2016/finals/maximinimax_flow.cpp

// MAXIMINIMAX FLOW
// Official 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-9;
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);
}

bool ReadLL(LL &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 500005
#define LIM2 1000000

LL BLT[2][2][LIM2+1];

void Update(int a,int b,int i,int v)
{
	for (; i<=LIM2; i+=(i&-i))
		BLT[a][b][i]+=v;
}

void Update2(int a,int i,int v)
{
	Update(a,0,i,v);
	Update(a,1,i,i*v);
}

LL Query(int a,int b,LL ii)
{
	int i=(int)min(ii,(LL)LIM2);
	LL v=0;
		for(; i>0; i-=(i&-i))
			v+=BLT[a][b][i];
	return(v);
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	//vars
	int T,t;
	int N,M;
	int i,j,k;
	LL r1,r2,m,m2;
	LL tot,rem,cnt,sum;
	LL ans;
	static vector<PR> con[LIM];
	static int C[LIM],dep[LIM],cyc[LIM];
	static PR par[LIM];
	queue<int> Q;
	set<PR> S;
	set<PR>::iterator I;
	//testcase loop
	Read(T);
		Fox1(t,T)
		{
			//input
			Read(N),Read(M);
				Fox(i,N)
				{
					Read(j),Read(k),Read(C[i]);
					j--,k--;
					con[j].pb(mp(k,i));
					con[k].pb(mp(j,i));
				}
			//BFS to find the single cycle
			Fill(dep,-1);
			Q.push(0),dep[0]=0;
				for(;;)
				{
					i=Q.front(),Q.pop();
						Fox(j,Sz(con[i]))
							if ((k=con[i][j].x)!=par[i].x)
								if (dep[k]>=0)
									goto Done;
								else
									Q.push(k),dep[k]=dep[i]+1,par[k]=mp(i,con[i][j].y);
				}
			//retrace all edges in the cycle
Done:;
			Fill(cyc,0);
			cyc[con[i][j].y]=1;
				while (i!=k)
					if (dep[i]>dep[k])
					{
						cyc[par[i].y]=1;
						i=par[i].x;
					}
					else
					{
						cyc[par[k].y]=1;
						k=par[k].x;
					}
			//init BLTs
				Fox(i,N)
				{
					Update2(cyc[i],C[i],1);
						if (cyc[i])
							S.insert(mp(C[i],i));
				}
			//handle operations
			ans=0;
				while (M--)
				{
					Read(i);
						if (i==1)
						{
							//delete and re-add the adge
							Read(i),i--;
							Update2(cyc[i],C[i],-1);
								if (cyc[i])
									S.erase(mp(C[i],i));
							Read(C[i]);
							Update2(cyc[i],C[i],1);
								if (cyc[i])
									S.insert(mp(C[i],i));
						}
						else
						{
							//binary search on the answer
							ReadLL(tot);
							r1=1,r2=(LL)1e13;
								while (r2>r1)
								{
									m=(r1+r2+1)>>1;
									rem=tot;
									//non-cycle edges
									cnt=Query(0,0,m);
									sum=Query(0,1,m);
									rem-=cnt*m - sum;
										if (rem<0)
											goto Bad;
									//cycle edges
									I=S.begin(),i=I->x;
									I++,j=I->x;
										if (m<=(j<<1))
											rem-=max(0LL,m - (i+j));
										else
										{
											m2=(m+1)>>1;
											cnt=Query(1,0,m2);
											sum=Query(1,1,m2);
											rem-=cnt*m2 - sum;
												if (m&1)
													rem++;
										}
										if (rem<0)
										{
Bad:;
											r2=m-1;
											continue;
										}
									r1=m;
								}
							ans+=r1;
						}
				}
			//output
			printf("Case #%d: ",t);
			cout << ans << endl;
			//reset
				Fox(i,N)
					con[i].clear();
				while (!Q.empty())
					Q.pop();
			S.clear();
			Fill(BLT,0);
		}
	return(0);
}