Memoization Methodology for backtracking
1. Start with a backtracking algorithm
2. Look up the problem in a table; if there's a valid entry for it, return that value
3. Otherwise, compute the problem recursively, and then store the result in the table before returning the value
Consider the solution presented in the backtracking chapter for the Longest Common Subsequence problem. In the execution of that algorithm, many common subproblems were computed repeatedly. As an optimization, we can compute these subproblems once and then store the result to read back later. A recursive memoization algorithm can be turned "bottom-up" into an iterative algorithm that fills in a table of solutions to subproblems. Some of the subproblems solved might not be needed by the end result (and that is where dynamic programming differs from memoization), but dynamic programming can be very efficient because the iterative version can better use the cache and have less call overhead. Asymptotically, dynamic programming and memoization have the same complexity.
1. Start with a backtracking algorithm
2. Look up the problem in a table; if there's a valid entry for it, return that value
3. Otherwise, compute the problem recursively, and then store the result in the table before returning the value
Consider the solution presented in the backtracking chapter for the Longest Common Subsequence problem. In the execution of that algorithm, many common subproblems were computed repeatedly. As an optimization, we can compute these subproblems once and then store the result to read back later. A recursive memoization algorithm can be turned "bottom-up" into an iterative algorithm that fills in a table of solutions to subproblems. Some of the subproblems solved might not be needed by the end result (and that is where dynamic programming differs from memoization), but dynamic programming can be very efficient because the iterative version can better use the cache and have less call overhead. Asymptotically, dynamic programming and memoization have the same complexity.
