2017/finals/moles.cpp

// Hacker Cup 2017
// Final Round
// Fox Moles
// Jacob Plachta

#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); }

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

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 900009

int K,A,B;
map<int,int> M;
vector<int> con[LIM],con2[LIM];
bool col0[LIM];
int col[LIM],ind[LIM],P1[LIM],P2[LIM],dist[LIM];

int Make(int i)
{
		if (M.count(i))
			return(M[i]);
	return(M[i]=K++);
}

bool DFS(int i,int c)
{
	// conflict?
		if ((col0[i]) && (c) || (col[i]>=0) && (c!=col[i]))
			return(0);
	// already coloured?
		if (col[i]>=0)
			return(1);
	// colour node and its neighbours
	col[i]=c;
	int j;
		Fox(j,Sz(con[i]))
			if (!DFS(con[i][j],1-c))
				return(0);
	return(1);
}

bool MatchBFS()
{
	int i,a,b,a2;
	queue<int> Q;
	Fill(dist,60);
		Fox(a,A)
			if (P1[a]<0)
				dist[a]=0,Q.push(a);
		while (!Q.empty())
		{
			a=Q.front(),Q.pop();
				if (dist[a]<dist[A])
					Fox(i,Sz(con2[a]))
					{
						b=con2[a][i];
						a2=P2[b];
							if (dist[a2]>=INF)
								dist[a2]=dist[a]+1,Q.push(a2);
					}
		}
	return(dist[A]<INF);
}

bool MatchDFS(int a)
{
		if (a==A)
			return(1);
	int i,b,a2;
		Fox(i,Sz(con2[a]))
		{
			b=con2[a][i];
			a2=P2[b];
				if ((dist[a2]==dist[a]+1) && (MatchDFS(a2)))
				{
					P1[a]=b;
					P2[b]=a;
					return(1);
				}
		}
	dist[a]=INF;
	return(0);
}

int MaxMatching()
{
	int a,b,m=0;
	Fill(P1,-1);
		Fox(b,B)
			P2[b]=A;
		while (MatchBFS())
		{
			Fox(a,A)
				if ((P1[a]<0) && (MatchDFS(a)))
					m++;
		}
	return(m);
}

int main()
{
	// vars
	int T,t;
	int N=0;
	int i,j,a,b,p,r,z,ans;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// init
				Fox(i,K)
					con[i].clear();
				Fox(i,A)
					con2[i].clear();
			K=0;
			M.clear();
			Fill(col0,0);
			Fill(col,-1);
			Fill(ind,-1);
			Fill(P1,-1);
			Fill(P2,-1);
			// input
			Read(N);
				while (N--)
				{
					Read(p),Read(r);
					i=Make(p),a=Make(p-r),b=Make(p+r);
					col0[i]=1;
					con[a].pb(b);
					con[b].pb(a);
				}
			// attempt to 2-color the graph (initially just from forced nodes)
				Fox(z,2)
					Fox(i,K)
						if (col[i]<0)
						{
							if ((!z) && (!col0[i]))
								continue;
							if (!DFS(i,0))
							{
								ans=-1;
								goto Done;
							}
						}
			// construct the bipartite graph, ignoring forced nodes
			A=B=0;
				Fox(i,K)
					if (!col0[i])
					{
						Fox(j,Sz(con[i]))
							if (col0[con[i][j]])
								goto Skip;
						if (!col[i])
							ind[i]=A++;
						else
							ind[i]=B++;
Skip:;
					}
				Fox(i,K)
					if ((ind[i]>=0) && (!col[i]))
					{
						a=ind[i];
							Fox(j,Sz(con[i]))
							{
								b=ind[con[i][j]];
									if (b>=0)
										con2[a].pb(b);
							}
					}
			ans=A+B-MaxMatching()+1;
			// output
Done:;
			printf("Case #%d: %d\n",t,ans);
		}
	return(0);
}