The 0/1 knapsack problem is a classic optimization problem where you must choose items with given weights and values to maximize the total value without exceeding a weight limit. A recursive solution to this problem considers two possibilities for each item: either include the item in the knapsack or skip it. The recursive approach builds the solution by making decisions for each item, calculating the maximum value obtainable for each case. In TypeScript, the recursive solution can be implemented with a base case that checks if all items have been considered or if the weight limit has been reached. For each item, you recursively compute the value of including it in the knapsack (if it fits within the weight limit) and the value of excluding it. The maximum value between these two options is returned as the solution. Although the recursive solution has exponential time complexity (O(2^n)), it forms the foundation for the more efficient dynamic programming solution. Understanding the recursive approach is essential for solving the knapsack problem and similar problems involving decision-making and optimization, such as resource allocation and project selection.