链式前向星建图与搜索

链式前向星建图与搜索

很少使用这种建图法。\(\tt dfs\) ：标准复杂度为 \(\mathcal O(N+M)\)。节点子节点的数量包含它自己（至少为 \(1\)），深度从 \(0\) 开始（根节点深度为 \(0\)）。\(\tt bfs\) ：深度从 \(1\) 开始（根节点深度为 \(1\)）。\(\tt topsort\) ：有向无环图（包括非联通）才拥有完整的拓扑序列（故该算法也可用于判断图中是否存在环）。每次找到入度为 \(0\) 的点并将其放入待查找队列。

namespace Graph {const int N = 1e5 + 7;const int M = 1e6 + 7;int tot, h[N], ver[M], ne[M];int deg[N], vis[M];void clear(int n) {tot = 0; //多组样例清空for (int i = 1; i <= n; ++i) {h[i] = 0;deg[i] = vis[i] = 0;}}void add(int x, int y) {ver[++tot] = y, ne[tot] = h[x], h[x] = tot;++deg[y];}void dfs(int x) {a.push_back(x); // DFS序siz[x] = vis[x] = 1;for (int i = h[x]; i; i = ne[i]) {int y = ver[i];if (vis[y]) continue;dis[y] = dis[x] + 1;dfs(y);siz[x] += siz[y];}a.push_back(x);}void bfs(int s) {queue<int> q;q.push(s);dis[s] = 1;while (!q.empty()) {int x = q.front();q.pop();for (int i = h[x]; i; i = ne[i]) {int y = ver[i];if (dis[y]) continue;d[y] = d[x] + 1;q.push(y);}}}bool topsort() {queue<int> q;vector<int> ans;for (int i = 1; i <= n; ++i)if (deg[i] == 0) q.push(i);while (!q.empty()) {int x = q.front();q.pop();ans.push_back(x);for (int i = h[x]; i; i = ne[i]) {int y = ver[i];--deg[y];if (deg[y] == 0) q.push(y);}}return ans.size() == n; //判断是否存在拓扑排序}
} // namespace Graph