U `_K@sdZdZddlZddlZddlmZmZmZmZm Z m Z dddgZ edee e fZed eeeZd Zd Zd Zd ZdZGdddeZeZdZGdddeZGdddZd`ee e egefedddZdaee eddddZedkrdddgdddgdd dggd!fdddd"gdddd#gdd dd$ggd%fd&d&d'gd(d'd"gd(d)d*ggd+fd,d-d.gd/d0d1gd2d3d4ggd5fd&d&d'd6gd(d'd"d"gd(d)d*d&ggd7fd8d9d:d;gdd?gd@dAdBdCggdDfd*dEdFegd"d(dGd6gedEd*egdGdGdGd&ggdHfdIdJdKegdLdMdNdOgedPdQegdRdSdTdUggdVfd"eeeged#eegeed$egeeed*ggd&fdWeeegedXeegeedYegeeedZggd[fg Z eZ!e D]t\Z"Z#ee"d\d]e!$e"Z%dZ&e%D]0\Z'Z(e"e'e(Z)e&e)7Z&e*d^e'e(e)fqe*d_e&e#e&kst+qdS)ba! Introduction ============ The Munkres module provides an implementation of the Munkres algorithm (also called the Hungarian algorithm or the Kuhn-Munkres algorithm), useful for solving the Assignment Problem. For complete usage documentation, see: https://software.clapper.org/munkres/ ZmarkdownN)UnionNewTypeSequenceTupleOptionalCallableMunkresmake_cost_matrix DISALLOWEDAnyNumMatrixz1.1.4zBrian Clapper, bmc@clapper.orgz%https://software.clapper.org/munkres/z(c) 2008-2020 Brian M. ClapperzApache Software Licensec@s eZdZdS)DISALLOWED_OBJN)__name__ __module__ __qualname__rr&lib/python3.8/site-packages/munkres.pyr +sr Dc@seZdZdZdS)UnsolvableMatrixz2 Exception raised for unsolvable matrices N)rrr__doc__rrrrr4src@sTeZdZdZddZd3eeedddZeee eefdd d Z eed d d Z ee edddZ edddZedddZedddZedddZedddZedddZe dddZd4eee eefd d!d"Zee ed#d$d%Zee ed&d'd(Zedd)d*Zeeeed+d,d-d.Zd+dd/d0Zd+dd1d2Zd+S)5rzy Calculate the Munkres solution to the classical assignment problem. See the module documentation for usage. cCs4d|_g|_g|_d|_d|_d|_d|_d|_dS)zCreate a new instanceNr)C row_covered col_coverednZ0_rZ0_cmarkedpath)selfrrr__init__DszMunkres.__init__r)matrix pad_valuereturnc Csd}t|}|D]}t|t|}qt||}g}|D]<}t|}|dd}||krh||g||7}||g7}q6t||kr||g|g7}qt|S)a Pad a possibly non-square matrix to make it square. **Parameters** - `matrix` (list of lists of numbers): matrix to pad - `pad_value` (`int`): value to use to pad the matrix **Returns** a new, possibly padded, matrix rN)lenmax) rr r!Z max_columnsZ total_rowsrowZ new_matrixZrow_lenZnew_rowrrr pad_matrixOs     zMunkres.pad_matrix) cost_matrixr"c Cs0|||_t|j|_t||_t|d|_ddt|jD|_ddt|jD|_d|_ d|_ | |jdd|_ | |jd|_ d}d}|j|j|j|j|j|jd}|sz||}|}Wqtk rd }YqXqg}t|jD]8}t|jD](}|j ||dkr|||fg7}qq|S) a Compute the indexes for the lowest-cost pairings between rows and columns in the database. Returns a list of `(row, column)` tuples that can be used to traverse the matrix. **WARNING**: This code handles square and rectangular matrices. It does *not* handle irregular matrices. **Parameters** - `cost_matrix` (list of lists of numbers): The cost matrix. If this cost matrix is not square, it will be padded with zeros, via a call to `pad_matrix()`. (This method does *not* modify the caller's matrix. It operates on a copy of the matrix.) **Returns** A list of `(row, column)` tuples that describe the lowest cost path through the matrix rcSsg|]}dqSFr.0irrr sz#Munkres.compute..cSsg|]}dqSr(rr)rrrr,sF)r.r-T)r&rr#rZoriginal_lengthZoriginal_widthrangerrrr_Munkres__make_matrixrr_Munkres__step1_Munkres__step2_Munkres__step3_Munkres__step4_Munkres__step5_Munkres__step6KeyError) rr'donestepZstepsfuncresultsr+jrrrcomputers>     zMunkres.compute)r r"cCs t|S)z+Return an exact copy of the supplied matrix)copydeepcopy)rr rrrZ __copy_matrixszMunkres.__copy_matrix)rvalr"cs2g}t|D] }|fddt|Dg7}q |S)z@Create an *n*x*n* matrix, populating it with the specific value.csg|]}qSrr)r*r@rDrrr,sz)Munkres.__make_matrix..)r3)rrrDr r+rrErZ __make_matrixs zMunkres.__make_matrix)r"cCs|j}|j}t|D]p}dd|j|D}t|dkrFtd|t|}t|D],}|j||tk rV|j|||8<qVqdS)z For each row of the matrix, find the smallest element and subtract it from every element in its row. Go to Step 2. cSsg|]}|tk r|qSr)r )r*xrrrr,sz#Munkres.__step1..rzRow {0} is entirely DISALLOWED.r-)rrr3r#rformatminr )rrrr+Zvalsminvalr@rrrZ__step1s   zMunkres.