Optimize brute-force solutions by pruning unnecessary paths, using memoization, or switching to more efficient algorithms like dynamic programming or greedy methods.

Brute-force solutions often involve checking all possible outcomes, which can be slow and inefficient for large input sizes. To optimize brute-force solutions, the first step is to look for ways to prune unnecessary paths early. For example, in a backtracking problem, if a partial solution is invalid, you can stop exploring further down that path. This is called pruning the search space. Another effective optimization technique is memoization, where you store the results of previously computed subproblems to avoid redundant calculations. For example, in problems with overlapping subproblems like Fibonacci or dynamic programming problems, storing intermediate results can dramatically speed up the computation. In some cases, switching to more efficient algorithms is necessary. Brute-force is a good starting point for simple problems, but for complex problems, techniques like dynamic programming, greedy algorithms, or divide-and-conquer approaches can significantly reduce the time complexity. Analyzing the problem's structure to find patterns, symmetries, or opportunities for optimization is key to improving brute-force solutions. As you gain more experience, you'll start recognizing these patterns and instinctively know when and how to optimize your approach.