#596349 (PyPy3) No.1324 Approximate the Matrix

• 問題: No.1324 Approximate the Matrix
• ユーザー: shotoyoo
• 提出日時: 2020-12-22 00:23:35
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 335 ms / 2,000 ms
• コード長: 6,232 bytes
• コンパイル時間: 311 ms
• コンパイル使用メモリ: 82,240 KB
• 実行使用メモリ: 89,664 KB
• 最終ジャッジ日時: 2024-09-21 13:29:41
• 合計ジャッジ時間: 8,095 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 42

ソースコード

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import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(2*10**5+10)
write = lambda x: sys.stdout.write(x+"\n")
from typing import NamedTuple, Optional, List, Tuple, cast
from heapq import heappush, heappop
class MCFGraph:
    class Edge(NamedTuple):
        src: int
        dst: int
        cap: int
        flow: int
        cost: int
    class _Edge:
        def __init__(self, dst: int, cap: int, cost: int) -> None:
            self.dst = dst
            self.cap = cap
            self.cost = cost
            self.rev: Optional[MCFGraph._Edge] = None
    def __init__(self, n: int, neg=False, negf=None) -> None:
        self._neg = neg
        if neg:
            n += 2
            self._negs = n-2
            self._negt = n-1
            self._negf = negf
            self._negfsum = 0
            self._negcsum = 0
            self._negdone = False            
        self._n = n
        self._g: List[List[MCFGraph._Edge]] = [[] for _ in range(n)]
        self._edges: List[MCFGraph._Edge] = []    
    def add_edge(self, src: int, dst: int, cap: int, cost: int) -> int:
        assert 0 <= src < self._n
        assert 0 <= dst < self._n
        assert 0 <= cap
        if cost<0 and self._neg:
            if not self._negdone:
                global s,t
                self._negdone = True
                self.add_edge(self._negs, s, self._negf, 0)
                self.add_edge(t, self._negt, self._negf, 0)
                # 後で指定した流量を流すための処理
#                 self._inf = 10**12
#                 self._negE = self.add_edge(self._negt, self._negs, self._negf, -self._inf)
            self.add_edge(self._negs, dst, cap, 0)
            self.add_edge(src, self._negt, cap, 0)
            self.add_edge(dst, src, cap, -cost)
            self._negfsum += cap
            self._negcsum += cap*cost
        else:
            m = len(self._edges)
            e = MCFGraph._Edge(dst, cap, cost)
            re = MCFGraph._Edge(src, 0, -cost)
            e.rev = re
            re.rev = e
            self._g[src].append(e)
            self._g[dst].append(re)
            self._edges.append(e)
            return m
    def get_edge(self, i: int) -> Edge:
        assert 0 <= i < len(self._edges)
        e = self._edges[i]
        re = cast(MCFGraph._Edge, e.rev)
        return MCFGraph.Edge(
            re.dst,
            e.dst,
            e.cap + re.cap,
            re.cap,
            e.cost
        )
    def edges(self) -> List[Edge]:
        return [self.get_edge(i) for i in range(len(self._edges))]
    def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> Tuple[int, int]:
        if self._neg:
            flow_limit += self._negfsum
            val = self.slope(self._negs, self._negt, flow_limit)[-1]
            return (val[0], val[1] + self._negcsum)
        else:
            return self.slope(s, t, flow_limit)[-1]
    def slope(self, s: int, t: int, flow_limit: Optional[int] = None) -> List[Tuple[int, int]]:
        assert 0 <= s < self._n
        assert 0 <= t < self._n
        assert s != t
        if flow_limit is None:
            flow_limit = cast(int, sum(e.cap for e in self._g[s]))
        dual = [0] * self._n
        prev: List[Optional[Tuple[int, MCFGraph._Edge]]] = [None] * self._n
        def refine_dual() -> bool:
            pq = [self.enc(0, s)]
            visited = [False] * self._n
            dist: List[Optional[int]] = [None] * self._n
            dist[s] = 0
            while pq:
                dist_v, v = self.dec(heappop(pq))
                if visited[v]:
                    continue
                visited[v] = True
                if v == t:
                    break
                dual_v = dual[v]
                for e in self._g[v]:
                    w = e.dst
                    if visited[w] or e.cap == 0:
                        continue
                    reduced_cost = e.cost - dual[w] + dual_v
                    new_dist = dist_v + reduced_cost
                    dist_w = dist[w]
                    if dist_w is None or new_dist < dist_w:
                        dist[w] = new_dist
                        prev[w] = v, e
                        heappush(pq, self.enc(new_dist, w))
            else:
                return False
            dist_t = dist[t]
            for v in range(self._n):
                if visited[v]:
                    dual[v] -= cast(int, dist_t) - cast(int, dist[v])
            return True
        flow = 0
        cost = 0
        prev_cost_per_flow: Optional[int] = None
        result = [(flow, cost)]
        while flow < flow_limit:
            if not refine_dual():
                break
            f = flow_limit - flow
            v = t
            while prev[v] is not None:
                u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
                f = min(f, e.cap)
                v = u
            v = t
            while prev[v] is not None:
                u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
                e.cap -= f
                assert e.rev is not None
                e.rev.cap += f
                v = u
            c = -dual[s]
            flow += f
            cost += f * c
            if c == prev_cost_per_flow:
                result.pop()
            result.append((flow, cost))
            prev_cost_per_flow = c
        return result
    def enc(self,d,v):
        return d*(self._n)+v
    def dec(self,val):
        return divmod(val,self._n)
n,k = list(map(int, input().split()))
a = list(map(int, input().split()))
b = list(map(int, input().split()))
p = [list(map(int, input().split())) for _ in range(n)]
num = 2*n + 2
# g = MCFGraph(num, neg=True, negf=k)
g = MCFGraph(num)
s = num-2
t = num-1
for i in range(n):
    for j in range(n):
        for ind in range(min(a[i],b[j])):
            cost = -2*p[i][j] + 1 + 2*ind
            g.add_edge(i,n+j,1,cost)
#             print(i,j,cost)
            # g.add_edge(pij(i,j), t, a[i]+b[j], cost) # cost<0のときは？
for i in range(n):
    g.add_edge(s, i, a[i], 0)
for j in range(n):
    g.add_edge(n+j, t, b[j], 0)
val = g.flow(s,t,k)
ans = sum(p[i][j]**2 for i in range(n) for j in range(n)) + val[1]
print(ans)
 
 
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