結果

問題 No.2026 Yet Another Knapsack Problem
ユーザー gew1fw
提出日時 2025-06-12 20:32:03
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,482 bytes
コンパイル時間 339 ms
コンパイル使用メモリ 81,912 KB
実行使用メモリ 171,324 KB
最終ジャッジ日時 2025-06-12 20:34:03
合計ジャッジ時間 61,178 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 35 TLE * 1 -- * 6
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

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    c = []
    v = []
    for _ in range(N):
        ci = int(input[ptr])
        vi = int(input[ptr+1])
        c.append(ci)
        v.append(vi)
        ptr += 2

    # Initialize DP for other items (excluding the first item)
    dp_other = [[-float('inf')] * (N + 1) for _ in range(N + 1)]
    dp_other[0][0] = 0

    # Process items from 2 to N (index 1 to N-1 in the list)
    for i in range(1, N):
        current_i = i + 1  # weight is i+1 as per problem statement
        current_c = c[i]
        current_v = v[i]
        max_t = min(current_c, N // current_i)
        if max_t == 0:
            continue  # cannot take any of this item

        # Binary decomposition
        s = 1
        remaining = max_t
        while remaining > 0:
            take = min(s, remaining)
            weight = take * current_i
            value = take * current_v
            # Update DP in reverse to avoid overwriting
            for k in range(N, take - 1, -1):
                for w in range(N, weight - 1, -1):
                    if dp_other[k - take][w - weight] != -float('inf'):
                        if dp_other[k][w] < dp_other[k - take][w - weight] + value:
                            dp_other[k][w] = dp_other[k - take][w - weight] + value
            remaining -= take
            s *= 2

    # Preprocess max_val[k][w] which is the maximum value for k items with weight <= w
    max_val = [[-float('inf')] * (N + 1) for _ in range(N + 1)]
    for k in range(N + 1):
        current_max = -float('inf')
        for w in range(N + 1):
            if dp_other[k][w] > current_max:
                current_max = dp_other[k][w]
            max_val[k][w] = current_max

    # Process the first item (weight 1, count c[0] = N)
    v1 = v[0]
    ans = [-float('inf')] * (N + 1)
    for k in range(1, N + 1):
        max_total = -float('inf')
        for k_prime in range(0, k + 1):
            t = k - k_prime
            w_max = N - t
            if w_max < 0:
                continue
            w_max = min(w_max, N)
            current_max = max_val[k_prime][w_max]
            if current_max == -float('inf'):
                continue
            total = current_max + t * v1
            if total > max_total:
                max_total = total
        ans[k] = max_total

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

if __name__ == '__main__':
    main()
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