Given n input vectors x1, x2, …, xn, generate a p*n matrix y whose rows contain all element-wise combinations of the vectors x1, x2, …, xn, where p = numel(x1)*numel(x2)*…* numel(xn). The rows of y are organized in an "increasing" ordering; see examples below.

• Example 1 (character array, n = 2): Input: x1 = 'ab'; x2 = 'cde'; Output:

    y = ['ac'
         'ad'
         'ae'
         'bc'
         'bd'
         'be'] 

• Example 2 (numeric array, n = 3): Input: x1 = [0 1], x2 = [0 1]; x3 = [0 1]; Output:

    y = [0 0 0
         0 0 1
         0 1 0
         0 1 1
         1 0 0
         1 0 1
         1 1 0
         1 1 1]

You may assume that all inputs are valid vectors whose lengths are at least 1.

Note: The Statistics and Machine Learning toolbox provides two useful functions for full factorial design, namely ff2n (for binary case) and fullfact (for general cases). However, they do not directly accomplish the task in Example 1. The purpose of this problem is to create a toolbox independent function to achieve our goal. Have fun!