結果

問題 No.2026 Yet Another Knapsack Problem
ユーザー gew1fw
提出日時 2025-06-12 16:50:37
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 1,928 bytes
コンパイル時間 223 ms
コンパイル使用メモリ 82,412 KB
実行使用メモリ 251,912 KB
最終ジャッジ日時 2025-06-12 16:52:17
合計ジャッジ時間 33,664 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 35 TLE * 1 -- * 6
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ソースコード

diff # 

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    
    groups = []
    for i in range(1, N+1):
        c_i = int(input[idx])
        v_i = int(input[idx+1])
        idx += 2
        groups.append((i, c_i, v_i))
    
    # Separate group 1 (i=1)
    group1 = groups[0]
    i1, c1, v1 = group1
    assert i1 == 1 and c1 == N
    
    other_groups = groups[1:]
    
    # Initialize DP[x][s] = max value using x items from other groups, sum (i-1)*t_i = s
    INF = -1 << 60
    dp = [[INF] * (N + 1) for _ in range(N + 1)]
    dp[0][0] = 0
    
    for i, c_i, v_i in other_groups:
        weight = i
        value_diff = v_i - v1
        excess_per = weight - 1
        
        # Process this group
        # We need to consider taking t items from this group, t from 0 to c_i
        # For each possible t, update the DP
        # To handle this efficiently, we can use a temporary array and iterate backwards
        temp = [row[:] for row in dp]
        
        for t in range(1, c_i + 1):
            t_excess = t * excess_per
            t_value = t * value_diff
            for x in range(N, t - 1, -1):
                for s in range(N, t_excess - 1, -1):
                    if temp[x - t][s - t_excess] != INF:
                        if dp[x][s] < temp[x - t][s - t_excess] + t_value:
                            dp[x][s] = temp[x - t][s - t_excess] + t_value
    
    # Precompute the maximum for each x and s
    # For each k, the answer is k*v1 + max(dp[x][s] where x <=k and s <= N -k)
    for k in range(1, N + 1):
        max_extra = INF
        for x in range(0, k + 1):
            max_s = N - k
            if max_s < 0:
                continue
            for s in range(0, max_s + 1):
                if dp[x][s] > max_extra:
                    max_extra = dp[x][s]
        print(max_extra + k * v1)

if __name__ == '__main__':
    main()
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