<think>
Okay, I need to implement the fork_paths function. Let's see the problem statement again. The function takes a pattern string and expands it into all possible paths by replacing each fork segment with its options. Each fork is a segment enclosed in curly braces, with comma-separated options. The key is to process each segment, determine if it's a fork or a literal, and then generate all combinations.

First, I need to parse the pattern into segments. Each segment is either a literal or a fork. So, I need to split the pattern into parts separated by slashes. But wait, the forks are in the form of {options}, so I need to identify which parts are forks.

But how to split the pattern into segments? For example, a pattern like "s/{i,j}/{1,2}" would split into ["s/", "{i,j}", "{1,2}"]. Wait, no. Wait, the original pattern is "s/{i,j}/{1,2}". Splitting by '/' gives ["s", "{i,j}", "{1,2}"]. Oh right, because each segment is between slashes. So the first segment is "s", then the next is "{i,j}", then "{1,2}".

So the first step is to split the input pattern into segments. Each segment is either a literal or a fork. But how to detect if a segment is a fork? A fork is a segment that starts with '{' and ends with '}', and contains comma-separated options. Also, the problem says that any occurrence of '{' or '}' inside a literal segment or an option is invalid. So, during parsing, I need to check that any '{' or '}' in a segment is part of a fork, not part of a literal.

So the first step is to split the pattern into segments. Then, for each segment, check if it's a fork. If it's a fork, extract the options. If not, it's a literal.

But how to split the pattern into segments? The pattern is a string, and each segment is separated by '/'. But the segments can contain slashes? No, because the segments are the parts between the slashes. So, for example, "a/b/c" is split into ["a", "b", "c"], but if a segment is like "a/b", then that's part of a fork? Wait, no. Because the fork is a segment that is enclosed in curly braces. So, the segments are split by '/', but the segments themselves can contain other slashes? No, because the fork is a segment that is enclosed in curly braces. So, the segments are split by '/', and each segment is either a literal (without any { or }) or a fork (with { and }).

So, the first step is to split the pattern into segments. Then, for each segment, check if it's a fork. If it's a fork, then extract the options. If not, it's a literal.

But how to split the pattern into segments? The split on '/' would split the pattern into parts. However, if a segment is empty, that's invalid. Also, the problem says that the pattern must be a non-empty string, and each segment can't be empty. So, during parsing, if any segment is empty, that's invalid.

So, the first step is to split the pattern into segments. Then, for each segment, check if it's a fork. If it's a fork, then extract the options. If not, it's a literal.

But how to check if a segment is a fork? A fork is a segment that starts with '{' and ends with '}', and contains comma-separated options. Also, the segment must not contain any other '{