快速排序实现

快速排序的原理见http://en.wikipedia.org/wiki/Quicksort

快速排序采用分而治之的策略，即partition-sort。先对待排序的序列进行partition操作，即从序列中选择一个基准值(pivot)，将序列中的元素与基准值比较，排序(sort)成小于和大于基准值的两个序列；再从两个序列中分别选择新的基准值，对两个序列再进行排序；直至整个序列不能再分，完成总体的排序。

假设序列的长度为N，需进行x次partition-sort，则有2^x=N，则快速排序的时间复杂度为O(logN)。

In-place快速排序不需要额外的存储空间，其实现伪代码为：

// left is the index of the leftmost element of the array   // right is the index of the rightmost element of the array (inclusive)   //   number of elements in subarray = right-left+1   function partition(array, 'left', 'right', 'pivotIndex')      'pivotValue' := array['pivotIndex']      swap array['pivotIndex'] and array['right']  // Move pivot to end      'storeIndex' := 'left'      for 'i' from 'left' to 'right' - 1  // left ≤ i < right          if array['i'] < 'pivotValue'              swap array['i'] and array['storeIndex']              'storeIndex' := 'storeIndex' + 1      swap array['storeIndex'] and array['right']  // Move pivot to its final place      return 'storeIndex'

 

 function quicksort(array, 'left', 'right')       // If the list has 2 or more items      if 'left' < 'right'           // See "Choice of pivot" section below for possible choices          choose any 'pivotIndex' such that 'left' ≤ 'pivotIndex' ≤ 'right'           // Get lists of bigger and smaller items and final position of pivot          'pivotNewIndex' := partition(array, 'left', 'right', 'pivotIndex')           // Recursively sort elements smaller than the pivot          quicksort(array, 'left', 'pivotNewIndex' - 1)           // Recursively sort elements at least as big as the pivot          quicksort(array, 'pivotNewIndex' + 1, 'right')

 

下图是in-place快速排序的示意图：

In-place partition in action on a small list. The boxed element is the pivot element, blue elements are less or equal, and red elements are larger.

实现代码为：

void my_swap(int& a, int& b){int temp = a;a = b;b = temp;}int partition(int* a, int left, int right){int pivotIndex = (left + right) / 2;int pivotValue = a[pivotIndex];my_swap(a[pivotIndex], a[right]);int storedIndex = left;for( int i = left; i < right; i++ ){if( a[i] < pivotValue ){my_swap( a[i], a[storedIndex] );storedIndex ++;}}my_swap( a[right], a[storedIndex] );return storedIndex;}int quick_sort( int* a, int left, int right ){if( left < right ){int index = partition(a, left, right);quick_sort(a, left, index-1);quick_sort(a, index+1, right);}else{return 1;}}