Added arc165_e

contest/arc165/arc165_e.cpp

@@ -0,0 +1,111 @@
+#include <bits/stdc++.h>
+
+using ll = long long int;
+using hash_t = uint64_t;
+
+const int MAXN = 109, MOD = 998244353;
+
+constexpr int qpow(int a, int b) {
+    int res = 1;
+    while (b) {
+        if (b & 1) {
+            res = (ll)res * a % MOD;
+        }
+        a = (ll)a * a % MOD, b >>= 1;
+    }
+    return res;
+}
+
+void add(auto &a, const auto &b) {
+    a = (a + b) % MOD;
+}
+
+int n, k;
+std::vector<int> G[MAXN];
+
+int size[MAXN];
+std::vector<std::vector<int>> dp[MAXN], tmp;
+// i subtree, take j, leave k to father
+
+void dfs(int node, int f) {
+    size[node] = 0;
+    dp[node] = {{1}};
+
+    for (int to : G[node]) {
+        if (to == f) {
+            continue;
+        }
+        dfs(to, node);
+
+        tmp.resize(size[node] + size[to] + 1);
+        for (int x = 0; x <= size[node] + size[to]; ++x) {
+            tmp[x].clear();
+            tmp[x].resize(size[node] + size[to] - x + 1);
+        }
+
+        for (int x = size[node]; x >= 0; --x) {
+            for (int y = size[node] - x; y >= 0; --y) {
+                for (int u = 0; u <= size[to]; ++u) {
+                    for (int v = 0; u + v <= size[to]; ++v) {
+                        add(tmp[x + u][y + v], (ll)dp[node][x][y] * dp[to][u][v]);
+                    }
+                }
+            }
+        }
+        dp[node].swap(tmp);
+
+        size[node] += size[to];
+    }
+
+    size[node] += 1;
+    tmp.resize(size[node] + 1);
+    for (int x = 0; x <= size[node]; ++x) {
+        tmp[x].clear();
+        tmp[x].resize(size[node] - x + 1);
+    }
+
+    for (int x = size[node] - 1; x >= 0; --x) {
+        for (int y = size[node] - 1 - x; y >= 0; --y) {
+            add(tmp[x + 1][0], dp[node][x][y]);
+            add(tmp[x][y + 1], dp[node][x][y]);
+        }
+    }
+    dp[node].swap(tmp);
+}
+
+int fact[MAXN];
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin >> n >> k;
+    for (int i = 2; i <= n; ++i) {
+        int u, v;
+        std::cin >> u >> v;
+        G[u].push_back(v);
+        G[v].push_back(u);
+    }
+
+    fact[0] = 1;
+    for (int i = 1; i <= n; ++i) {
+        fact[i] = (ll)fact[i - 1] * i % MOD;
+    }
+
+    int ans = 0;
+    for (int rt = 1; rt <= n; ++rt) {
+        dfs(rt, 0);
+        for (int i = 0; i < n; ++i) {
+            int res = 0;
+            for (int j = k + 1; i + j <= n; ++j) {
+                add(res, dp[rt][i][j]);
+            }
+            add(ans, (ll)res * fact[n - i - 1] % MOD * fact[i]);
+        }
+    }
+
+    ans = (ll)ans * qpow(fact[n], MOD - 2) % MOD;
+    std::cout << ans << '\n';
+
+    return 0;
+}