結果

問題 No.2019 Digits Filling for All Substrings
ユーザー gew1fw
提出日時 2025-06-12 14:03:50
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,138 bytes
コンパイル時間 232 ms
コンパイル使用メモリ 82,168 KB
実行使用メモリ 101,544 KB
最終ジャッジ日時 2025-06-12 14:04:32
合計ジャッジ時間 4,086 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 4
other TLE * 1 -- * 29
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 defaultdict

MOD = 998244353

def main():
    N = int(sys.stdin.readline())
    S = sys.stdin.readline().strip()

    # Precompute prefix sum_mod and cnt_q
    prefix_sum = [0] * (N + 1)
    prefix_cnt_q = [0] * (N + 1)
    for i in range(1, N+1):
        c = S[i-1]
        if c == '?':
            prefix_cnt_q[i] = prefix_cnt_q[i-1] + 1
            prefix_sum[i] = prefix_sum[i-1]
        else:
            digit = int(c)
            prefix_sum[i] = (prefix_sum[i-1] + digit) % 3
            prefix_cnt_q[i] = prefix_cnt_q[i-1]

    # Precompute dp[k][s] for 0 <= k <= N, 0 <= s <3
    max_k = N
    dp = [[0]*3 for _ in range(max_k + 1)]
    dp[0][0] = 1
    for k in range(max_k):
        for s in range(3):
            if dp[k][s] == 0:
                continue
            # Multiply by the transition counts
            add0 = dp[k][s] * 4  # contribute 0 mod3
            add1 = dp[k][s] * 3  # contribute 1 mod3
            add2 = dp[k][s] * 3  # contribute 2 mod3
            dp[k+1][(s + 0) % 3] += add0
            dp[k+1][(s + 1) % 3] += add1
            dp[k+1][(s + 2) % 3] += add2
            # Mod the values to prevent overflow, though not necessary for correctness
            for s_new in range(3):
                dp[k+1][s_new] %= MOD

    # Now, compute the total using the prefix arrays and dynamic approach
    total = 0
    freq = defaultdict(int)
    freq[(0, 0)] = 1  # initial state: count 0 ? and sum 0

    for i in range(1, N+1):
        current_cnt = prefix_cnt_q[i]
        current_sum = prefix_sum[i]
        temp = 0
        # Iterate through all (c, s) in freq
        for (c, s), cnt in freq.items():
            k = current_cnt - c
            if k < 0:
                continue
            t = (s - current_sum) % 3
            if k > max_k:
                ways = 0
            else:
                ways = dp[k][t]
            temp += ways * cnt
        total = (total + temp) % MOD
        # Update freq with current state
        freq_key = (current_cnt, current_sum)
        freq[freq_key] += 1

    print(total % MOD)

if __name__ == "__main__":
    main()
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