找到可能的組合與特定條件

Question

我想計算1:16與10個子集的所有可能的組合。

combos = combntns(1:16,10) 

但條件是，返回的連擊應具有以下矢量的至少1個構件：

V1=1:4,V2=5:8,V3=9:12,V4=13:16, 

任何溶液？

Answer 1

這一問題大小，你都不能生成所有組合，然後選擇那些符合要求：

n = 16; %// number of elements to choose from 
c = 10; %// combination size 
s = 4; %// size of each group (size of V1, V2 etc) 

combos = nchoosek(1:n, c); 
ind = all(any(any(bsxfun(@eq, combos, reshape(1:n, 1,1,s,[])),2),3),4); 
combos = combos(ind,:); 

這可以概括爲通用元素和任意條件載體，假設所有向量是相同的大小：

elements = 1:16;     %// elements to choose from 
c = 10;        %// combination size 
vectors = {1:4, 5:8, 9:12, 13:16}; %// cell array of vectors 

s = numel(vectors{1}); 
combos = nchoosek(elements, c); 
ind = all(any(any(bsxfun(@eq, combos, reshape(cat(1,vectors{:}).', 1,1,s,[])),2),3),4); %' 
combos = combos(ind,:);