在查看您的代码之前，我解决了编写自己的实现的问题。我的第一次尝试与您已经拥有的非常相似:)
%# some parameters
NUM_ITER = 100000; %# number of simulations to run
DRAW_SZ = 12; %# number of cards we are dealing
SET_SZ = 3; %# number of cards in a set
FEAT_NUM = 4; %# number of features (symbol,color,number,shading)
FEAT_SZ = 3; %# number of values per feature (eg: red/purple/green, ...)
%# cards features
features = {
'oval' 'squiggle' 'diamond' ; %# symbol
'red' 'purple' 'green' ; %# color
'one' 'two' 'three' ; %# number
'solid' 'striped' 'open' %# shading
};
fIdx = arrayfun(@(k) grp2idx(features(k,:)), 1:FEAT_NUM, 'UniformOutput',0);
%# list of all cards. Each card: [symbol,color,number,shading]
[W X Y Z] = ndgrid(fIdx{:});
cards = [W(:) X(:) Y(:) Z(:)];
%# all possible sets: choose 3 from 12
setsInd = nchoosek(1:DRAW_SZ,SET_SZ);
%# count number of valid sets in random draws of 12 cards
counterValidSet = 0;
for i=1:NUM_ITER
%# pick 12 cards
ord = randperm( size(cards,1) );
cardsDrawn = cards(ord(1:DRAW_SZ),:);
%# check for valid sets: features are all the same or all different
for s=1:size(setsInd,1)
%# set of 3 cards
set = cardsDrawn(setsInd(s,:),:);
%# check if set is valid
count = arrayfun(@(k) numel(unique(set(:,k))), 1:FEAT_NUM);
isValid = (count==1|count==3);
%# increment counter
if isValid
counterValidSet = counterValidSet + 1;
break %# break early if found valid set among candidates
end
end
end
%# ratio of found-to-notfound
fprintf('Size=%d, Set=%d, NoSet=%d, Set:NoSet=%g\n', ...
DRAW_SZ, counterValidSet, (NUM_ITER-counterValidSet), ...
counterValidSet/(NUM_ITER-counterValidSet))
在使用 Profiler 发现热点之后，可以通过尽可能早地退出循环来进行一些改进。主要瓶颈是对 UNIQUE 函数的调用。上面我们检查有效集合的那两行可以重写为：
%# check if set is valid
isValid = true;
for k=1:FEAT_NUM
count = numel(unique(set(:,k)));
if count~=1 && count~=3
isValid = false;
break %# break early if one of the features doesnt meet conditions
end
end
不幸的是，对于较大的模拟，模拟仍然很慢。因此，我的下一个解决方案是矢量化版本，对于每次迭代，我们从 12 张抽出的牌中构建所有可能的 3 张牌组的单个矩阵。对于所有这些候选集，我们使用逻辑向量来指示存在什么特征，从而避免调用 UNIQUE/NUMEL（我们希望集合的每张卡片上的特征都相同或不同）。
我承认现在的代码可读性降低并且难以理解（因此我发布了两个版本以进行比较）。原因是我试图尽可能地优化代码，以便每个迭代循环都是完全矢量化的。这是最终代码：
%# some parameters
NUM_ITER = 100000; %# number of simulations to run
DRAW_SZ = 12; %# number of cards we are dealing
SET_SZ = 3; %# number of cards in a set
FEAT_NUM = 4; %# number of features (symbol,color,number,shading)
FEAT_SZ = 3; %# number of values per feature (eg: red/purple/green, ...)
%# cards features
features = {
'oval' 'squiggle' 'diamond' ; %# symbol
'red' 'purple' 'green' ; %# color
'one' 'two' 'three' ; %# number
'solid' 'striped' 'open' %# shading
};
fIdx = arrayfun(@(k) grp2idx(features(k,:)), 1:FEAT_NUM, 'UniformOutput',0);
%# list of all cards. Each card: [symbol,color,number,shading]
[W X Y Z] = ndgrid(fIdx{:});
cards = [W(:) X(:) Y(:) Z(:)];
%# all possible sets: choose 3 from 12
setsInd = nchoosek(1:DRAW_SZ,SET_SZ);
%# optimizations: some calculations taken out of the loop
ss = setsInd(:);
set_sz2 = numel(ss)*FEAT_NUM/SET_SZ;
col = repmat(1:set_sz2,SET_SZ,1);
col = FEAT_SZ.*(col(:)-1);
M = false(FEAT_SZ,set_sz2);
%# progress indication
%#hWait = waitbar(0./NUM_ITER, 'Simulation...');
%# count number of valid sets in random draws of 12 cards
counterValidSet = 0;
for i=1:NUM_ITER
%# update progress
%#waitbar(i./NUM_ITER, hWait);
%# pick 12 cards
ord = randperm( size(cards,1) );
cardsDrawn = cards(ord(1:DRAW_SZ),:);
%# put all possible sets of 3 cards next to each other
set = reshape(cardsDrawn(ss,:)',[],SET_SZ)';
set = set(:);
%# check for valid sets: features are all the same or all different
M(:) = false; %# if using PARFOR, it will complain about this
M(set+col) = true;
isValid = all(reshape(sum(M)~=2,FEAT_NUM,[]));
%# increment counter if there is at least one valid set in all candidates
if any(isValid)
counterValidSet = counterValidSet + 1;
end
end
%# ratio of found-to-notfound
fprintf('Size=%d, Set=%d, NoSet=%d, Set:NoSet=%g\n', ...
DRAW_SZ, counterValidSet, (NUM_ITER-counterValidSet), ...
counterValidSet/(NUM_ITER-counterValidSet))
%# close progress bar
%#close(hWait)
如果您有并行处理工具箱，您可以轻松地将普通 FOR 循环替换为并行 PARFOR（您可能希望再次将矩阵 M 的初始化移动到循环内：将 M(:) = false; 替换为 @987654327 @)
以下是 50000 次模拟的一些示例输出（PARFOR 与 2 个本地实例池一起使用）：
» tic, SET_game2, toc
Size=12, Set=48376, NoSet=1624, Set:NoSet=29.7882
Elapsed time is 5.653933 seconds.
» tic, SET_game2, toc
Size=15, Set=49981, NoSet=19, Set:NoSet=2630.58
Elapsed time is 9.414917 seconds.
一百万次迭代（PARFOR 为 12，no-PARFOR 为 15）：
» tic, SET_game2, toc
Size=12, Set=967516, NoSet=32484, Set:NoSet=29.7844
Elapsed time is 110.719903 seconds.
» tic, SET_game2, toc
Size=15, Set=999630, NoSet=370, Set:NoSet=2701.7
Elapsed time is 372.110412 seconds.
优势比与Peter Norvig报告的结果一致。