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perms.m: Add new input option "unique" to return only unique permutations (bug #60364) perms.m: Add new function to return only unique permutations, expand input validation, expand docstring. NEWS.8.md: Add note about perms taking a new input option.
author Arun Giridhar <arungiridhar@gmail.com>
date Wed, 25 May 2022 17:58:13 -0400
parents 5d3faba0342e
children 8629bb61ef17
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2001-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{P} =} perms (@var{v})
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28 ## @deftypefnx {} {@var{P} =} perms (@var{v}, "unique")
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29 ## Generate all permutations of vector @var{v} with one row per permutation.
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30 ##
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31 ## Results are returned in inverse lexicographic order. The result has size
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32 ## @code{factorial (@var{n}) * @var{n}}, where @var{n} is the length of
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33 ## @var{v}. Any repetitions are included in the output.
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34 ##
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35 ## If the optional second argument is the string "unique", then only unique
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36 ## permutations are returned, using a method that uses less memory than
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37 ## @code{unique (perms (@var{v}), "rows")} and can be faster for
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38 ## certain inputs. In this case, the results are not guaranteed to be in any
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39 ## particular order.
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40 ##
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41 ## Example 1
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42 ## @example
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43 ## @group
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44 ## perms ([1, 2, 3])
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45 ## @result{}
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46 ## 3 2 1
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47 ## 3 1 2
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48 ## 2 3 1
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49 ## 2 1 3
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50 ## 1 3 2
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51 ## 1 2 3
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52 ## @end group
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53 ## @end example
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54 ##
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55 ## Example 2
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56 ## @example
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57 ## @group
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58 ## perms ([1, 1, 2, 2], "unique")
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59 ## @result{}
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60 ## 2 2 1 1
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61 ## 2 1 2 1
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62 ## 2 1 1 2
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63 ## 1 2 2 1
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64 ## 1 2 1 2
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65 ## 1 1 2 2
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66 ## @end group
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67 ## @end example
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68 ##
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69 ## Programming Notes: If the "unique" argument is not used, the length of
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70 ## @var{v} should be no more than 10-12 to limit memory consumption. To get
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71 ## unique results, test both @code{perms (@var{v}, "unique")} and
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72 ## @code{unique (perms (@var{v}), "rows")} to compare speed and
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73 ## memory usage.
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74 ## @seealso{permute, randperm, nchoosek}
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75 ## @end deftypefn
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76
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77 ## FIXME: In principle it should be more efficient to do indexing using uint8
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78 ## type. However, benchmarking shows doubles are faster. If this changes in
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79 ## a later version of Octave the index variables here can be made uint8.
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80
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81 function P = perms (v, opt)
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82
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83 if (nargin < 1)
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84 print_usage ();
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85 elseif (nargin == 2)
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86 if (! isequal (opt, "unique"))
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87 error ("perms: Second option must be the string ""unique"".");
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88 else
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89 tmp = numel (unique (v));
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90 if (tmp == 1)
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91 P = reshape (v, 1, []);
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92 return
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93 elseif (tmp < numel (v))
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94 P = __perms_unique__ (v);
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95 return
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96 endif
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97 endif
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98 endif
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99
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100 ## If we are here, then we want all permutations, not just unique ones.
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101 ## Or the user passed the "unique" option but the input had no repetitions.
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102 v = v(:).';
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103 if (isnumeric (v) || ischar (v))
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104 ## Order of output is only dependent on the actual values for
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105 ## character and numeric arrays.
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106 v = sort (v, "ascend");
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107 endif
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108 n = numel (v);
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109
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110 if (n < 4) # special cases for small n
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111 switch (n)
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112 case 0
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113 P = reshape (v, 1, 0);
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114 case 1
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115 P = v;
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116 case 2
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117 P = [v([2 1]);v];
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118 case 3
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119 P = v([3 2 1; 3 1 2; 2 3 1; 2 1 3; 1 3 2; 1 2 3]);
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120 endswitch
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121 else
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122 v = v(end:-1:1);
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123 n-= 1;
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124
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125 idx = zeros (factorial (n), n);
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126 idx(1:6, n-2:n) = [1, 2, 3;1, 3, 2;2, 1, 3;2, 3, 1;3, 1, 2;3, 2, 1]+(n-3);
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127 f = 2; # jump-start for efficiency with medium n
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128 for j = 3:n-1
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129 b = 1:n;
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130 f *= j;
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131 perm = idx(1:f, n-(j-1):n);
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132 idx(1:(j+1)*f, n-j) = (n-j:n)(ones (f, 1),:)(:);
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133 for i=0:j
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134 b(i+n-j) -= 1;
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135 idx((1:f)+i*f, n-(j-1):n) = b(perm);
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136 endfor
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137 endfor
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138
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139 n += 1;
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140 f *= n-1;
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141 P = v(1)(ones (factorial (n), n));
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142 P(:,1) = v(ones (f, 1),:)(:);
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143
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144 for i = 1:n
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145 b = v([1:i-1 i+1:n]);
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146 P((1:f)+(i-1)*f, 2:end) = b(idx);
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147 endfor
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148 endif
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149
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150 endfunction
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151
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152 function P = __perms_unique__ (v)
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153 uvec = unique (v);
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154 len = numel (v);
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155 lenvec = (1:len);
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156 ulen = numel (uvec);
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157
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158 ## Calculate frequencies. Slightly faster to not use hist() or histc().
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159 for i = ulen:-1:1
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160 freq (i) = nnz (v == uvec(i));
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161 endfor
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162
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163 ## Performance is improved by handling the most frequent elements first.
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164 ## This can mess with the output order though. Currently we do not promise
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165 ## the results will be in any specific order.
