#1028192 (PyPy3) No.2955 Pizza Delivery Plan

• 問題: No.2955 Pizza Delivery Plan
• ユーザー: LyricalMaestro
• 提出日時: 2024-11-24 19:24:33
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 273 ms / 2,000 ms
• コード長: 2,493 bytes
• コンパイル時間: 278 ms
• コンパイル使用メモリ: 82,404 KB
• 実行使用メモリ: 86,232 KB
• 最終ジャッジ日時: 2024-11-24 19:24:40
• 合計ジャッジ時間: 7,057 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 28

ソースコード

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## https://yukicoder.me/problems/no/2955
import math
def main():
    N, K = map(int, input().split())
    xy = []
    for _ in range(N):
        x, y = map(int, input().split())
        xy.append((x, y))
    # 原点からの距離を計算
    dists_from_origins = []
    for x, y in xy:
        d = math.sqrt(x ** 2 + y ** 2)
        dists_from_origins.append(d)
    # 点i -> 点jのの移動距離の計算
    matrix = [[-1] * N for _ in range(N)]
    for i in range(N):
        for j in range(N):
            x1, y1 = xy[i]
            x2, y2 = xy[j]
            d = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2 )
            matrix[i][j] = d
    
    # popcountがK以下のbit(一度に宅配できる住宅の組み合わせ)ごとに最短でどれくらい帰ってくるかの計算を実施
    base_bits = [[] for _ in range(K + 1)]
    for bit in range(2 ** N):
        popcount = 0
        for i in range(N):
            if bit & (1 << i) > 0:
                popcount += 1
        if popcount <= K:
            base_bits[popcount].append(bit)
    dp = {}
    for i in range(N):
        if (1 << i) not in dp:
            dp[1 << i] = {}
        dp[1 << i][i] = dists_from_origins[i]
    
    for k in range(1, K):
        b_bits = base_bits[k]
        for bit in b_bits:
            for j in range(N):
                if bit & (1 << j) > 0:
                    continue
                new_bit = bit | (1 << j)
                for last, cost in dp[bit].items():
                    new_cost = cost + matrix[last][j]
                    if new_bit not in dp:
                        dp[new_bit] = {}
                    if j not in dp[new_bit]:
                        dp[new_bit][j] = float("inf")
                    dp[new_bit][j] = min(dp[new_bit][j], new_cost)
    new_bit = {}    
    for bit, bit_map in dp.items():
        base_cost = float("inf")
        for key, cost in bit_map.items():
            c = dists_from_origins[key] + cost
            base_cost = min(base_cost, c)
        new_bit[bit] = base_cost
    # ---------
    answer_dp = [float("inf")] * ( 2 ** N) 
    answer_dp[0] = 0.0
    for bit in range(1, 2 ** N):
        b = bit
        while b > 0:
            b_ = bit - b
            if b in new_bit:
                ans = new_bit[b] + answer_dp[b_]
                answer_dp[bit] = min(answer_dp[bit], ans)
            b = (b - 1) & bit
    
    print(answer_dp[2 ** N - 1])
            
    
if __name__ == "__main__":
    main()
 
 
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