最大的分量里是哪几个
还是那七个点,这次把 5 → 3 那条边加回来,于是图里有了环。
运行下面这段程序:
#include <algorithm>
#include <climits>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <utility>
#include <vector>
using namespace std;
using Edges = vector<pair<int, int>>;
const int N = 7;
// 七个构建任务,(a, b) 表示 a 做完才能做 b
const Edges DEP = {{0, 1}, {0, 2}, {1, 3}, {2, 3}, {3, 4}, {4, 5}, {4, 6}};
// 同一张图再加一条 5 → 3,于是有了环
const Edges G = {{0, 1}, {0, 2}, {1, 3}, {2, 3}, {3, 4}, {4, 5}, {5, 3}, {4, 6}};
vector<vector<int>> build(const Edges& edges, int n = N) {
vector<vector<int>> g(n);
for (auto [a, b] : edges) g[a].push_back(b);
for (auto& adj : g) sort(adj.begin(), adj.end());
return g;
}
// 第一遍:用手写栈做 DFS,记下每个点「完成」的先后
vector<int> order_by_finish(const vector<vector<int>>& g) {
vector<bool> seen(N, false);
vector<int> order;
for (int s = 0; s < N; s++) {
if (seen[s]) continue;
vector<pair<int, int>> st = {{s, 0}}; // (点, 下一条要看的边)
seen[s] = true;
while (!st.empty()) {
int u = st.back().first;
int i = st.back().second;
if (i < (int)g[u].size()) {
st.back().second++;
int v = g[u][i];
if (!seen[v]) {
seen[v] = true;
st.push_back({v, 0});
}
} else {
order.push_back(u);
st.pop_back();
}
}
}
return order;
}
// Kosaraju:第二遍在反图上、按完成顺序的逆序收点;返回排好序的分量列表
vector<vector<int>> kosaraju(const Edges& edges, bool second_reversed = true) {
vector<vector<int>> g = build(edges);
Edges rev;
for (auto [a, b] : edges) rev.push_back({b, a});
vector<vector<int>> rg = build(rev);
vector<int> order = order_by_finish(g);
const vector<vector<int>>& second = second_reversed ? rg : g;
vector<bool> seen(N, false);
vector<vector<int>> groups;
for (int k = N - 1; k >= 0; k--) {
int s = order[k];
if (seen[s]) continue;
vector<int> st = {s}, grp;
seen[s] = true;
while (!st.empty()) {
int u = st.back();
st.pop_back();
grp.push_back(u);
for (int v : second[u]) {
if (!seen[v]) {
seen[v] = true;
st.push_back(v);
}
}
}
sort(grp.begin(), grp.end());
groups.push_back(grp);
}
sort(groups.begin(), groups.end());
return groups;
}
int main() {
vector<vector<int>> gs = kosaraju(G);
vector<int> big;
for (auto& x : gs) {
if (x.size() > big.size()) big = x;
}
for (size_t i = 0; i < big.size(); i++) cout << (i ? "/" : "") << big[i];
cout << endl;
}
(本题用 g++ -std=c++17 -O0 编译。)
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