To handle dynamic programming (DP) problems, break the problem into overlapping subproblems and define a recurrence relation. Store solutions to subproblems in a table to avoid redundant calculations.

Dynamic programming (DP) is a powerful technique used to solve optimization problems by breaking them down into smaller, overlapping subproblems. The key to solving DP problems is recognizing that you can use previously computed solutions to solve larger instances of the same problem. To start, you need to identify the base cases and formulate a recurrence relation that describes how the solution to a larger problem can be built from solutions to smaller subproblems. Once you have the recurrence relation, store the results of these subproblems in a table (usually an array) to avoid recalculating them. This technique, known as memoization, significantly reduces the time complexity of your solution. For example, in the classic Fibonacci problem, you can store previously calculated Fibonacci numbers to avoid recalculating them repeatedly, reducing the time complexity from exponential (O(2^n)) to linear (O(n)). DP problems often require careful thought to determine the state variables and transitions between states. In more complex problems, you may need a multi-dimensional table to store intermediate results, as seen in problems like the knapsack problem or matrix chain multiplication. Another common approach in DP is the bottom-up method, where you start with the smallest subproblems and build up to the solution of the main problem iteratively, rather than using recursion. Practice with DP problems will help you develop an intuition for recognizing when this technique is applicable and how to implement it efficiently.