Solve four OA string/array/matrix/graph tasks

Coding Challenge: Meta Core Competencies

Solve the following four independent tasks. Implement your solutions in Python 3.

Task 1: String Character Balance

Given a string s containing only lowercase English letters, return True if every character that appears in the string appears the same number of times, and False otherwise. is_balanced(s: str) -> bool Example: is_balanced("aabbcc") returns True, is_balanced("abb") returns False.

Task 2: Linear Movement Simulation

You are given an array of integers positions representing people on a 1D line and a string directions ("L" or "R") of equal length. Every second, each person moves 1 unit in their given direction. If two people move into the same position at the same time, they collide and stop moving permanently. Return the final positions of all people. final_positions(positions: List[int], directions: str) -> List[int]

Task 3: Matrix Row-Column Swap

Given an n x n binary matrix grid, perform a "flip" operation: for every row i, if grid[i][0] is 1, invert all values in that row (0 becomes 1, 1 becomes 0). After that, for every column j, if the sum of elements in that column is less than n/2, invert all values in that column. Return the final matrix. transform_matrix(grid: List[List[int]]) -> List[List[int]]

Task 4: Undirected Path Reconstruction

Given an undirected graph represented by an adjacency list adj and two nodes start and end, return the path as a list of nodes. If multiple paths exist, return the one with the fewest number of edges. If no path exists, return an empty list. find_shortest_path(adj: Dict[int, List[int]], start: int, end: int) -> List[int]

Constraints

• For all tasks, input sizes n are between 1 and 500.
• Matrix elements are strictly 0 or 1.
• The graph is undirected and may contain cycles.