To figure out a set of numbers from a set of data and sum to a specific number, different algorithms can be used, depending on the size of the problem and the nature of the data. Here are a few common methods:
Violence Law: For small-scale datasets, you can try all possible combinations of numbers to check if their sum equals a specific number. The time complexity of this approach is exponential and is generally not suitable for large-scale datasets.
Retrospective: Backtracking is an improved brute force search method that prunes during the search process, i.e., stops further searches when it finds that the current combination is unlikely to meet the conditions. This method is more efficient than the method of violence, but in the worst-case scenario it may still take exponential time.
Dynamic programming: For problems where the sum is a specific number, if it is an integer and the dataset is not very large, dynamic programming can be used to solve it. Especially for subset sum problems, dynamic programming algorithms can be used to determine if there is a subset whose elements add up to a specific number.
Hash table: For the problem of the sum of two numbers, a hash table can be used to store the numbers that have been traversed, so as to find the sum of two numbers for a specific number within the time complexity of o(n).
Sort with double pointer: If the problem is to find out and sum two numbers for a specific number, you can sort the array first and then use the two-pointer technique. One pointer moves backwards from the beginning of the array, and the other moves forward from the end of the array until a pair or two pointers meet a pair of numbers for a specific number.
Divide and conquer: For more complex problems, you can try divide and conquer, divide the data set into smaller parts, solve them separately, and then merge the results.
Approximation algorithm: When the dataset is very large or the exact solution to the problem is not necessary, an approximation algorithm or heuristic algorithm can be used to find an approximate solution.
Problem-specific optimization algorithms: There may be a specific optimization algorithm for some specific types of problems. For example, for a sequence of consecutive positive integers with a sum of a specific number, you can use the sliding window technique.
In practice, the choice of which method to choose depends on the size of the data, the type of problem, and the requirements for the efficiency of the algorithm. For most practical problems, there is often a trade-off between time complexity and space complexity.