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## Python: Generating All Suffixes of a String In computer science and text processing, a **suffix** of a string is a substring that starts at any given position within the string and extends to the very end. Generating all suffixes of a string is a fundamental operation used in various algorithms, such as building suffix trees, suffix arrays, and performing pattern matching. In Python, the most efficient and idiomatic way to extract suffixes is by using **string slicing**. This tutorial demonstrates how to generate all suffixes of a string using clean, readable Python code. --- ### Understanding String Slicing for Suffixes Python's slicing syntax is formatted as `string[start:stop:step]`. To get a suffix starting at index `i` and going to the end of the string, we omit the `stop` parameter: ```python string[i:] ``` By iterating through every index `i` from `0` to the length of the string, we can systematically extract every possible suffix. --- ### Code Example: Generating All Suffixes Below is a complete, reusable Python function that takes a string as input and returns a list of all its suffixes. ```python def get_all_suffixes(s): """ Generates and returns a list of all suffixes of the input string. """ suffixes = [] # Iterate through each character index in the string for i in range(len(s)): # Slice from index 'i' to the end of the string and append to the list suffixes.append(s[i:]) return suffixes # Example usage sample_string = "hello" all_suffixes = get_all_suffixes(sample_string) print(f"Original String: '{sample_string}'") print("All Suffixes:", all_suffixes) ``` #### Output: ```python ['hello', 'ello', 'llo', 'lo', 'o'] ``` --- ### Code Explanation 1. **`def get_all_suffixes(s):`** Defines a function named `get_all_suffixes` that accepts a single string parameter `s`. 2. **`suffixes = []`** Initializes an empty list to store the generated suffixes. 3. **`for i in range(len(s)):`** Loops through the indices of the string from `0` up to `len(s) - 1`. 4. **`suffixes.append(s[i:])`** Uses the slice `s[i:]` to extract the substring starting at index `i` to the end of the string, then appends it to our list. 5. **`return suffixes`** Returns the final list containing all the extracted suffixes. --- ### Advanced Variations #### 1. List Comprehension (Pythonic One-Liner) For a more concise and Pythonic approach, you can achieve the exact same result using a list comprehension: ```python s = "hello" suffixes = [s[i:] for i in range(len(s))] print(suffixes) # Output: ['hello', 'ello', 'llo', 'lo', 'o'] ``` #### 2. Including the Empty Suffix In formal language theory, the empty string (`""`) is often considered a trivial suffix of any string. If your algorithm requires the empty suffix, you can extend the range by `+ 1`: ```python s = "hello" suffixes_with_empty = [s[i:] for i in range(len(s) + 1)] print(suffixes_with_empty) # Output: ['hello', 'ello', 'llo', 'lo', 'o', ''] ``` --- ### Complexity Analysis * **Time Complexity:** $\mathcal{O}(N^2)$, where $N$ is the length of the string. This is because there are $N$ suffixes, and copying a substring of length $k$ takes $\mathcal{O}(k)$ time. * **Space Complexity:** $\mathcal{O}(N^2)$ to store the resulting list of suffixes in memory.