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Related problems include approximate sorting (sorting a sequence to within a certain amount of the correct order), partial sorting (sorting only the k smallest elements of a list, or finding the k smallest elements, but unordered) and selection (computing the kth smallest element). These can be solved inefficiently by a total sort, but more ...
Bowley, Roger (5 December 2011). "6174 is Kaprekar's Constant". Numberphile. University of Nottingham: Brady Haran. Sample (Perl) code to walk any four-digit number to Kaprekar's Constant; Sample (Python) code to walk any four-digit number to Kaprekar's Constant; Sample (C) code to walk the first 10000 numbers and their steps to Kaprekar's Constant
On each: If the two smallest remaining small items do not fit, skip this bin. Otherwise, place the smallest remaining small item and the largest remaining small item that fits. Proceed forward through all bins. If the smallest remaining item of any size class does not fit, skip this bin. Otherwise, place the largest item that fits and stay on ...
Some numbers map to themselves; these are the fixed points of the Kaprekar mapping, [5] and are called Kaprekar's constants. Zero is a Kaprekar's constant for all bases , and so is called a trivial Kaprekar's constant. All other Kaprekar's constants are nontrivial Kaprekar's constants. For example, in base 10, starting with 3524,
Python's standard library includes heapq.nsmallest and heapq.nlargest functions for returning the smallest or largest elements from a collection, in sorted order. The implementation maintains a binary heap , limited to holding k {\displaystyle k} elements, and initialized to the first k {\displaystyle k} elements in the collection.
For example, the items are books, the sort key is the title, subject or author, and the order is alphabetical. A new sort key can be created from two or more sort keys by lexicographical order. The first is then called the primary sort key, the second the secondary sort key, etc.
For example, bubble sort and timsort are both algorithms to sort a list of items from smallest to largest. Bubble sort organizes the list in time proportional to the number of elements squared ( O ( n 2 ) {\textstyle O(n^{2})} , see Big O notation ), but only requires a small amount of extra memory which is constant with respect to the length ...
Example: The following table shows the steps for sorting the sequence {3, 7, 4, 9, 5, 2, 6, 1}. In each step, the key under consideration is underlined. The key that was moved (or left in place because it was the biggest yet considered) in the previous step is marked with an asterisk.