diff --git a/backtracking/word_break.py b/backtracking/word_break.py new file mode 100644 index 000000000000..1f2ab073f499 --- /dev/null +++ b/backtracking/word_break.py @@ -0,0 +1,71 @@ +""" +Word Break Problem is a well-known problem in computer science. +Given a string and a dictionary of words, the task is to determine if +the string can be segmented into a sequence of one or more dictionary words. + +Wikipedia: https://en.wikipedia.org/wiki/Word_break_problem +""" + + +def backtrack(input_string: str, word_dict: set[str], start: int) -> bool: + """ + Helper function that uses backtracking to determine if a valid + word segmentation is possible starting from index 'start'. + + Parameters: + input_string (str): The input string to be segmented. + word_dict (set[str]): A set of valid dictionary words. + start (int): The starting index of the substring to be checked. + + Returns: + bool: True if a valid segmentation is possible, otherwise False. + + Example: + >>> backtrack("leetcode", {"leet", "code"}, 0) + True + + >>> backtrack("applepenapple", {"apple", "pen"}, 0) + True + + >>> backtrack("catsandog", {"cats", "dog", "sand", "and", "cat"}, 0) + False + """ + + # Base case: if the starting index has reached the end of the string + if start == len(input_string): + return True + + # Try every possible substring from 'start' to 'end' + for end in range(start + 1, len(input_string) + 1): + if input_string[start:end] in word_dict and backtrack( + input_string, word_dict, end + ): + return True + + return False + + +def word_break(input_string: str, word_dict: set[str]) -> bool: + """ + Determines if the input string can be segmented into a sequence of + valid dictionary words using backtracking. + + Parameters: + input_string (str): The input string to segment. + word_dict (set[str]): The set of valid words. + + Returns: + bool: True if the string can be segmented into valid words, otherwise False. + + Example: + >>> word_break("leetcode", {"leet", "code"}) + True + + >>> word_break("applepenapple", {"apple", "pen"}) + True + + >>> word_break("catsandog", {"cats", "dog", "sand", "and", "cat"}) + False + """ + + return backtrack(input_string, word_dict, 0) diff --git a/data_structures/linked_list/has_loop.py b/data_structures/linked_list/has_loop.py index bc06ffe150e8..f49e01579adc 100644 --- a/data_structures/linked_list/has_loop.py +++ b/data_structures/linked_list/has_loop.py @@ -14,11 +14,11 @@ def __init__(self, data: Any) -> None: def __iter__(self): node = self - visited = [] + visited = set() while node: if node in visited: raise ContainsLoopError - visited.append(node) + visited.add(node) yield node.data node = node.next_node diff --git a/data_structures/stacks/next_greater_element.py b/data_structures/stacks/next_greater_element.py index 7d76d1f47dfa..216850b4b894 100644 --- a/data_structures/stacks/next_greater_element.py +++ b/data_structures/stacks/next_greater_element.py @@ -6,9 +6,20 @@ def next_greatest_element_slow(arr: list[float]) -> list[float]: """ - Get the Next Greatest Element (NGE) for all elements in a list. - Maximum element present after the current one which is also greater than the - current one. + Get the Next Greatest Element (NGE) for each element in the array + by checking all subsequent elements to find the next greater one. + + This is a brute-force implementation, and it has a time complexity + of O(n^2), where n is the size of the array. + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element_slow(arr) == expect True """ @@ -28,9 +39,21 @@ def next_greatest_element_slow(arr: list[float]) -> list[float]: def next_greatest_element_fast(arr: list[float]) -> list[float]: """ - Like next_greatest_element_slow() but changes the loops to use - enumerate() instead of range(len()) for the outer loop and - for in a slice of arr for the inner loop. + Find the Next Greatest Element (NGE) for each element in the array + using a more readable approach. This implementation utilizes + enumerate() for the outer loop and slicing for the inner loop. + + While this improves readability over next_greatest_element_slow(), + it still has a time complexity of O(n^2). + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element_fast(arr) == expect True """ @@ -47,14 +70,23 @@ def next_greatest_element_fast(arr: list[float]) -> list[float]: def next_greatest_element(arr: list[float]) -> list[float]: """ - Get the Next Greatest Element (NGE) for all elements in a list. - Maximum element present after the current one which is also greater than the - current one. - - A naive way to solve this is to take two loops and check for the next bigger - number but that will make the time complexity as O(n^2). The better way to solve - this would be to use a stack to keep track of maximum number giving a linear time - solution. + Efficient solution to find the Next Greatest Element (NGE) for all elements + using a stack. The time complexity is reduced to O(n), making it suitable + for larger arrays. + + The stack keeps track of elements for which the next greater element hasn't + been found yet. By iterating through the array in reverse (from the last + element to the first), the stack is used to efficiently determine the next + greatest element for each element. + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element(arr) == expect True """ diff --git a/dynamic_programming/floyd_warshall.py b/dynamic_programming/floyd_warshall.py index 2331f3e65483..b92c6667fb5c 100644 --- a/dynamic_programming/floyd_warshall.py +++ b/dynamic_programming/floyd_warshall.py @@ -12,19 +12,58 @@ def __init__(self, n=0): # a graph with Node 0,1,...,N-1 ] # dp[i][j] stores minimum distance from i to j def add_edge(self, u, v, w): + """ + Adds a directed edge from node u + to node v with weight w. + + >>> g = Graph(3) + >>> g.add_edge(0, 1, 5) + >>> g.dp[0][1] + 5 + """ self.dp[u][v] = w def floyd_warshall(self): + """ + Computes the shortest paths between all pairs of + nodes using the Floyd-Warshall algorithm. + + >>> g = Graph(3) + >>> g.add_edge(0, 1, 1) + >>> g.add_edge(1, 2, 2) + >>> g.floyd_warshall() + >>> g.show_min(0, 2) + 3 + >>> g.show_min(2, 0) + inf + """ for k in range(self.n): for i in range(self.n): for j in range(self.n): self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j]) def show_min(self, u, v): + """ + Returns the minimum distance from node u to node v. + + >>> g = Graph(3) + >>> g.add_edge(0, 1, 3) + >>> g.add_edge(1, 2, 4) + >>> g.floyd_warshall() + >>> g.show_min(0, 2) + 7 + >>> g.show_min(1, 0) + inf + """ return self.dp[u][v] if __name__ == "__main__": + import doctest + + doctest.testmod() + + # Example usage graph = Graph(5) graph.add_edge(0, 2, 9) graph.add_edge(0, 4, 10) @@ -38,5 +77,9 @@ def show_min(self, u, v): graph.add_edge(4, 2, 4) graph.add_edge(4, 3, 9) graph.floyd_warshall() - graph.show_min(1, 4) - graph.show_min(0, 3) + print( + graph.show_min(1, 4) + ) # Should output the minimum distance from node 1 to node 4 + print( + graph.show_min(0, 3) + ) # Should output the minimum distance from node 0 to node 3