| # | Submission time | Handle | Problem | Language | Result | Execution time | Memory |
|---|---|---|---|---|---|---|---|
| 981188 | 2024-05-13T01:52:43 Z | Lib | Swapping Cities (APIO20_swap) | C++14 | 0 ms | 0 KB |
#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];
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;
}
}
}
Par[RootID]=-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
if(Depth[x]>Depth[y]){
swap(x,y);
}
while(Depth[x]<Depth[y]){
x=Par[x];
}
while(x!=y){
x=Par[x];
y=Par[y];
}
while(x!=-1){
if(Toggle[x]){
return Val[x];
}
x=Par[x];
}
return -1;
}