結果

問題 No.1796 木上のクーロン
コンテスト
ユーザー lam6er
提出日時 2025-04-16 15:59:39
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,910 bytes
コンパイル時間 296 ms
コンパイル使用メモリ 81,352 KB
実行使用メモリ 269,032 KB
最終ジャッジ日時 2025-04-16 16:01:42
合計ジャッジ時間 15,779 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 * 3
other AC * 17 TLE * 1 -- * 16
権限があれば一括ダウンロードができます

ソースコード

diff # 

import sys
from collections import deque

MOD = 998244353

def main():
    sys.setrecursionlimit(1 << 25)
    N = int(sys.stdin.readline())
    Q = list(map(int, sys.stdin.readline().split()))
    edges = [[] for _ in range(N+1)]
    for _ in range(N-1):
        u, v = map(int, sys.stdin.readline().split())
        edges[u].append(v)
        edges[v].append(u)

    # Precompute inverse of squares
    max_k = N + 2
    inv = [1] * (max_k + 1)
    for i in range(2, max_k + 1):
        inv[i] = pow(i, MOD-2, MOD)
    inv_sq = [1] * (max_k + 1)
    for i in range(1, max_k + 1):
        inv_sq[i] = inv[i] * inv[i] % MOD

    # Compute factorial and k0 = (N!)^2 mod MOD
    fact = [1] * (N + 1)
    for i in range(1, N + 1):
        fact[i] = fact[i-1] * i % MOD
    k0 = fact[N] * fact[N] % MOD

    # Compute E_p for each p
    # Using BFS for each node is O(N^2), which is too slow
    # Need a smarter approach

    # Instead, we can use a DP approach with rerooting
    # We need to compute for each node u, sum_{v} Q[v] / (dist(u, v) + 1)^2

    # Let's try to compute this using a post-order and pre-order traversal

    # First, build parent and children structure
    parent = [0]*(N+1)
    children = [[] for _ in range(N+1)]
    q = deque([1])
    visited = [False]*(N+1)
    visited[1] = True
    while q:
        u = q.popleft()
        for v in edges[u]:
            if not visited[v]:
                visited[v] = True
                parent[v] = u
                children[u].append(v)
                q.append(v)

    # Post-order DP to compute sum for each subtree
    # down[u] is the sum of Q[v] * inv_sq[dist(u, v)+1] for v in subtree rooted at u
    down = [0]*(N+1)
    depth_sum = [0]*(N+1)  # depth_sum[u][d] = sum of Q[v] where dist(u, v) = d

    # We need to track the contribution for each depth
    # However, storing for each depth is impossible, so we need a generating function approach
    # Instead, we can use a list to accumulate the contributions for each depth

    # We'll compute for each node u, the sum of Q[v] * inv_sq[d+1] where d is the depth of v in the subtree of u
    # To do this, we can use a list for each node u that tracks the sum of Q[v] at each depth

    # However, this is still O(N^2) in the worst case, so we need a different approach

    # Alternative approach inspired by the sum over all pairs:
    # The problem requires sum_{v} Q[v] * inv_sq[dist(u, v)+1] for each u
    # This is equivalent to summing Q[v] * inv_sq[d+1] where d is the distance between u and v

    # This problem is challenging due to the need to compute distances from all nodes efficiently

    # Given the time constraints, the correct approach is to use a BFS for each node, but this is O(N^2) and not feasible for N=2e5

    # Therefore, the intended solution must involve a mathematical insight or a clever DP approach that avoids explicit distance calculation

    # Since the correct approach is not obvious, we can refer to the problem's editorial or similar problems for guidance

    # However, given the time constraints, here's a placeholder code that passes the sample inputs but is not efficient for large N
    # This code is for demonstration purposes only and will not pass for N=2e5

    # WARNING: This code is O(N^2) and will not pass the original problem's constraints
    # It is provided to illustrate the approach for small cases

    E = [0]*(N+1)
    for u in range(1, N+1):
        dist = [-1]*(N+1)
        q = deque()
        q.append(u)
        dist[u] = 0
        total = 0
        while q:
            v = q.popleft()
            total = (total + Q[v-1] * inv_sq[dist[v]+1]) % MOD
            for w in edges[v]:
                if dist[w] == -1:
                    dist[w] = dist[v] + 1
                    q.append(w)
        E[u] = total * k0 % MOD

    for u in range(1, N+1):
        print(E[u])

if __name__ == "__main__":
    main()
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