const int inc[SIDES * N] = {7,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-7,-7,-7,-7,-7,-7,-7,1,1,1,1,1,1,1};
int possible[N * N], results[N][N];
bool vis[N * N];
vector<int> my_clues;
void set_value(int x, int v) {
int m = MASK ^ (1 << v);
int s_row = x - x % N;
int s_col = x % N;
for (int i = 0; i < N; i++) {
possible[s_row + i] &= m;
possible[s_col + i * N] &= m;
}
possible[x] = 1 << v;
}
int check_unique() {
int n_decides = 0;
for (int i = 0; i < SIDES / 2 * N; i++) {
map<int, vector<int> > possible_indices;
for (int j = s[i], k = 0; k < N; j += inc[i], k++) {
for (int l = 0; l < N; l++)
if ((1 << l) & possible[j]) {
possible_indices[l].push_back(j);
}
}
for (auto const &iter : possible_indices) {
int val = iter.first;
if (iter.second.size() == 1) {
int idx = iter.second[0];
if (possible[idx] != (1 << val)) {
n_decides++;
set_value(idx, val);
}
}
}
}
return n_decides;
}
int filter2 () {
int cnt = 0;
for (int i = 0; i < SIDES * N; i++) {
if (my_clues[i] == 2) {
int mask = MASK;
for (int l = N - 1; l >= 0; l--) {
int m = (1 << l) & possible[s[i]];
mask ^= 1 << l;
if (m) break;
}
for (int j = s[i] + inc[i], k = 1; k < N; j += inc[i], k++) {
int m = (1 << (N - 1)) & possible[j];
if (m) break;
if ((possible[j] | mask) != mask) {
possible[j] &= mask;
cnt++;
}
}
}
}
return cnt;
}
int count_possible(int val) {
int n = 0;
while (val) {
n += val & 1;
val >>= 1;
}
return n;
}
bool valid() {
for (int i = 0; i < SIDES * N; i++) {
if (my_clues[i] == 0) continue;
bool is_decided = true;
for (int j = s[i], k = 0; k < N; j += inc[i], k++) {
if (count_possible(possible[j]) != 1) {
is_decided = false;
break;
}
}
if (is_decided) {
int largest = 0, n_clue = 0;
for (int j = s[i], k = 0; k < N; j += inc[i], k++) {
if (largest < possible[j]) {
n_clue++;
largest = possible[j];
}
}
if (n_clue != my_clues[i]) return false;
}
}
return true;
}
void write_results() {
for (int i = 0; i < N * N; i++) {
int x = i / N, y = i % N;
for (int j = 0; j < N; j++) {
if ((1 << j) == possible[i]) {
results[x][y] = j + 1;
break;
}
}
}
}
bool dfs(int idx) {
int i = -1, tmp = 10000;
for (int _i = 0; _i < N * N; _i++) {
int c = count_possible(possible[_i]);
if (tmp > c && !vis[_i]) {
tmp = c;
i = _i;
}
}
if (i == -1) {
if (valid()) {
write_results();
return true;
}
return false;
}
int possible_bak[N * N];
memcpy(possible_bak, possible, sizeof(int) * N * N);
for (int j = N - 1; j >= 0; j--) {
int m = (1 << j) & possible[i];
if (m == 0) continue;
vis[i] = true;
set_value(i, j);
bool found = false;
if (valid()) {
found = dfs(idx + 1);
}
vis[i] = false;
memcpy(possible, possible_bak, sizeof(int) * N * N);
if (found) {
return true;
}
}
return false;
}
void init() {
for (int i = 0; i < N * N; i++) {
possible[i] = MASK;
vis[i] = true;
}
}
void pre_process() {
for (int i = 0; i < SIDES * N; i++)
{
if (my_clues[i] == 0) continue;
for (int j = s[i], k = 0; k < N; j += inc[i], k++) {
int m = MASK;
for (int l = N + k - my_clues[i] + 1; l < N; l++) m ^= 1 << l;
possible[j] &= m;
}
}
while (check_unique() > 0 );
filter2();
}
vector<vector<int>> SolvePuzzle(const vector<int> &clues) {
vector<vector<int>> r;
init();
my_clues = clues;
pre_process();
vector<pair<int, int>> idx_npos;
for (int i = 0; i < N * N; i++) {
int n_possible = count_possible(possible[i]);
if (n_possible > 1) {
vis[i] = false;
}
}
dfs(0);
for (int i = 0; i < N; i++) {
vector<int> vec;
for (int j = 0; j < N; j++) vec.push_back(results[i][j]);
r.push_back(vec);
}
return r;
}