Merge sort is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations of merge sort are stable, which means that the relative order of equal elements is the same between the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.