#3280. 「JOISC 2020 Day4」首都城市

https://loj.ac/s/1696059

LibreOJ/3280/3280.cpp

@@ -0,0 +1,208 @@
+#include <iostream>
+#include <stack>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+
+int n, k, c[N], cnt, ans = 0x3f3f3f3f;
+int id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
+std::vector<int> g[N], g2[N], pos[N];
+int dfn[N], low[N], scc_cnt, scc_id[N];
+int res_siz[N], deg[N];
+std::stack<int> st;
+bool vis[N];
+
+struct node {
+    int l, r;
+
+    node(const int &_l = 0, const int &_r = 0)
+        : l(_l), r(_r) {}
+} tr[N << 2];
+
+void dfs1(int u, int f) {
+    fa[u] = f;
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+
+    for (int v : g[u]) {
+        if (v == f) continue;
+
+        dfs1(v, u);
+        siz[u] += siz[v];
+
+        if (siz[son[u]] < siz[v]) son[u] = v;
+    }
+}
+
+void dfs2(int u, int t) {
+    static int cnt = 0;
+
+    rid[id[u] = ++cnt] = u;
+    top[u] = t;
+
+    if (son[u]) dfs2(son[u], t);
+
+    for (int v : g[u]) {
+        if (v == fa[u] || v == son[u]) continue;
+
+        dfs2(v, v);
+    }
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+    cnt++;
+
+    if (l == r) {
+        g2[k + u].emplace_back(c[rid[l]]);
+
+        return;
+    }
+
+    int mid = (l + r) >> 1;
+
+    build(u << 1, l, mid);
+    build(u << 1 | 1, mid + 1, r);
+
+    g2[k + u].emplace_back(k + (u << 1));
+    g2[k + u].emplace_back(k + (u << 1 | 1));
+}
+
+void modify(int u, int l, int r, int x) {
+    if (l <= tr[u].l && tr[u].r <= r) {
+        g2[x].emplace_back(k + u);
+
+        return;
+    }
+
+    int mid = (tr[u].l + tr[u].r) >> 1;
+
+    if (l <= mid) modify(u << 1, l, r, x);
+    if (r > mid) modify(u << 1 | 1, l, r, x);
+}
+
+void modify_path(int u, int v) {
+    int x = c[u];
+
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+
+        modify(1, id[top[u]], id[u], x);
+        u = fa[top[u]];
+    }
+
+    if (dep[v] > dep[u]) std::swap(u, v);
+
+    modify(1, id[v], id[u], x);
+}
+
+void tarjan(int u) {
+    static int cnt = 0;
+
+    dfn[u] = low[u] = ++cnt;
+    st.emplace(u);
+    vis[u] = true;
+
+    for (int v : g2[u]) {
+        if (!dfn[v]) {
+            tarjan(v);
+
+            low[u] = std::min(low[u], low[v]);
+        } else if (vis[v]) {
+            low[u] = std::min(low[u], dfn[v]);
+        }
+    }
+
+    if (dfn[u] == low[u]) {
+        scc_cnt++;
+
+        int v;
+        do {
+            v = st.top();
+            st.pop();
+            scc_id[v] = scc_cnt;
+            vis[v] = false;
+        } while (v != u);
+    }
+}
+
+int lca(int u, int v) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+
+        u = fa[top[u]];
+    }
+
+    return dep[u] < dep[v] ? u : v;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> k;
+
+    for (int i = 1, x, y; i < n; i++) {
+        cin >> x >> y;
+
+        g[x].emplace_back(y);
+        g[y].emplace_back(x);
+    }
+
+    for (int i = 1; i <= n; i++) {
+        cin >> c[i];
+
+        pos[c[i]].emplace_back(i);
+    }
+
+    dfs1(1, 1);
+    dfs2(1, 1);
+    build(1, 1, n);
+
+    for (int i = 1; i <= k; i++) {
+        if (pos[i].size() <= 1) continue;
+
+        int p = pos[i][0];
+
+        for (int j = 1; j < pos[i].size(); j++) {
+            int l = lca(pos[i][0], pos[i][j]);
+
+            if (l != pos[i][j]) modify_path(pos[i][j], l);
+            if (dep[l] < dep[p]) p = l;
+        }
+
+        if (p != pos[i][0]) {
+            modify_path(pos[i][0], p);
+        }
+    }
+
+    for (int i = 1; i <= k + cnt; i++) {
+        if (!dfn[i]) tarjan(i);
+    }
+
+    for (int i = 1; i <= k; i++) {
+        res_siz[scc_id[i]]++;
+    }
+
+    for (int i = 1; i <= k + cnt; i++) {
+        for (int v : g2[i]) {
+            if (scc_id[i] != scc_id[v]) {
+                deg[scc_id[i]]++;
+            }
+        }
+    }
+
+    for (int i = 1; i <= k; i++) {
+        if (deg[scc_id[i]] == 0) {
+            ans = std::min(ans, res_siz[scc_id[i]] - 1);
+        }
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}