結果

問題 No.1614 Majority Painting on Tree
ユーザー 👑 ygussany
提出日時 2021-06-12 19:17:43
言語 C
(gcc 13.3.0)
結果
AC  
実行時間 1,262 ms / 5,000 ms
コード長 2,536 bytes
コンパイル時間 422 ms
コンパイル使用メモリ 33,280 KB
実行使用メモリ 10,416 KB
最終ジャッジ日時 2024-07-17 15:10:43
合計ジャッジ時間 19,032 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 4
other AC * 45
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.c:4:43: warning: built-in function 'pow' declared as non-function [-Wbuiltin-declaration-mismatch]
    4 | long long fact[100001], fact_inv[100001], pow[2][100001];
      |                                           ^~~

ソースコード

diff #
プレゼンテーションモードにする

#include <stdio.h>
const int Mod = 998244353;
long long fact[100001], fact_inv[100001], pow[2][100001];
long long div_mod(long long x, long long y, long long z)
{
    if (x % y == 0) return x / y;
    else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}
long long combination(int n, int k)
{
    return fact[n] * fact_inv[k] % Mod * fact_inv[n-k] % Mod;
}
typedef struct List {
    struct List *next;
    int v;
} list;
long long solve(int N, int C, list* adj[])
{
    if (C == 1) return 1;
    
    int i, r = 1, u, w, head, tail;
    static int par[100001] = {}, q[100001];
    list *p;
    if (par[r] == 0) {
        par[r] = r;
        q[0] = r;
        for (head = 0, tail = 1; head < tail; head++) {
            u = q[head];
            for (p = adj[u]; p != NULL; p = p->next) {
                w = p->v;
                if (par[w] == 0) {
                    par[w] = u;
                    q[tail++] = w;
                }
            }
        }
    } else head = N;
    int k;
    static long long dp[100001], prod;
    for (head--; head > 0; head--) {
        u = q[head];
        for (p = adj[u], k = 0, prod = 1; p != NULL; p = p->next) {
            w = p->v;
            if (w == par[u]) continue;
            prod = prod * dp[w] % Mod;
            k++;
        }
        dp[u] = pow[0][k];
        for (i = (k + 1) / 2; i < k; i++) dp[u] += Mod - combination(k, i) * pow[1][k-i] % Mod;
        for (i = (k + 3) / 2; i <= k; i++) dp[u] += Mod - combination(k, i) * pow[1][k-i+1] % Mod;
        dp[u] = dp[u] % Mod * prod % Mod;
    }
    for (p = adj[r], k = 0, prod = 1; p != NULL; p = p->next) {
        w = p->v;
        prod = prod * dp[w] % Mod;
        k++;
    }
    dp[r] = pow[0][k-1];
    for (i = k / 2 + 1; i < k; i++) dp[r] += Mod - combination(k, i) * pow[1][k-i] % Mod;
    return dp[r] % Mod * prod % Mod * C % Mod;
}
int main()
{
    int i, k, N, C, u, w;
    list *adj[100001] = {}, e[200001];
    scanf("%d %d", &N, &C);
    for (i = 0; i < N - 1; i++) {
        scanf("%d %d", &u, &w);
        e[i*2].v = w;
        e[i*2+1].v = u;
        e[i*2].next = adj[u];
        e[i*2+1].next = adj[w];
        adj[u] = &(e[i*2]);
        adj[w] = &(e[i*2+1]);
    }
    for (i = 1, fact[0] = 1; i <= N; i++) fact[i] = fact[i-1] * i % Mod;
    for (i = N - 1, fact_inv[N] = div_mod(1, fact[N], Mod); i >= 0; i--) fact_inv[i] = fact_inv[i+1] * (i + 1) % Mod;
    for (k = 1, pow[1][0] = 1; k <= N; k++) pow[1][k] = pow[1][k-1] * C % Mod;
    
    long long ans = 0;
    for (i = C; i >= 1; i--) {
        for (k = 0; k <= N; k++) pow[0][k] = pow[1][k];
        for (k = 1, pow[1][0] = 1; k <= N; k++) pow[1][k] = pow[1][k-1] * (i - 1) % Mod;
        if ((C - i) % 2 == 0) ans += solve(N, i, adj) * combination(C, i) % Mod;
        else ans += Mod - solve(N, i, adj) * combination(C, i) % Mod;
    }
    printf("%lld\n", ans % Mod);
    fflush(stdout);
    return 0;
}
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