結果

問題 No.1324 Approximate the Matrix
ユーザー tamato
提出日時 2020-12-21 10:47:57
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,292 ms / 2,000 ms
コード長 2,942 bytes
コンパイル時間 196 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 88,928 KB
最終ジャッジ日時 2024-09-21 12:44:48
合計ジャッジ時間 15,423 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 * 42
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 # 

mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.buffer.readline
    from heapq import heappush, heappop

    class Mincostflow():
        def __init__(self, N):
            self.N = N
            self.adj = [[] for _ in range(N + 1)]
            self.inf = 1 << 60

        def add_edge(self, fr, to, cap, cost):
            # [to, cap, cost, rev]
            if cap == 0:
                return
            forward = [to, cap, cost, None]
            backward = forward[3] = [fr, 0, -cost, forward]
            self.adj[fr].append(forward)
            self.adj[to].append(backward)

        def flow(self, s, t, f):
            N = self.N
            adj = self.adj
            inf = self.inf

            res = 0
            H = [0] * (N + 1)
            prev_v = [0] * (N + 1)
            prev_e = [None] * (N + 1)

            dist0 = [inf] * (N + 1)
            dist = [inf] * (N + 1)

            while f:
                dist[:] = dist0
                dist[s] = 0
                pq = [(0, s)]
                while pq:
                    d, v = heappop(pq)
                    if d > dist[v]:
                        continue
                    r0 = dist[v] + H[v]
                    for e in adj[v]:
                        u, cap, cost, _ = e
                        if cap > 0 and r0 + cost - H[u] < dist[u]:
                            dist[u] = r = r0 + cost - H[u]
                            heappush(pq, (r, u))
                            prev_v[u] = v
                            prev_e[u] = e

                # flow f doesn't exist
                if dist[t] == inf:
                    return None

                for i in range(1, N + 1):
                    H[i] += dist[i]

                g = f
                v = t
                while v != s:
                    g = min(g, prev_e[v][1])
                    v = prev_v[v]
                f -= g
                res += g * H[t]
                v = t
                while v != s:
                    e = prev_e[v]
                    e[1] -= g
                    e[-1][1] += g
                    v = prev_v[v]

            return res

    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    P = []
    for _ in range(N):
        P.append(list(map(int, input().split())))

    s = N*2 + 1
    t = s + 1
    mcf = Mincostflow(t)
    for i, a in enumerate(A):
        va = i+1
        mcf.add_edge(s, va, a, 0)
        for j, b in enumerate(B):
            vb = N+j+1
            p = P[i][j]
            for f in range(min(a, b)):
                mcf.add_edge(va, vb, 1, 40000 - (p-f)**2 + (p-f-1)**2)
    for j, b in enumerate(B):
        vb = N+j+1
        mcf.add_edge(vb, t, b, 0)
    ans = mcf.flow(s, t, K) - 40000 * K
    for i in range(N):
        for j in range(N):
            ans += P[i][j] ** 2
    print(ans)


if __name__ == '__main__':
    main()
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