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Copy pathheavyLightDecomp.cpp
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172 lines (167 loc) · 3.43 KB
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#include "bits/stdc++.h"
using namespace std;
#define MAXN 100000
struct node
{
int val,par=0,sbtsz=1,seg_base=0,chainId,depth=0;
};
node nodes[MAXN+1];
vector<int> adj[MAXN+1];
int n;
int head[MAXN+1],segPos,chainId;
int par[MAXN+1][20];
int base_array[MAXN+1],tree[6*MAXN+1];
void hld(int s,int prev){
if(head[chainId] == 0){
head[chainId] = s;
}
nodes[s].chainId = chainId;
nodes[s].seg_base = segPos;
base_array[segPos] = nodes[s].val;
segPos ++;
int count = 0;
for(auto v:adj[s]){
if(v != prev){
if(count) chainId ++;
hld(v,s);
count++;
}
}
}
int dfs(int s,int prev){
nodes[s].depth = nodes[nodes[s].par].depth + 1;
for(auto v:adj[s]){
if(v != prev){
nodes[v].par = s;
par[v][0] = s;
nodes[s].sbtsz += dfs(v,s);
}
}
return nodes[s].sbtsz;
}
void preComputeSparseMatrix(){
for(int i=1;i<=n;i++){
for(int j=1;j<20;j++){
if(par[i][j-1] != -1)
par[i][j] = par[par[i][j-1]][j-1];
}
}
}
void buildHLD(int startNode){
dfs(startNode,0);
preComputeSparseMatrix();
//sort childs by subtree Size
vector<pair<int,int>> vc;
for(int i=1;i<=n;i++){
vc.clear();
for(auto v:adj[i]){
vc.push_back({nodes[v].sbtsz,v});
}
sort(vc.begin(), vc.end());
adj[i].clear();
for(auto v:vc) adj[i].push_back(v.second);
reverse(adj[i].begin(), adj[i].end());
}
hld(startNode,0);
// for(int i=1;i<=n;i++){
// cout<<i<<"--> ChainID: "<<nodes[i].chainId<<" seg_base: "<<nodes[i].seg_base<<endl;
// }
// for(int i=0;i<5;i++)
// cout<<head[i]<<endl;
}
int lca(int u,int v){
if(nodes[v].depth < nodes[u].depth) swap(u,v);
int diff = nodes[v].depth - nodes[u].depth;
for(int i=0;i<20;i++){
if((diff>>i) & 1) v = par[v][i];
}
if(u == v) return u;
for(int i=19;i>=0;i--){
if(par[u][i] != par[v][i]){
u = par[u][i];
v = par[v][i];
}
}
return par[u][0];
}
void treeInput(){
int m,x,y; cin>>n;
for(int i=1;i<=n;i++){
cin>>x;
nodes[i].val = x;
}
cin>>m;
while(m--){
cin>>x>>y;
adj[x].push_back(y);
adj[y].push_back(x);
}
}
void buildSegTree(int nd,int a,int b){
if(a > b) return;
if(a == b){
tree[nd] = base_array[a];
return;
}
buildSegTree(nd*2,a,(a+b)/2);
buildSegTree(nd*2+1,(a+b)/2+1,b);
tree[nd] = min(tree[nd*2],tree[nd*2+1]);
}
void upSegTree(int nd,int a,int b,int idx,int val){
if(a > b or idx < a or idx > b) return;
if(a == b){
tree[nd] = val;
return;
}
upSegTree(nd*2,a,(a+b)/2,idx,val);
upSegTree(nd*2+1,(a+b)/2+1,b,idx,val);
tree[nd] = min(tree[nd*2],tree[nd*2+1]);
}
void change(int posNode, int val){
upSegTree(1,0,n-1,nodes[posNode].seg_base,val);
}
int RMQ(int nd,int a,int b,int l,int r){
if(a > b or r < a or l > b) return INT_MAX;
if(a >= l and b <= r){
return tree[nd];
}
int q1 = RMQ(nd*2,a,(a+b)/2,l,r);
int q2 = RMQ(nd*2+1,(a+b)/2+1,b,l,r);
return min(q1,q2);
}
int search(int u,int v){
int chain_u,chain_v = nodes[v].chainId,ans = INT_MAX;
while(true){
chain_u = nodes[u].chainId;
if(chain_u == chain_v){
ans = min(ans,RMQ(1,0,n-1,nodes[v].seg_base,nodes[u].seg_base));
break;
}
else{
ans = min(ans,RMQ(1,0,n-1,nodes[head[chain_u]].seg_base,nodes[u].seg_base));
u = nodes[head[chain_u]].par;
}
}
return ans;
}
int minInPath(int u,int v){
int LCA = lca(u,v);
return min(search(u,LCA),search(v,LCA));
}
int main(int argc, char const *argv[])
{
treeInput();
buildHLD(1);
buildSegTree(1,0,n-1);
int q; cin>>q;
while(q--){
int qt,a,b; cin>>qt>>a>>b;
if(qt){
cout<<minInPath(a,b)<<endl;
}
else{
change(a,b);
}
}
return 0;
}