From adabac506a6b0f90438cd16edca8697151e7b5f5 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Fri, 14 Oct 2022 15:30:31 +0800
Subject: [PATCH] J - Mex Tree

https://codeforces.com/gym/103941/submission/176114533
---
 Gym/103941/J/J.cpp | 95 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 95 insertions(+)
 create mode 100644 Gym/103941/J/J.cpp

diff --git a/Gym/103941/J/J.cpp b/Gym/103941/J/J.cpp
new file mode 100644
index 00000000..b6556751
--- /dev/null
+++ b/Gym/103941/J/J.cpp
@@ -0,0 +1,95 @@
+#include <iostream>
+#include <algorithm>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+
+int n, a[N], mex[N], ans[N];
+int cnt, id[N], rid[N], lid[N], min[N], siz[N], son[N];
+bool vis[N];
+std::vector<int> g[N];
+
+void dfs1(int u) {
+    rid[id[u] = ++cnt] = u;
+    siz[u] = 1;
+    min[u] = a[u];
+
+    for (int v : g[u]) {
+        dfs1(v);
+
+        siz[u] += siz[v];
+        min[u] = std::min(min[u], min[v]);
+
+        if (siz[v] > siz[son[u]]) son[u] = v;
+    }
+
+    lid[u] = cnt;
+}
+
+void dfs2(int u, bool clean = true) {
+    for (int v : g[u]) {
+        if (v != son[u]) dfs2(v);
+    }
+
+    if (son[u]) dfs2(son[u], false);
+
+    for (int v : g[u]) {
+        if (v == son[u]) continue;
+
+        for (int i = id[v]; i <= lid[v]; i++) {
+            vis[a[rid[i]]] = true;
+        }
+    }
+
+    vis[a[u]] = true;
+    while (vis[cnt]) cnt++;
+    mex[u] = cnt;
+
+    if (clean) {
+        for (int i = id[u]; i <= lid[u]; i++) {
+            vis[a[rid[i]]] = false;
+        }
+        cnt = 0;
+    }
+}
+
+void dfs3(int u) {
+    ans[mex[u]] = std::max(ans[mex[u]], siz[u]);
+    ans[min[u]] = std::max(ans[min[u]], n - siz[u]);
+
+    for (int v : g[u]) dfs3(v);
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+
+    for (int i = 2, x; i <= n; i++) {
+        cin >> x;
+
+        g[x].emplace_back(i);
+    }
+
+    dfs1(1);
+    cnt = 0;
+    dfs2(1);
+    dfs3(1);
+
+    for (int i = 0; i < n; i++) {
+        cout << ans[i] << ' ';
+    }
+
+    cout << n << endl;
+
+    return 0;
+}