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  2. Multiple subset sum - Wikipedia

    en.wikipedia.org/wiki/Multiple_subset_sum

    The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.

  3. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    Let A be the sum of the negative values and B the sum of the positive values; the number of different possible sums is at most B-A, so the total runtime is in (()). For example, if all input values are positive and bounded by some constant C , then B is at most N C , so the time required is O ( N 2 C ) {\displaystyle O(N^{2}C)} .

  4. Maximum subarray problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_subarray_problem

    In the th step, it computes the subarray with the largest sum ending at ; this sum is maintained in variable current_sum. [ note 3 ] Moreover, it computes the subarray with the largest sum anywhere in A [ 1 … j ] {\displaystyle A[1\ldots j]} , maintained in variable best_sum , [ note 4 ] and easily obtained as the maximum of all values of ...

  5. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    Summation by parts is frequently used to prove Abel's theorem and Dirichlet's test. One can also use this technique to prove Abel's test: If is a convergent series, and a bounded monotone sequence, then = = converges. Proof of Abel's test.

  6. Kahan summation algorithm - Wikipedia

    en.wikipedia.org/wiki/Kahan_summation_algorithm

    The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...

  7. 3-partition problem - Wikipedia

    en.wikipedia.org/wiki/3-partition_problem

    For each triplet t = {w i,x j,y k} in E, the set A contains an element u t = 10r 4-kr 3-jr 2-ir. For each triplet t = {w i,x j,y k} in E, the set B contains w it, C contains x jt, and D contains y kt. So for each of w i, x j, y k, there may be many corresponding elements in B, C, D - one for each triplet in which they appear. We consider one of ...

  8. Partition problem - Wikipedia

    en.wikipedia.org/wiki/Partition_problem

    Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...

  9. Longest common subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_common_subsequence

    That is, for source code where the average line is 60 or more characters long, the hash or checksum for that line might be only 8 to 40 characters long. Additionally, the randomized nature of hashes and checksums would guarantee that comparisons would short-circuit faster, as lines of source code will rarely be changed at the beginning.