結果

問題 No.2026 Yet Another Knapsack Problem
ユーザー suisen
提出日時 2022-04-22 02:01:50
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 3,945 ms / 10,000 ms
コード長 2,089 bytes
コンパイル時間 413 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 132,208 KB
最終ジャッジ日時 2024-06-27 12:15:58
合計ジャッジ時間 26,199 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 42
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ソースコード

diff #
プレゼンテーションモードにする

from collections import deque
from typing import Deque, Tuple
class SlidingWindowMaximum:
    l : int
    r : int
    dq : Deque[Tuple[int, int]]
    def __init__(self) -> None:
        self.clear()
    def clear(self) -> None:
        self.l = 0
        self.r = 0
        self.dq = deque()
    
    def push_back(self, v : int) -> None:
        while self.dq and self.dq[-1][0] < v:
            self.dq.pop()
        self.dq.append((v, self.r))
        self.r += 1
    
    def pop_front(self) -> None:
        assert self.size()
        if self.dq[0][1] == self.l:
            self.dq.popleft()
        self.l += 1
    def query(self) -> int:
        return self.dq[0][0]
    def size(self) -> int:
        return self.r - self.l
N = int(input())
items = [(int(0), int(0))]
for _ in range(N):
    c, v = map(int, input().split())
    items.append((c, v))
INF = 1 << 60
dp = [[-INF] * (N + 1) for i in range(N + 1)]
dp[0][0] = 0
sw = SlidingWindowMaximum()
for i in reversed(range(1, N + 1)):
    max_num = min(N, N // i)
    max_sum = N
    c, v = items[i]
    # dp[num][sum] = max{ pd[num-p][sum-p*i]-(num-p)*v[i] | 0<=p<=c[i] } ⋃ {-∞} + num*v[i]
    for num in range(max_num + 1):
        for sum in range(i if num else max_sum + 1):
            max_p = min(max_num - num, (max_sum - sum) // i)
            if max_p <= c:
                max_val = -INF
                for p in range(max_p + 1):
                    max_val = max(max_val, dp[num + p][sum + i * p] - (num + p) * v)
                    dp[num + p][sum + i * p] = max_val + (num + p) * v
            else:
                sw.clear()
                for p in range(c + 1):
                    sw.push_back(dp[num + p][sum + i * p] - (num + p) * v)
                    dp[num + p][sum + i * p] = sw.query() + (num + p) * v
                for p in range(c + 1, max_p + 1):
                    sw.push_back(dp[num + p][sum + i * p] - (num + p) * v)
                    sw.pop_front()
                    dp[num + p][sum + i * p] = sw.query() + (num + p) * v
for k in range(1, N + 1):
    print(max(dp[k]))
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