What is a sequence run?

Question

If i have a sequence of bits. Say it is 010001011101. What is a sequence run?

I am trying to make a script that will check Golomb and this has to do with one of the three tests.

Answer 1

A run of a sequence $(a_1, a_2, \ldots, a_n)$ is a maximal subsequence consisting of a single character repeated. That is, a subsequence $(a_i, a_{i+1}, \ldots, a_j)$ (with $i \leqslant j$) is a run if and only if the following three conditions are satisfied:

• (Consists of a single character.) There is a character $z \in \{0,1\}$ such that $z = a_i = a_{i+1} = \cdots = a_j$.
• (The subsequence cannot be extended to the left.) Either $i = 1$ or $a_{i-1} \neq z$.
• (The subsequence cannot be extended to the right.) Either $j = n$ or $a_{j+1} \neq z$.

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For example, the sequence $$\huge \color{Magenta}{0} \color{cyan}{1} \color{Red}{000} \color{Black}{1} \color{DarkOrange}{0} \color{DarkGreen}{111} \color{maroon}{0} \color{Blue}{1}$$ has eight runs as the color coding shows.