USACO4.4.3 Frame Up (frameup)

用1~26表示每种字母

统计每种字母的最小与最大的x与y坐标，这样就知道了每个矩形的边框。

从最上层开始dfs，找到当前所有边框上都是同样数字的矩形，则这个矩形一定是最上层的，继续dfs。

每次dfs找到一个矩形时，将该矩形的边框上的所有数字设为负数，负数可以看作是任何一种数字。回溯时再还原。

dfs到最后一层时记录答案，最后排序输出。

/*
ID:shijiey1
LANG:C++
PROG:frameup
*/
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>

using namespace std;

int n, m;
int arr[35][35];
int x1[28];
int y1[28];
int x2[28];
int y2[28];
int T;
int min(int a, int b) {
if (a == -1) return b;
if (b == -1) return a;
return a < b ? a : b;
}

void init() {
memset(x1, -1, sizeof(x1));
memset(y1, -1, sizeof(y1));
memset(x2, -1, sizeof(x2));
memset(y2, -1, sizeof(y2));
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (!arr[i][j]) continue;
x1[arr[i][j]] = min(x1[arr[i][j]], i);
y1[arr[i][j]] = min(y1[arr[i][j]], j);
x2[arr[i][j]] = max(x2[arr[i][j]], i);
y2[arr[i][j]] = max(y2[arr[i][j]], j);
}
}
for (int i = 1; i <= 26; i++)
if (x1[i] != -1) T++;
}

int done[28];
vector<int> ans;
vector<vector<int> > last;
void dfs(int step) {
if (step == T) {
last.push_back(ans);
return;
}
for (int i = 1; i <= 26; i++) {

if (x1[i] == -1 || done[i]) continue;
bool flag = true;
for (int j = x1[i]; j <= x2[i]; j++) {
if (arr[j][y1[i]] != i && arr[j][y1[i]] > 0 || (arr[j][y2[i]] != i && arr[j][y2[i]] > 0)) {
flag = false;
break;
}
}
if (!flag) continue;
for (int j = y1[i]; j <= y2[i]; j++) {
if (arr[x1[i]][j] != i && arr[x1[i]][j] > 0 || (arr[x2[i]][j] != i && arr[x2[i]][j] > 0)) {
flag = false;
break;
}
}
if (!flag) continue;

for (int j = x1[i]; j <= x2[i]; j++) {
if (arr[j][y1[i]] == i) {
arr[j][y1[i]] = -i - 1;
}
if (arr[j][y2[i]] == i) {
arr[j][y2[i]] = -i - 1;
}
}
for (int j = y1[i]; j <= y2[i]; j++) {
if (arr[x1[i]][j] == i) {
arr[x1[i]][j] = -i - 1;
}
if (arr[x2[i]][j] == i) {
arr[x2[i]][j] = -i - 1;
}
}
done[i] = 1;
ans.push_back(i);
dfs(step + 1);
ans.pop_back();
done[i] = 0;
for (int j = x1[i]; j <= x2[i]; j++) {
if (arr[j][y1[i]] == -i - 1) {
arr[j][y1[i]] = i;
}
if (arr[j][y2[i]] == -i - 1) {
arr[j][y2[i]] = i;
}
}
for (int j = y1[i]; j <= y2[i]; j++) {
if (arr[x1[i]][j] == -i - 1) {
arr[x1[i]][j] = i;
}
if (arr[x2[i]][j] == -i - 1) {
arr[x2[i]][j] = i;
}
}
}
}

int cmp(vector<int> a, vector<int> b) {
for (int i = T - 1; i >= 0; i--) {
if (a[i] != b[i])
return a[i] < b[i];
}
return 0;
}

int main() {
freopen("frameup.in", "r", stdin);
freopen("frameup.out", "w", stdout);
scanf("%d %d\n", &n, &m);
char c;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
scanf("%c", &c);
if (c != '.') arr[i][j] = c - 'A' + 1;
}
getchar();
}
init();
dfs(0);
sort(last.begin(), last.end(), cmp);
for (int i = 0; i < last.size(); i++) {
ans = last[i];
for (int j = T - 1; j >= 0; j--) {
printf("%c", ans[j] + 'A' - 1);
}
printf("\n");
}

return 0;
}