結果

問題 No.2026 Yet Another Knapsack Problem
ユーザー gew1fw
提出日時 2025-06-12 20:30:14
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,354 bytes
コンパイル時間 237 ms
コンパイル使用メモリ 81,732 KB
実行使用メモリ 88,080 KB
最終ジャッジ日時 2025-06-12 20:31:14
合計ジャッジ時間 58,301 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30 TLE * 1 -- * 11
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
import math
from collections import defaultdict

def main():
    sys.setrecursionlimit(1 << 25)
    N = int(sys.stdin.readline())
    items = []
    c1, v1 = 0, 0
    for i in range(N):
        c, v = map(int, sys.stdin.readline().split())
        if i == 0:
            c1, v1 = c, v
        else:
            items.append((i+1, c, v))  # weight is i+1 (since i starts from 0 in 0-based)

    # Initialize other_dp[j][w]: max value with j items (excluding weight 1) and total weight w
    other_dp = [[-float('inf')] * (N + 1) for _ in range(N + 1)]
    other_dp[0][0] = 0

    for weight, cnt, val in items:
        # Binary split
        k = 1
        remaining = cnt
        while remaining > 0:
            take = min(k, remaining)
            s = take
            s_weight = s * weight
            s_val = s * val
            # Update other_dp in reverse
            for j in range(N, -1, -1):
                for w in range(N, -1, -1):
                    if other_dp[j][w] == -float('inf'):
                        continue
                    new_j = j + s
                    new_w = w + s_weight
                    if new_j > N or new_w > N:
                        continue
                    if other_dp[new_j][new_w] < other_dp[j][w] + s_val:
                        other_dp[new_j][new_w] = other_dp[j][w] + s_val
            remaining -= take
            k *= 2

    # Preprocess max_other[j][t] = max{ other_dp[j][w] for w <= t }
    max_other = [[-float('inf')] * (N + 1) for _ in range(N + 1)]
    for j in range(N + 1):
        current_max = -float('inf')
        for t in range(N + 1):
            if other_dp[j][t] > current_max:
                current_max = other_dp[j][t]
            max_other[j][t] = current_max

    # Now handle the weight 1 items
    ans = [-float('inf')] * (N + 1)
    for k in range(1, N + 1):
        max_val = -float('inf')
        max_j = min(k, N)
        for j in range(0, max_j + 1):
            t = k - j
            if t < 0 or t > c1:
                continue
            t_max = N - t
            if t_max < 0:
                continue
            current_val = max_other[j][t_max] + t * v1
            if current_val > max_val:
                max_val = current_val
        ans[k] = max_val

    for k in range(1, N + 1):
        print(ans[k])

if __name__ == '__main__':
    main()
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