SCC

fsjhhh Lv2

SCC(缩点)

洛谷P3387

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struct SCC {
int n;
std::vector<std::vector<int>> edges; // 边
std::vector<int> stk; // 栈
std::vector<int> dfn, low, bel; // 公共祖先,强连通分量
int cur, cnt; // cur: dfn序,cnt: 强连通分量数

SCC() {}
SCC(int n) {
init(n);
}

void init(int n) {
this -> n = n;
edges.assign(n, {});
stk.clear();
dfn.assign(n, -1);
low.resize(n);
bel.assign(n, -1);
cur = cnt = 0;
}

void addEdge(int u, int v) {
edges[u].push_back(v);
}

void dfs(int x) {
dfn[x] = low[x] = cur ++ ;
stk.push_back(x);

for (auto y : edges[x]) {
if (dfn[y] == -1) {
dfs(y);
low[x] = std::min(low[x], low[y]);
// if (low[y] >= dfn[x]) x为割点
// if (low[y] > dfn[x]) x与y的边为桥
} else if (bel[y] == -1) {
low[x] = std::min(low[x], dfn[y]);
}
}

if (dfn[x] == low[x]) {
int y;
do {
y = stk.back();
bel[y] = cnt;
stk.pop_back();
} while (y != x);
cnt ++ ;
}
}

std::vector<int> work() {
for (int i = 0; i < n; i++) {
if (dfn[i] == -1) {
dfs(i);
}
}
return bel;
}

};

void solve() {
int n, m;
std::cin >> n >> m;

std::vector<int> a(n);
for (int i = 0; i < n; i++) {
std::cin >> a[i];
}

SCC g(n);
for (int i = 0; i < m; i++) {
int u, v;
std::cin >> u >> v;
u -- ;
v -- ;
g.addEdge(u, v);
}

auto bel = g.work();
int cnt = g.cnt;
std::vector<std::vector<int>> edges(n);
std::vector<LL> z(cnt);
for (int i = 0; i < n; i++) {
z[bel[i]] += a[i];
for (auto j : g.edges[i]) {
if (bel[i] != bel[j]) {
edges[bel[i]].push_back(bel[j]);
}
}
}

std::vector<LL> dp(n);
for (int i = cnt - 1; i >= 0; i--) {
dp[i] += z[i];
for (auto j : edges[i]) {
dp[j] = std::max(dp[j], dp[i]);
}
}

LL ans = 0;
for (int i = 0; i < cnt; i++) {
ans = std::max(ans, dp[i]);
}

std::cout << ans << "\n";

}

  • 标题: SCC
  • 作者: fsjhhh
  • 创建于 : 2023-11-28 21:54:04
  • 更新于 : 2024-08-29 18:10:38
  • 链接: https://fsjhhh.github.io/2023/11/28/SCC/
  • 版权声明: 本文章采用 CC BY-NC-SA 4.0 进行许可。
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