Algorithm Design Questions Medium
Memoization is a technique used in dynamic programming algorithms to optimize the computation of a function by storing the results of expensive function calls and reusing them when the same inputs occur again. It involves creating a lookup table or cache to store the computed values of the function for different inputs.
In dynamic programming, problems are often solved by breaking them down into smaller subproblems, and the solutions to these subproblems are combined to solve the larger problem. However, without memoization, the same subproblems may be solved multiple times, leading to redundant computations and inefficiency.
By using memoization, the results of the subproblems are stored in the cache, and before solving a subproblem, the algorithm checks if the solution is already available in the cache. If it is, the stored result is directly returned, avoiding the need for recomputation. If the solution is not in the cache, the algorithm computes it and stores it in the cache for future use.
Memoization significantly improves the efficiency of dynamic programming algorithms by eliminating redundant computations. It reduces the time complexity of the algorithm by effectively trading off space complexity. The cache size grows with the number of unique inputs encountered during the algorithm's execution.
Overall, memoization is a powerful technique that enhances the performance of dynamic programming algorithms by storing and reusing computed results, thereby avoiding unnecessary computations and improving efficiency.