The algorithm is essentially performing a bottom-up mergesort. Instead of dividing the input array into smaller subarrays and merging them back, it is using a queue data structure to represent the subarrays and merging them one by one. Here's why the algorithm correctly sorts the input: At each iteration of the main loop, two queues are pulled from the front of the main queue. These two queues are then merged into a single queue and added to the rear of the main queue. The merging of the two queues is performed such that the elements are compared and added in sorted order to the resulting queue. This ensures that the elements in each queue are sorted, and that the resulting queue is also sorted. After each iteration, the number of queues in the main queue decreases by 1. This continues until there is only one queue left in the main queue, which represents the sorted input array. The contents of this queue are then moved back to an output array. The runtime complexity of this algorithm is SO(n \log n)S, where $n$ is the number of elements in the input array. This is because each iteration reduces the number of queues in the main queue by half, and the number of iterations is proportional to $\log n$. The merging of two queues takes SO(n)$ time in the worst case, but this happens only $\log n$ times, so the overall time complexity is SO(n Vlog n)$.