Submission #981230

#	Time	Username	Problem	Language	Result	Execution time	Memory
981230		Lib	Swapping Cities (APIO20_swap)	C++14	0 / 100	3 ms	12724 KiB

swap

#include <bits/stdc++.h>
using namespace std;
int n,m;
vector <vector <int> > InComponents;
vector <vector <int> > adj; //the edge list of the KRT
vector <int> TVector;
int RootID; //ID of the root node of the KRT;
struct Edge{
	long long Weight;
	int Start;
	int End;
};
bool operator< (const Edge &x, const Edge &y){
	return x.Weight<y.Weight;
}
Edge Elist[500003];
int Depth[500003];
int Deg[500003];
int CurRep[500003]; //id of the respresentative node on the KRT
int Par[500003]; //Parent of node with id i on the KRT;
int Toggle[500003]; //is the i-th node on the KRT toggled?
int Check[500003];
int Ancestor[500003][20];
long long Val[500003];//the value of the i-th node of the KRT
vector <int> KRTID;
void DSU(int id, int u, int v, int w){
	Deg[u]++;
	Deg[v]++;
	//u and v belongs to the same component. The component now has a cycle. Immediately toggle the root node of the current 
	//subtree that includes both u and v on the KRT
	if(CurRep[u]==CurRep[v]){
		//The node isn't toggled just yet. Toggle it immediately
		if(!Toggle[CurRep[u]]){
			Toggle[CurRep[u]]=1;
			Val[CurRep[u]]=w;
		}else{
		//The node is already toggled by an edge with lower edge. Only a fucking dumbass would touch it - already minimized
		//toggle value. Just leave it alone
		}
	}else{
		//u and v doesn't belong to the same component. Merge them
		int CurID=n-1+id;
		int OldComp1=CurRep[u], OldComp2=CurRep[v];
		adj[CurRep[u]].push_back(CurID);
		adj[CurRep[v]].push_back(CurID);
		adj[CurID].push_back(CurRep[u]);
		adj[CurID].push_back(CurRep[v]);
		Par[CurRep[u]]=CurID;
		Par[CurRep[v]]=CurID;
		if(InComponents[u].size()>InComponents[v].size()){
			swap(u,v);
			//Small to large merging
		}
		for(int i=0;i<InComponents[u].size();i++){
			InComponents[CurID].push_back(InComponents[u][i]);
			CurRep[InComponents[u][i]]=CurID;
		}
		for(int i=0;i<InComponents[v].size();i++){
			InComponents[CurID].push_back(InComponents[v][i]);
			CurRep[InComponents[v][i]]=CurID;
		}
		Val[CurID]=w;
		//if either of the components are toggled already (having a cycle OR a vertex with degree >3)
		//OR the merged component has a vertex with degree >3 (either u or v), toggle immediately
		if(Toggle[OldComp1]||Toggle[OldComp2]||Deg[u]>2||Deg[v]>2){
			Toggle[CurID]=1;
		}
		KRTID.push_back(CurID);
		RootID=CurID;
	}
}
void init(int N, int M, vector <int> U, vector <int> V, vector <int> W){
	n=N;
	m=M;
	for(int i=0;i<n+m+5;i++){
		InComponents.push_back(TVector);
		adj.push_back(TVector);
	}
	for(int i=1;i<=m;i++){
		Elist[i].Weight=W[i-1];
		Elist[i].Start=U[i-1];
		Elist[i].End=V[i-1];
	}
	sort(Elist+1,Elist+m+1);
	for(int i=0;i<n;i++){
		CurRep[i]=i;
		InComponents[i].push_back(i);
		KRTID.push_back(i);
	}
	for(int i=1;i<=m;i++){
		DSU(i,Elist[i].Start,Elist[i].End,Elist[i].Weight);
	}
	//The KRT is now built. BFS from the root node and initialize LCA or something
	deque <int> dq;
	dq.push_back(RootID);
	Check[RootID]=1;
	int Cur;
	while(!dq.empty()){
		Cur=dq.front();
		for(int i=0;i<adj[Cur].size();i++){
			if(!Check[adj[Cur][i]]){
				dq.push_back(adj[Cur][i]);
				Check[adj[Cur][i]]=1;
				Depth[adj[Cur][i]]=Depth[Cur]+1;
			}
		}
		dq.pop_front();
	}
	Par[RootID]=500000;
	Par[500000]=500000;
	Toggle[500000]=1;
	for(int i=0;i<=19;i++){
		for(int k=0;k<KRTID.size();k++){
			if(i==0){
				Ancestor[KRTID[k]][i]=Par[KRTID[k]];
			}else{
				Ancestor[KRTID[k]][i]=Ancestor[Ancestor[KRTID[k]][i-1]][i-1];
			}
		}
	}
}

int getMinimumFuelCapacity(int x, int y){
	//I thought that we actually need to use binary lifting to find LCA and then jump from the LCA to find the nearest
	//toggled node on the KRT
	//But apparently small-to-large merging ensures that the depth of the tree is always logN or something, so bruteforcing
	//it is
	//ok nvm this guy is a fucking moron lmao LogN depth my ass. Wrong analysis, wasted 5 minutes. Fuck me
	if(Depth[x]<Depth[y]){
		swap(x,y);
	}
	int JumpLevel=Depth[x]-Depth[y];
	for(int i=19;i>=0;i--){
		if(JumpLevel >> i & 1){
			x=Ancestor[x][i];
		}
	}
	for(int i=19;i>=0;i--){
		if(Ancestor[x][i]!=Ancestor[y][i]){
			x=Ancestor[x][i];
			y=Ancestor[y][i];
		}
	}
	x=Par[x];
	y=Par[y];
	SkipPoint:;
	if(Toggle[x]){
		return Val[x];
	}
	/*int cnt=0;
	while(!Toggle[Par[x]]&&Par[x]!=500000){
		x=Par[x];
	}*/
	for(int i=19;i>=0;i--){
		if(!Toggle[Ancestor[x][i]]){
			x=Ancestor[x][i];
		}
	}
	x=Par[x];
	if(x!=500000){
		return Val[x];
	}
	return -1;
}

Compilation message (stderr)

swap.cpp: In function 'void DSU(int, int, int, int)':
swap.cpp:54:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   54 |   for(int i=0;i<InComponents[u].size();i++){
      |               ~^~~~~~~~~~~~~~~~~~~~~~~
swap.cpp:58:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   58 |   for(int i=0;i<InComponents[v].size();i++){
      |               ~^~~~~~~~~~~~~~~~~~~~~~~
swap.cpp: In function 'void init(int, int, std::vector<int>, std::vector<int>, std::vector<int>)':
swap.cpp:100:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  100 |   for(int i=0;i<adj[Cur].size();i++){
      |               ~^~~~~~~~~~~~~~~~
swap.cpp:113:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  113 |   for(int k=0;k<KRTID.size();k++){
      |               ~^~~~~~~~~~~~~
swap.cpp: In function 'int getMinimumFuelCapacity(int, int)':
swap.cpp:146:2: warning: label 'SkipPoint' defined but not used [-Wunused-label]
  146 |  SkipPoint:;
      |  ^~~~~~~~~

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• Subtask 3: 0 / 17
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• Subtask 6: 0 / 27