From f493d87ede55e7b5f254168a759dc9ed53b51bc0 Mon Sep 17 00:00:00 2001
From: Fei Pan <pan-fei@outlook.com>
Date: Wed, 18 Dec 2024 00:59:52 +0800
Subject: [PATCH] qoj/8055

---
 code/qoj/8055.cpp | 206 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 206 insertions(+)
 create mode 100644 code/qoj/8055.cpp

diff --git a/code/qoj/8055.cpp b/code/qoj/8055.cpp
new file mode 100644
index 0000000..b33b7f1
--- /dev/null
+++ b/code/qoj/8055.cpp
@@ -0,0 +1,206 @@
+#include <bits/stdc++.h>
+
+struct SCC {
+    int n;
+    std::vector<std::vector<int>> adj;
+    std::vector<int> stk;
+    std::vector<int> dfn, low, bel;
+    int cur, cnt;
+    void dfs(int x, int p) {
+        dfn[x] = low[x] = cur++;
+        stk.push_back(x);
+
+        bool skipped = false;
+        for (int to : adj[x]) {
+            if (to == p && !skipped) {
+                skipped = true;
+                continue;
+            }
+            if (dfn[to] == -1) {
+                dfs(to, x);
+                low[x] = std::min(low[x], low[to]);
+            } else if (bel[to] == -1) {
+                low[x] = std::min(low[x], dfn[to]);
+            }
+        }
+        if (dfn[x] == low[x]) {
+            int y;
+            do {
+                y = stk.back();
+                bel[y] = cnt;
+                stk.pop_back();
+            } while (y != x);
+            ++cnt;
+        }
+    }
+
+public:
+    explicit SCC(int n)
+        : n(n), adj(n), dfn(n, -1), low(n), bel(n, -1), cur(0), cnt(0) {};
+
+    void add_edge(int u, int v) {
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+
+    std::vector<int> operator()() {
+        for (int i = 0; i < n; ++i)
+            if (dfn[i] == -1) dfs(i, -1);
+        return bel;
+    }
+};
+
+void solve() {
+    int n, m;
+    std::cin >> n >> m;
+
+    std::vector<std::pair<int, int>> edge(m);
+    for (auto &[u, v] : edge) {
+        std::cin >> u >> v;
+        --u, --v;
+    }
+
+    std::vector<int> a(n);
+    for (int &i : a) std::cin >> i;
+
+    if (std::unordered_set<int>{a.begin(), a.end()}.size() == 1) {
+        std::cout << "Yes\n";
+        std::copy(a.begin(), a.end(),
+                  std::ostream_iterator<int>(std::cout, " "));
+        std::cout << '\n';
+        return;
+    }
+
+    SCC _g(n);
+    for (auto [u, v] : edge) _g.add_edge(u, v);
+    auto bel = _g();
+
+    const int N = *std::max_element(bel.begin(), bel.end()) + 1;
+    std::vector<std::vector<int>> adj(N);
+    for (auto [u, v] : edge) {
+        if (bel[u] != bel[v]) {
+            adj[bel[u]].push_back(bel[v]);
+            adj[bel[v]].push_back(bel[u]);
+        }
+    }
+    std::vector<std::vector<int>> com(N);
+    for (int i = 0; i < n; ++i) com[bel[i]].push_back(i);
+
+    // Discretize
+    std::vector<int> tmp(a);
+    std::sort(tmp.begin(), tmp.end());
+    tmp.resize(std::unique(tmp.begin(), tmp.end()) - tmp.begin());
+
+    // Count of each value
+    std::vector<int> cnt(tmp.size());
+    for (int &i : a)
+        cnt[std::lower_bound(tmp.begin(), tmp.end(), i) - tmp.begin()]++;
+
+    std::vector<int> presum(tmp.size());
+    std::partial_sum(cnt.begin(), cnt.end(), presum.begin());
+
+    std::unordered_set<int> S;
+    for (int i = 0; i + 1 < tmp.size(); ++i) S.insert(n - 2 * presum[i]);
+
+    int rt = 19 % N; // Just a random root
+
+    std::vector<int> sz(N);
+    std::vector<int> f(N), g(N);
+
+    auto F = [&](int x) { return S.find(n - 2 * sz[x]) != S.end(); };
+    auto G = [&](int x) { return S.find(2 * sz[x] - n) != S.end(); };
+
+    auto dfs = [&](auto &self, int x, int p) -> void {
+        for (int to : adj[x]) {
+            if (to == p) continue;
+            self(self, to, x);
+            sz[x] += sz[to];
+            f[x] = std::max(f[x], f[to]);
+            g[x] = std::max(g[x], g[to]);
+        }
+        sz[x] += com[x].size();
+        if (F(x)) f[x] += 1;
+        if (G(x)) g[x] += 1;
+    };
+    dfs(dfs, rt, -1);
+
+    auto output = [&](int x, int y, int z) -> void {
+        std::vector<int> col(N, -1);
+        auto dfs1 = [&](auto &self, int x, int p, int c, auto &dp,
+                        auto &&fn) -> void {
+            col[x] = c;
+
+            int son = -1;
+            for (int to : adj[x]) {
+                if (to == p) continue;
+                if (son == -1 || dp[son] < dp[to]) son = to;
+            }
+
+            if (son != -1) self(self, son, x, c - fn(son), dp, fn);
+        };
+
+        int c = x != -1 ? f[x] : tmp.size() - 1 - g[z];
+
+        col[y] = c;
+        if (x != -1) dfs1(dfs1, x, y, c - F(x), f, F);
+        if (z != -1)
+            dfs1(dfs1, z, y, c + G(z), g, [&](int x) { return -G(x); });
+
+        auto dfs2 = [&](auto &self, int x, int p) -> void {
+            for (int to : adj[x]) {
+                if (to == p) continue;
+                if (col[to] == -1) col[to] = col[x];
+                self(self, to, x);
+            }
+        };
+        dfs2(dfs2, y, -1);
+
+        for (int i = 0; i < n; ++i) a[i] = tmp[col[bel[i]]];
+
+        std::cout << "Yes\n";
+        std::copy(a.begin(), a.end(),
+                  std::ostream_iterator<int>(std::cout, " "));
+        std::cout << '\n';
+    };
+
+    auto check = [&](int x) -> bool {
+        int pf = -1, pg = -1;
+        for (int to : adj[x]) {
+            if (sz[to] > sz[x]) continue;
+            if (pf != -1 && f[pf] + g[to] >= tmp.size() - 1) {
+                output(pf, x, to);
+                return true;
+            }
+            if (pg != -1 && f[to] + g[pg] >= tmp.size() - 1) {
+                output(to, x, pg);
+                return true;
+            }
+            if (pf == -1 || f[to] > f[pf]) pf = to;
+            if (pg == -1 || g[to] > g[pg]) pg = to;
+
+            if (f[to] >= tmp.size() - 1) {
+                output(to, x, -1);
+                return true;
+            }
+            if (g[to] >= tmp.size() - 1) {
+                output(-1, x, to);
+                return true;
+            }
+        }
+        return false;
+    };
+
+    for (int i = 0; i < N; ++i)
+        if (check(i)) return;
+    std::cout << "No\n";
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    int t;
+    std::cin >> t;
+
+    while (t--) solve();
+}