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166 [freq, order] = sort (freq, "descend");
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167 uvec = uvec (order);
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168
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169 ## Call nchoosek for each choice and do a Cartesian set product,
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170 ## avoiding collisions.
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171 indx = nchoosek (lenvec, freq(1));
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172 for i = 2:ulen
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173 this = nchoosek (lenvec, freq(i));
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174
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175 new = zeros (rows (indx) + 1e5, columns (indx) + columns (this));
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176 ## Preallocate 1e5 extra rows.
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177 pos = 0;
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178 for j = 1:rows (this)
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179 tmp = indx;
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180 for k = this(j,:)
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181 tmp = tmp (all (tmp ~= k, 2), :);
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182 endfor
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183
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184 r = rows (tmp);
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185 c = columns (tmp);
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186 if (pos + r > rows(new)) # allocate more memory on the fly
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187 new (pos+r+1e5, 1) = 0;
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188 endif
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189
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190 new ((pos+1):(pos+r), 1:c) = tmp;
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191 new ((pos+1):(pos+r), (c+1):end) = repmat (this(j,:), r, 1);
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192 pos += r;
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193
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194 # fprintf (1, "%d\t%d\t%d\t%d\t%d\t%f\n", i, j, r, pos, rows(new), toc);
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195 endfor
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196 indx = new (1:pos, :);
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197 endfor
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198 clear new tmp this # clear large variables before building P
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199
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200 indx = (indx-1) * rows (indx) + (1:rows (indx))';
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201
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202 ## Initialize P to be the same size as indx with the same class as v.
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203 P = repmat (v, rows(indx), 1);
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204 pos = 0;
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205 for i = 1:ulen
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206 P (indx (:, (pos + 1):(pos + freq(i)))) = uvec (i);
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207 pos += freq(i);
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208 endfor
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209
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210 endfunction
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211
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212 %!assert (rows (perms (1:6)), factorial (6))
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213 %!assert (perms (pi), pi)
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214 %!assert (perms ([pi, e]), [pi, e; e, pi])
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215 %!assert (perms ([1,2,3]), [3,2,1;3,1,2;2,3,1;2,1,3;1,3,2;1,2,3])
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216 %!assert (perms (1:5), perms ([2 5 4 1 3]'))
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217 %!assert (perms ("abc"), char ("cba", "cab", "bca", "bac", "acb", "abc"))
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218 %!assert (perms ("fobar"), sortrows (unique (perms ("fobar"), "rows"), -(1:5)))
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219 %!assert (unique (perms (1:5)(:))', 1:5)
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220 %!assert (perms (int8 (1:4)), int8 (perms (1:4)))
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221
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222 %!assert (sortrows (perms ("abb", "unique")), ["abb"; "bab"; "bba"]);
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223 %!assert (size (perms ([1 1 1 1 2 2 2 3 3], "unique")), [1260 9])
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224 %!assert (size (perms (int8([1 1 1 1 1 2 2 2 2 3 3 3]), "unique")), [27720 12])
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225
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226 %!error <Invalid call> perms ()
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227 %!error <.*Second option must be the string.*> perms (1:5, "nonexistent")
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228 %!error <.*Second option must be the string.*> perms (1:5, {"foo"})
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229
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230 ## Should work for any array type, such as cells and structs, and not
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231 ## only for numeric data.
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232
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233 %!assert <*52431> (perms ({1}), {1})
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234 %!assert <*52431> (perms ({0.1, "foo"}), {"foo", 0.1; 0.1, "foo"})
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235 %!assert <*52431> (perms ({"foo", 0.1}), {0.1, "foo"; "foo", 0.1})
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236 %!assert <*52431> (perms ({"foo"; 0.1}), {0.1, "foo"; "foo", 0.1})
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237 %!assert <*52431> (perms ({0.1; "foo"}), {"foo", 0.1; 0.1, "foo"})
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238 %!assert <*52431> (perms ({"foo", "bar"}), {"bar", "foo"; "foo", "bar"})
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239 %!assert <*52431> (perms ({"bar", "foo"}), {"foo", "bar"; "bar", "foo"})
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240 %!
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241 %!assert <*52431> (perms (struct ()), struct ())
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242 %!assert <*52431> (perms (struct ("foo", {1, 2})),
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243 %! struct ("foo", {2, 1; 1, 2}))
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244 %!assert <*52431> (perms (struct ("foo", {1, 2}, "bar", {3, 4})),
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245 %! struct ("foo", {2, 1; 1, 2}, "bar", {4, 3; 3, 4}))
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246
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247 ## Also sort logical input with order dependent on the input order and
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248 ## not their values.
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249
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250 %!assert <*52431> (perms (logical ([1 0])), logical ([0 1;, 1 0]))
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251 %!assert <*52431> (perms (logical ([0 1])), logical ([1 0; 0 1]))
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252 %!assert <*52431> (perms (logical ([0 1 0])),
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253 %! logical ([0 1 0; 0 0 1; 1 0 0; 1 0 0; 0 0 1; 0 1 0]))
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254 %!assert <*52431> (perms (logical ([0 1 1])),
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255 %! logical ([1 1 0; 1 0 1; 1 1 0; 1 0 1; 0 1 1; 0 1 1]))
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256
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257 %!assert <*52432> (perms ([]), reshape ([], 1, 0))
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258 %!assert <*52432> (perms (single ([])), reshape (single ([]), 1, 0))
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259 %!assert <*52432> (perms (int8 ([])), reshape (int8 ([]), 1, 0))
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260 %!assert <*52432> (perms ({}), cell (1, 0))
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261
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262 %!test <*52432>
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263 %! s = struct ();
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264 %! s(1) = [];
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265 %! assert (perms (reshape (s, 0, 0)), reshape (s, 1, 0));
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266 %! assert (perms (reshape (s, 0, 1)), reshape (s, 1, 0));