在C ++中找到具有相等总和的两个集合的快速方法是什么？

Question

I need an efficient way to look through a list of sets of ints to see any two sets have the same sum. Specifically, in this case, I am generating the powerset of a list of ints that are given as an argument. From that powerset, I need to find a pair of subsets that sum to the same value.

Currently, I'm trying to use a dynamic programming approach (explanation below):

typedef std::vector<int> intvec;
typedef std::vector<std::vector<int> > intvecvec;
typedef std::multimap<int,int> intmap;

/* Functions previously shown here that were removed:
 * intvecvec search_for_sum(intvec num_list)
 * and
 * int sum_exists(std::vector<intvec> pset, int index, intmap &sums)
 */

/* This function was previously just called powerset(), and wasn't
 * shown because the problem wasn't happening here. After refactoring,
 * I removed the functions that were shown here previously and simply
 * iteratively checked for sum matches while generating the powerset
 */
intvecvec powerset_search(intvec num_list)
{
    intvecvec result;
    std::multimap<int, intvec> power_set;
    for (int c = 0; c < pow(2, num_list.size()); c++) {
        intvec temp;
        for (int i = 0; i < num_list.size(); i++) {
            if (c & (1 << i)) {
                temp.push_back(num_list.at(i));
            }
        }
        int sum = std::accumulate( temp.begin(), temp.end(), 0 );
        std::multimap<int, intvec>::iterator it = power_set.find(sum);
        if (it == power_set.end()) {
            power_set.insert(std::make_pair(sum, temp));
        } else {
            result.push_back(it->second);
            result.push_back(temp);
            break;
        }
    }
    return result;
}

search_for_sum() creates the powerset of the given list of ints , along with a multimap called sums. For every element in the powerset, its sum is calculated. If that sum has not yet been encountered, the sum and the current index is inserted into sums . Otherwise, the current set and the one that had already been inserted into sums is returned.

This works. The problem is that for large sizes of num_list , this can take a few minutes to come back with a solution if there is one. This is significantly slower than the brute force method of just doing a double for -loop and calculating sums each time to find a match. Is there a better way for me to do this?

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EDIT: So I was able to solve this by moving my sum-checking step up to when the powerset is actually being generated, iteratively checking all previously entered sums and returning if a match was found. But, as requested in the comments, I have also redone the problem description to (hopefully) remove the vagueness that was there initially.

Answer 1

通过将总和检查步骤移至实际生成幂集的过程，可以迭代检查所有先前输入的总和并返回是否找到匹配项，从而解决了这一问题。