2019/round2/bitstrings_as_a_service.cpp

// Bitstrings as a Service
// Solution by Jacob Plachta

#define DEBUG 0

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#if DEBUG
#define GETCHAR getchar
#else
#define GETCHAR getchar_unlocked
#endif

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=GETCHAR();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define LIM 4001

int N,M,K;
int comp[LIM],sz[LIM],val[LIM];
vector<int> con[LIM];
int dyn[LIM][LIM];

void rec(int i)
{
		if (comp[i]>=0)
			return;
	comp[i]=K;
	sz[K]++;
	int j;
		Fox(j,Sz(con[i]))
			rec(con[i][j]);
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int i,j;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// init
				Fox(i,N)
					con[i].clear();
			// input, and create graph of bit equalities
			Read(N),Read(M);
				while (M--)
				{
					Read(i),Read(j),i--,j--;
						while (j>i)
						{
							con[i].pb(j);
							con[j].pb(i);
							i++,j--;
						}
				}
			// find all components of equal bits
			K=0;
			Fill(sz,0);
			Fill(comp,-1);
				Fox(i,N)
					if (comp[i]<0)
					{
						rec(i);
						K++;
					}
			// DP on component value assignments
			Fill(dyn,-1);
			dyn[0][0]=0;
				Fox(i,K)
					Fox(j,N)
						if (dyn[i][j]>=0)
							dyn[i+1][j]=dyn[i+1][j+sz[i]]=j;
			// trace back to assign values to components
				Fox(i,N+1)
				{
					if (dyn[K][j=N/2+i]>=0)
						break;
					if (dyn[K][j=N/2-i]>=0)
						break;
				}
				FoxR1(i,K)
				{
					val[i-1]=(dyn[i][j]==j ? 0 : 1);
					j=dyn[i][j];
				}
			// output
			printf("Case #%d: ",t);
				Fox(i,N)
					printf("%d",val[comp[i]]);
			printf("\n");
		}
	return(0);
}