1. One or more non-transitory computer-readable media, storing computer-executable instructions that, when executed by a processor, cause a computing device to: receive an input set of N numbers corresponding to a plurality of N financial transactions, the input set of N numbers comprising a set of A positive numbers and a set of B negative numbers; determine a positive subset size X and a negative subset size Y for a first reconciliation attempt, wherein the positive subset size X is less than the number of positive numbers A in the input set, and the negative subset size Y is less than the number of negative numbers B in the input set; and perform the first reconciliation attempt, the first reconciliation attempt comprising: determining a positive subset sum range by calculating a maximum positive subset sum X max and a minimum positive subset sum X min ; determining a negative subset sum range by calculating a maximum negative subset sum Y max and a minimum negative subset sum Y min ; identifying one or more overlapping portions between the positive subset sum range and the negative subset sum range; identifying at least one non-overlapping portion between the positive subset sum range and the negative subset sum range; and for the one or more overlapping portions between the positive subset sum range and the negative subset sum range, performing a plurality of subset sum comparisons, wherein in each subset sum comparison a sum of X numbers selected from the set of A positive numbers is compared to a sum of Y numbers selected from the set of B negative numbers, wherein for the at least one non-overlapping portion between the positive subset sum range and the negative subset sum range, a corresponding plurality of subset sum comparisons are not performed.