2018/finals/claw.cpp

// The Claw
// 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 2100000

PR P[LIM],R[LIM],S[LIM];
vector<int> YP[LIM];
vector<PR> YR[LIM];
int sz;
int tree[LIM],lazy[LIM];

void Prop(int i)
{
	tree[i]+=lazy[i];
		if (i<sz)
		{
			lazy[i<<1]+=lazy[i];
			lazy[(i<<1)+1]+=lazy[i];
		}
	lazy[i]=0;
}

void Update(int i,int r1,int r2,int a,int b,int v)
{
	Prop(i);
		if ((a<=r1) && (r2<=b))
		{
			lazy[i]+=v;
			Prop(i);
			return;
		}
	int c=i<<1,m=(r1+r2)>>1;
		if (a<=m)
			Update(c,r1,m,a,b,v);
		if (b>m)
			Update(c+1,m+1,r2,a,b,v);
	Prop(c),Prop(c+1);
	tree[i]=max(tree[c],tree[c+1]);
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int N,M,K;
	int i,j,k,s,y,a,b,p,d;
	LL ans;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// init
				Fox(i,LIM)
					YP[i].clear(),YR[i].clear();
			// input
			Read(N),Read(M);
			ans=M;
				Fox(i,N)
				{
					Read(P[i].x),Read(P[i].y);
					ans-=P[i].y;
					YP[P[i].y].pb(P[i].x);
						if (i)
							R[i-1]=mp(max(P[i-1].x,P[i].x),min(P[i-1].x,P[i].x));
				}
			// associate intervals with their max contained heights
			sort(P,P+N);
			sort(R,R+N-1);
			j=s=0;
				Fox(i,N-1)
				{
					a=R[i].y,b=R[i].x;
					// maintain convex hull of max heights so far
						while ((j<N) && (P[j].x<=b))
						{
								while ((s) && (S[s-1].y<=P[j].y))
									s--;
							S[s++]=P[j++];
						}
					// binary search for max height no earlier than the start of this interval
					k=lower_bound(S,S+s,mp(a,0))-S;
					ans+=(y=S[k].y)+1;
					YR[y].pb(R[i]);
				}
			// process set of targets at each height
				Fox(i,LIM)
					if (K=Sz(YP[i]))
					{
						// sort targets/intervals at this height
						sort(All(YP[i]));
						sort(All(YR[i]));
						// segment-tree-assisted DP
							for(sz=1;sz<K+1;sz<<=1);
						memset(tree,0,sizeof(int)*sz*2);
						memset(lazy,0,sizeof(int)*sz*2);
						k=0,d=-1;
							Fox(j,K+1)
							{
								// update prior DP values for intervals ending at this target
								p=j==K ? INF : YP[i][j];
									while ((k<Sz(YR[i])) && (YR[i][k].x<p))
									{
										a=lower_bound(All(YP[i]),YR[i][k++].y)-YP[i].begin();
										Update(1,0,sz-1,0,a,1);
									}
								// compute DP value
								d=max(d+1,tree[1]);
								Update(1,0,sz-1,j,j,d);
							}
						ans-=d;
					}
			// output
			printf("Case #%d: %lld\n",t,ans*2);
		}
	return(0);
}