Hungarian
(expansion/graph/Hungarian.py)

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• Last update: 2023-07-04 23:57:10+09:00

概要

割り当て問題を解きます．

$N \times M, (N \le M)$ の行列 $A$ があるときに。 $\sum_{i = 0}^{N - 1} A_{i, p_i}$ を最小化する $p_i$ (重複なし) を構成します。

使い方

inf は十分に大きい値を適当に設定してください

cost, assignment = Hungarian(A, inf=1 << 60):

Code

def Hungarian(A, inf=1 << 60):
    n = len(A) + 1
    m = len(A[0]) + 1
    P = [0] * m
    way = [0] * m
    U = [0] * n
    V = [0] * m

    for i in range(1, n):
        P[0] = i
        minV = [inf] * m
        used = [False] * m
        j0 = 0
        while P[j0] != 0:
            i0 = P[j0]
            j1 = 0
            used[j0] = True
            delta = inf
            for j in range(1, m):
                if used[j]:
                    continue
                if i0 == 0 or j == 0:
                    cur = -U[i0] - V[j]
                else:
                    cur = A[i0 - 1][j - 1] - U[i0] - V[j]
                if cur < minV[j]:
                    minV[j] = cur
                    way[j] = j0
                if minV[j] < delta:
                    delta = minV[j]
                    j1 = j
            for j in range(m):
                if used[j]:
                    U[P[j]] += delta
                    V[j] -= delta
                else:
                    minV[j] -= delta
            j0 = j1
        P[j0] = P[way[j0]]
        while j0 != 0:
            j1 = way[j0]
            P[j0] = P[j1]
            j0 = j1

    ret = [-1] * (n - 1)
    for j in range(1, m):
        if P[j] != 0:
            ret[P[j] - 1] = j - 1

    return -V[0], ret

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/documentation/build.py", line 81, in _render_source_code_stat
    bundled_code = language.bundle(
                   ^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/languages/python.py", line 108, in bundle
    raise NotImplementedError
NotImplementedError

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