what is lexicographic ordering

### lexicographic ordering

lexicographic ordering, often referred to as dictionary or alphabetical order, is a method of ordering sequences (usually strings or lists) based on the order of their elements, similar to how words are arranged in a dictionary. in this order, sequences are compared element by element, and the first differing element determines which sequence is considered "less than" the other.

#### how lexicographic ordering works

1. **character by character comparison**: the sequences are compared character by character.
2. **length consideration**: if one sequence is a prefix of the other (e.g., "cat" and "catalog"), the shorter sequence is considered smaller.
3. **ascii values**: the comparison is typically based on the ascii (or unicode) values of the characters, meaning 'a' 'b', 'a' 'b', and so forth.

### example in python

let's illustrate lexicographic ordering with a python example. we'll compare a list of strings and sort them using python's built-in sorting capabilities.

### explanation of the code

1. **list of strings**: we start with a list called `words` containing several fruit names.
2. **sorting**: we use the `sorted()` function, which sorts the list in lexicographic order by default.
3. **output**: finally, we print the sorted list of words.

### output

when you run the above code, the output will be:

### lexicographic order in different contexts

- **numbers**: lexicographic order can also be applied to numbers, but they will be treated as strings. for example, "10" will come before "2" because the comparison starts with the first character ('1' '2').
- **lists**: lexicographic ordering can be applied to lists of elements as well. for example, comparing `[1, 2]` and `[1, 2, 3]`, the first one is considered smaller because it is a prefix of the second.

#### example with lists

### conclusion

lexicographic ordering is a fundamental concept in computer science and programming, widely used in string manipulation, sorti ...

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