基于倍增的LCA + kruskal重构树 + 并查集

P2245 星际导航

//基于倍增的LCA + kruskal重构树 + 并查集
#include<bits/stdc++.h>
#define endl '\n'
#define rep(_start_,_end_) for(int i =  _start_;i <= (_end_);i ++)
#define all0(x) (x).begin(),(x).end()
#define all1(x) (x).begin() + 1,(x).end()
using namespace std;
using ll = long long;const int N = 1e5 + 10; // 原图最大顶点数
const int M = 5e5 + 10; // 原图最大边数int n, m, q;
int par[N * 2];
int val[N * 2];//非叶子的权值
vector<int>trie[N * 2];struct EDGE
{int u, v, w;
};int Find(int x)
{return (par[x] == x) ? x : par[x] = Find(par[x]);
}
int new_node;
void build_kruskal(vector<EDGE>&edge)
{//初始化for(int i = 1;i <= 2 * n - 1;i ++)par[i] = i;//遍历所有边new_node = n;for(auto &[l,r,w] : edge){int rootl = Find(l);int rootr = Find(r);if(rootl != rootr){new_node ++;val[new_node] = w;
//			cout << "newnode: "<<new_node <<endl;trie[new_node].push_back(rootl);trie[new_node].push_back(rootr);par[rootl] = new_node;par[rootr] = new_node;}}
}int dep[N * 2],fa[N * 2][20];void dfs(int u,int u_father)
{dep[u] = dep[u_father] + 1;fa[u][0] = u_father;for(int j = 1;j <= 19;j ++){fa[u][j] = fa[fa[u][j - 1]][j - 1];}for(auto v:trie[u]){if(v != u_father){dfs(v,u);}}
}int get_lca(int l,int r)
{if(dep[l] < dep[r])swap(l,r);for(int i = 19;i >= 0;i --){if(dep[fa[l][i]] >= dep[r])l = fa[l][i];}if(l == r)return l;for(int i = 19;i >= 0;i --){if(fa[l][i] != fa[r][i])l = fa[l][i],r = fa[r][i];}return fa[l][0];
}void solve()
{cin >> n >> m; vector<EDGE> edge(m);rep(0, m - 1) cin >> edge[i].u >> edge[i].v >> edge[i].w;sort(all0(edge), [](const auto&i, const auto&j){return i.w < j.w;});//重构树build_kruskal(edge);//预处理dfsfor(int i = 1;i <= new_node ;i ++){if(par[i] == i){dfs(i,0);}}
//	for(int i = 1;i <= 2 * n - 1;i ++)cout << fa[i][0]<<" ";
//	cout << endl;cin >> q;while(q --){int l,r;cin >> l >> r;if(Find(l) != Find(r))cout << "impossible"<<endl;else{cout << val[get_lca(l,r)] <<endl;}}
}int main()
{ios_base::sync_with_stdio(false);cin.tie(NULL);int t;// cin >> t;t = 1;while(t --){solve();}return 0;
}