
Sorting Algorithm

This is a sorting algorithm.   It may be applied to a set of data in order to sort it.    
For comparing various sorts, see compare sorts.  
For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort


Use the quickselect algorithm on the vector

 [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]
To show the first, second, third, ... up to the tenth largest member of the vector, in order, here on this page.

 Note: Quicksort has a separate task. 


// this just helps make partition read better
function swap(items, firstIndex, secondIndex) {
  var temp = items[firstIndex];
  items[firstIndex] = items[secondIndex];
  items[secondIndex] = temp;
};
 
// many algorithms on this page violate
// the constraint that partition operates in place
function partition(array, from, to) {
  // https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/random
  var pivotIndex = getRandomInt(from, to),
      pivot = array[pivotIndex];
  swap(array, pivotIndex, to);
  pivotIndex = from;
 
  for(var i = from; i <= to; i++) {
    if(array[i] < pivot) {
      swap(array, pivotIndex, i);
      pivotIndex++;
    }
  };
  swap(array, pivotIndex, to);
 
  return pivotIndex;
};
 
// later versions of JS have TCO so this is safe
function quickselectRecursive(array, from, to, statistic) {
  if(array.length === 0 || statistic > array.length - 1) {
    return undefined;
  };
 
  var pivotIndex = partition(array, from, to);
  if(pivotIndex === statistic) {
    return array[pivotIndex];
  } else if(pivotIndex < statistic) {
    return quickselectRecursive(array, pivotIndex, to, statistic);
  } else if(pivotIndex > statistic) {
    return quickselectRecursive(array, from, pivotIndex, statistic);
  }
};
 
function quickselectIterative(array, k) {
  if(array.length === 0 || k > array.length - 1) {
    return undefined;
  };
 
  var from = 0, to = array.length,
      pivotIndex = partition(array, from, to);
 
  while(pivotIndex !== k) {
    pivotIndex = partition(array, from, to);
    if(pivotIndex < k) {
      from = pivotIndex;
    } else if(pivotIndex > k) {
      to = pivotIndex;
    }
  };
 
  return array[pivotIndex];
};
 
KthElement = {
  find: function(array, element) {
    var k = element - 1;
    return quickselectRecursive(array, 0, array.length, k);
    // you can also try out the Iterative version
    // return quickselectIterative(array, k);
  }
}