Consequently, we can make n − 1 nested calls before we reach a list of size 1. The typical examples for introducing divide and conquer are binary search and merge sort because they are relatively simple examples of how divide and conquer is superior (in terms of runtime complexity) to naive iterative implementations. comparisons (and also operations); these are in-place, requiring only additional , x Then the resulting parts of the partition have sizes i and n − i − 1, and i is uniform random from 0 to n − 1. of C is i n A selection algorithm chooses the kth smallest of a list of numbers; this is an easier problem in general than sorting. In the case where all elements are equal, Hoare partition scheme needlessly swaps elements, but the partitioning itself is best case, as noted in the Hoare partition section above. For variant quicksorts involving extra memory due to representations using pointers (e.g. Among these, merge sort is … Similarly, decrease and conquer only requires reducing the problem to a single smaller problem, such as the classic Tower of Hanoi puzzle, which reduces moving a tower of height n to moving a tower of height n − 1. Fix i and j