Algorithm

USACO Section4.4 frameup

Problem Summary

Given a picture of several overlapping frames, find all possible sequence of the frames in the order they were stacked from bottom to top.

Solution

Note that,

It is possible to see at least one part of each of the four sides of a frame. A corner is part of two sides.

So it is easy to get a partial order of the frames. Then we only need to search for all the possible total orders.

Code

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#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>
using namespace std;
const int maxn = 32;
int n,m,num;
char board[maxn][maxn];
bool g[maxn][maxn],used[maxn];
int under[maxn],now[maxn];
class Frame
{
public:
	char ch;
	int top,bottom,left,right;
	void init(char c,int a,int b)
	{
		ch=c;
		top=bottom=a;
		left=right=b;
	}
	void update(int a,int b,int c,int d)
	{
		top=min(top,a);
		bottom=max(bottom,b);
		left=min(left,c);
		right=max(right,d);
	}
} frames[30];
bool cmp(const Frame &a,const Frame &b)
{
	return (a.ch<b.ch);
}
bool find(int a,int b) /* return true if Frame b is on top of Frame a */
{
	int x1=frames[a].top,x2=frames[a].bottom,tar=frames[b].ch;
	for(int j=frames[a].left;j<=frames[a].right;j++)
		if(board[x1][j]==tar || board[x2][j]==tar)
			return true;
	int y1=frames[a].left,y2=frames[a].right;
	for(int i=frames[a].top;i<=frames[a].bottom;i++)
		if(board[i][y1]==tar || board[i][y2]==tar)
			return true;
	return false;
}
void generate(int cur,fstream *fout)
{
	if(cur>num)
	{
		for(int i=1;i<=num;i++)
			(*fout)<<frames[now[i]].ch;
		(*fout)<<endl;
		return;
	}
	for(int i=1;i<=num;i++)
		if(under[i]==0 && !used[i])
		{
			now[cur]=i;
			used[i]=true;
			for(int j=1;j<=num;j++)
				if(g[i][j])
					under[j]--;
			generate(cur+1,fout);
			for(int j=1;j<=num;j++)
				if(g[i][j])
					under[j]++;
			used[i]=false;
		}
}
int main()
{
	fstream fin("frameup.in",ios::in);
	fstream fout("frameup.out",ios::out);
	fin>>n>>m;
	num=0;
	int idx;
	for(int i=0;i<n;i++)
	{
		fin>>board[i];
		for(int j=0;j<m;j++)
			if(board[i][j]!='.')
			{
				idx=0;
				for(int k=1;k<=num;k++)
					if(frames[k].ch==board[i][j])
					{
						idx=k;
						break;
					}
				if(idx==0)
				{
					num++;
					frames[num].init(board[i][j],i,j);
				}
				else
					frames[idx].update(i,i,j,j);
			}
	}
	sort(frames+1,frames+num+1,cmp);
	for(int i=1;i<=num;i++)
		for(int j=1;j<=num;j++)
			if(i!=j)
			{
				g[i][j]=find(i,j);
				under[j]+=g[i][j];
			}
	generate(1,&fout);
	fout.close();
	return 0;
}