How does the choice of algorithmic paradigm (e.g., divide and conquer, greedy, dynamic programming) influence the time complexity of solving a given problem?

The algorithmic paradigm chosen can drastically affect time complexity. Divide and conquer (e.g., merge sort) often results in logarithmic depth recursion and O(n log n) complexity. Greedy algorithms (e.g., Kruskal’s MST) typically offer faster, often linear or O(n log n), solutions for optimization problems where local optimality ensures global optimality. Dynamic programming (e.g., the knapsack problem) transforms exponential time complexity to polynomial time, O(nW), by storing and reusing subproblem solutions, demonstrating the paradigm’s impact on efficiency.