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#include <iostream> #include <vector> #include <algorithm> #include <cstring> using namespace std; typedef long long ll; const int MAXN = 100005; const int MAXM = 100005; const int LOG = 17; const ll INF = 1e18; struct Edge { int u, v, w, id; bool inMST; } edges[MAXM]; bool cmpW(const Edge& a, const Edge& b) { return a.w < b.w; } bool cmpId(const Edge& a, const Edge& b) { return a.id < b.id; } int n, m; vector<pair<int, int>> g[MAXN]; // MST 树: to, weight, edge id? int parent[MAXN][LOG], depth[MAXN]; ll best[MAXN][LOG]; // 最小替代边权值 int uEdge[MAXN]; // 记录连接 u 和父节点的边的权值 int dsu[MAXN]; int find(int x) { return dsu[x] == x ? x : dsu[x] = find(dsu[x]); } void dfs(int u, int p, int w, int d) { parent[u][0] = p; uEdge[u] = w; depth[u] = d; for (int k = 1; k < LOG; k++) { parent[u][k] = parent[parent[u][k-1]][k-1]; best[u][k] = INF; } best[u][0] = INF; for (auto& e : g[u]) { int v = e.first; if (v == p) continue; dfs(v, u, e.second, d+1); } } int lca(int u, int v) { if (depth[u] < depth[v]) swap(u, v); int diff = depth[u] - depth[v]; for (int k = LOG-1; k >= 0; k--) { if (diff >> k & 1) { u = parent[u][k]; } } if (u == v) return u; for (int k = LOG-1; k >= 0; k--) { if (parent[u][k] != parent[v][k]) { u = parent[u][k]; v = parent[v][k]; } } return parent[u][0]; } void updatePath(int u, int anc, ll w) { int diff = depth[u] - depth[anc]; for (int k = LOG-1; k >= 0; k--) { if (diff >> k & 1) { best[u][k] = min(best[u][k], w); u = parent[u][k]; } } } int main() { ios::sync_with_stdio(false); cin.tie(0); cin >> n >> m; for (int i = 0; i < m; i++) { cin >> edges[i].u >> edges[i].v >> edges[i].w; edges[i].id = i; edges[i].inMST = false; } // Kruskal sort(edges, edges + m, cmpW); for (int i = 1; i <= n; i++) dsu[i] = i; ll MSTsum = 0; for (int i = 0; i < m; i++) { int u = edges[i].u, v = edges[i].v, w = edges[i].w; int fu = find(u), fv = find(v); if (fu != fv) { dsu[fu] = fv; MSTsum += w; edges[i].inMST = true; g[u].push_back({v, w}); g[v].push_back({u, w}); } } // 建 MST 树 dfs(1, 0, 0, 0); // 初始化 best for (int i = 1; i <= n; i++) { for (int k = 0; k < LOG; k++) { best[i][k] = INF; } } // 处理非树边 for (int i = 0; i < m; i++) { if (!edges[i].inMST) { int u = edges[i].u, v = edges[i].v, w = edges[i].w; int a = lca(u, v); updatePath(u, a, w); updatePath(v, a, w); } } // 下放 best for (int k = LOG-1; k >= 1; k--) { for (int i = 1; i <= n; i++) { if (best[i][k] < INF) { best[i][k-1] = min(best[i][k-1], best[i][k]); int p = parent[i][k-1]; best[p][k-1] = min(best[p][k-1], best[i][k]); } } } // 恢复边原始顺序 sort(edges, edges + m, cmpId); // 输出答案 for (int i = 0; i < m; i++) { if (!edges[i].inMST) { cout << MSTsum << "\n"; } else { int u = edges[i].u, v = edges[i].v; if (depth[u] < depth[v]) swap(u, v); // u 的父边就是这条边 if (best[u][0] == INF) { cout << "-1\n"; } else { cout << MSTsum - edges[i].w + best[u][0] << "\n"; } } } return 0; }解析版,你值得拥有!
Information
- ID
- 2899
- Time
- 1000ms
- Memory
- 256MiB
- Difficulty
- 10
- Tags
- # Submissions
- 4
- Accepted
- 4
- Uploaded By