__step1cCsz|j}t|D]^}t|D]P}|j||dkr|j|s|j|sd|j||<d|j|<d|j|<qqq|dS)z Find a zero (Z) in the resulting matrix. If there is no starred zero in its row or column, star Z. Repeat for each element in the matrix. Go to Step 3. rr.Tr/)rr3rrrr_Munkres__clear_covers)rrr+r@rrrZ__step2s    zMunkres.__step2cCsj|j}d}t|D]@}t|D]2}|j||dkr|j|sd|j|<|d7}qq||krbd}nd}|S)z Cover each column containing a starred zero. If K columns are covered, the starred zeros describe a complete set of unique assignments. In this case, Go to DONE, otherwise, Go to Step 4. rr.Tr0)rr3rr)rrcountr+r@r=rrrZ__step3s    zMunkres.__step3cCsd}d}d}d}d}|s|||\}}|dkr:d}d}qd|j||<||}|dkrt|}d|j|<d|j|<qd}||_||_d}q|S)ak Find a noncovered zero and prime it. If there is no starred zero in the row containing this primed zero, Go to Step 5. Otherwise, cover this row and uncover the column containing the starred zero. Continue in this manner until there are no uncovered zeros left. Save the smallest uncovered value and Go to Step 6. rFTr2r-r1)_Munkres__find_a_zeror_Munkres__find_star_in_rowrrrr)rr=r<r%colZstar_colrrrZ__step4s*   zMunkres.__step4cCsd}|j}|j||d<|j||d<d}|s|||d}|dkrv|d7}|||d<||dd||d<nd}|s*|||d}|d7}||dd||d<|||d<q*|||||dS)aG Construct a series of alternating primed and starred zeros as follows. Let Z0 represent the uncovered primed zero found in Step 4. Let Z1 denote the starred zero in the column of Z0 (if any). Let Z2 denote the primed zero in the row of Z1 (there will always be one). Continue until the series terminates at a primed zero that has no starred zero in its column. Unstar each starred zero of the series, star each primed zero of the series, erase all primes and uncover every line in the matrix. Return to Step 3 rr.FTr/)rrr_Munkres__find_star_in_col_Munkres__find_prime_in_row_Munkres__convert_pathrJ_Munkres__erase_primes)rrLrr<r%rPrrrZ__step5s*   zMunkres.__step5cCs|}d}t|jD]}t|jD]}|j||tkrs. #;!$     ) profit_matrixinversion_functionr"csLs"tdd|Dfddg}|D]}|fdd|Dq*|S)a Create a cost matrix from a profit matrix by calling `inversion_function()` to invert each value. The inversion function must take one numeric argument (of any type) and return another numeric argument which is presumed to be the cost inverse of the original profit value. If the inversion function is not provided, a given cell's inverted value is calculated as `max(matrix) - value`. This is a static method. Call it like this: from munkres import Munkres cost_matrix = Munkres.make_cost_matrix(matrix, inversion_func) For example: from munkres import Munkres cost_matrix = Munkres.make_cost_matrix(matrix, lambda x : sys.maxsize - x) **Parameters** - `profit_matrix` (list of lists of numbers): The matrix to convert from profit to cost values. - `inversion_function` (`function`): The function to use to invert each entry in the profit matrix. **Returns** A new matrix representing the inversion of `profix_matrix`. css|]}t|VqdSN)r$)r*r%rrr sz#make_cost_matrix..cs|Sr_r)rF)maximumrrz"make_cost_matrix..csg|] }|qSrr)r*value)r^rrr,sz$make_cost_matrix..)r$append)r]r^r'r%r)r^rarr s! )r msgr"c Csddl}|dk rt|d}|D],}|D]"}|tkr8t}t|tt|}q(q d|}|D]J}d}|D]0}|tkrvt}|d|}tj ||d}qftj dqZdS)z Convenience function: Displays the contents of a matrix. **Parameters** - `matrix` (list of lists of numbers): The matrix to print - `msg` (`str`): Optional message to print before displaying the matrix rNz%%%d[sz, z] ) mathprintr DISALLOWED_PRINTVALr$r#strrVstdoutwrite) r rfriwidthr%rDrGsep formattedrrr print_matrixs&  rr__main__iiiXi,iRr.r-r/i  rKr0g333333$@gffffff$@g @g"@g!@g?gffffff#@g333333@g@g3@ gQ$@g ףp= $@g(\ @gGz&@g"@gQ @gQ?gHzG?gGz."@gffffff@gq= ףp@g= ףp=$@gffffff.@r1r2 g/$@g5^I @gPn@gMb?g(\"@gPn(@g$&@gx&1@gK7 @gQ(@gʡ(@g/$(@g-$@gI +4@g?g@gffffff @g@g&@z cost matrix)rfz(%d, %d) -> %szlowest cost=%s)N)N),rZ __docformat__rVrBtypingrrrrrr__all__r\floatr r __version__ __author__Z__url__Z __copyright__Z __license__objectr r rk Exceptionrrr rlrrrZmatricesmr'Zexpected_totalrAZindexesZ total_costrcrFrjAssertionErrorrrrrs     *(                          B