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49 lines
1.4 KiB
Python
49 lines
1.4 KiB
Python
''' mbinary
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#########################################################################
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# File : work_dispatch.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2019-04-16 09:41
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# Description:
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#########################################################################
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'''
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'''
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设有n件工作要分配给n个人去完成，将工作i分配给第j个人所需费用为c_ij 。试设计一个算法，为每个人分配1件不同的工作，并使总费用达到最小。
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'''
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def dispatch(mat):
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'''mat: matrix of c_ij'''
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def _util(i,arrange,cost):
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''' for i-th work'''
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nonlocal total,used,rst
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if i==n:
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total=cost
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rst = arrange.copy() # copy is needed
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else:
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for j in range(n):
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if not used[j] and( total is None or cost+mat[i][j]<total):
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used[j]=True
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arrange[i] = j
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_util(i+1,arrange,cost+mat[i][j])
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used[j]=False
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total = None
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rst = None
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n = len(mat)
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used = [False for i in range(n)]
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_util(0,[-1]*n,0)
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return total,rst
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import random
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if __name__=='__main__':
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n = 10
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mat = [[random.randint(1,100) for i in range(n)] for i in range(n)]
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print('work matrix: c_ij: work_i and person_j')
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for i in range(n):
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print(mat[i])
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print('result: ',end='')
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print(dispatch(mat))
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