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This approach utilizes a hash (or map) to store computed results of the function, where the keys are generated based on the input parameters. By serializing the inputs into a unique key (e.g., using JSON), we can easily check whether a computation for the same inputs has been already done and retrieve the result from the cache if it has.
The time complexity of this solution is O(1) on average for each call due to hash map lookups. The space complexity is O(n) where n is the number of unique input sets to the function.
1def memoize(fn):
2 cache This Python solution uses a tuple of the arguments to uniquely identify each call to the function. The tuple is used as a key in a dictionary (hash map) to store results. If the inputs are repeated, the stored result is returned instead of calling the function again.
This approach is similar to hash-based memoization but emphasizes generating a custom key for complex input types that might not be directly hashable. This is particularly useful for composite objects or nested data structures where default serialization (as in JSON) is inadequate or inefficient.
The time complexity is O(1) on average for cache operations, assuming good hashCode implementations for objects. Space complexity is O(n) depending on unique input sets.
1import java.util.*;
2import java.util.stream.Collectors;
3
4public class Memoize {
5 public static <T, R> Function<T, R> memoizeFunction(Function<T, R> fn) {
6 Map<List<Object>, R> cache = new HashMap<>();
7 return args -> {
8 List<Object> key = Arrays.asList(args);
9 if (!cache.containsKey(key)) {
10 cache.put(key, fn.apply(args));
11 }
12 return cache.get(key);
13 };
14 }
15}The Java example uses a List to capture arguments, which makes it feasible to handle object arrays. This List is used as a key in a HashMap to store the function results, providing efficient lookup.