几大排序的稳定性_排序的稳定性指什么

class Solution {
public:
    //获取枢纽元素，这里不取第一个元素为枢纽元素，要避免这种愚蠢的做法
    int median(vector<int> &arr, int left, int right) {
        int center = left + right >> 1;
        if(arr[center] < arr[left]) swap(arr[center], arr[left]);
        if(arr[right] < arr[left]) swap(arr[left], arr[right]);
        if(arr[right] < arr[center]) swap(arr[right], arr[center]);

        swap(arr[center], arr[right - 1]);
        return arr[right - 1];

    }

    void quickSort(vector<int> &arr, int left, int right) {
        if(left + 10 <= right) {
            int pivot = median(arr, left, right);
            int i = left, j = right - 1;
            while(1) {
                while(arr[++i] < pivot);
                while(arr[--j] > pivot);
                if(i < j) swap(arr[i], arr[j]);
                else break;
            }
            swap(arr[i], arr[right - 1]);
            quickSort(arr, left, i - 1);
            quickSort(arr, i + 1, right);
        }
        else 
            insertionSort(arr, left, right);
    }

    void insertionSort(vector<int> &arr, int left, int right) {
        for(int i = left + 1; i <= right; ++i) {
            auto tmp = arr[i];
            int j;
            for(j = i; j > 0 && tmp < arr[j - 1]; --j) {
                arr[j] = arr[j - 1];
            }
            arr[j] = tmp;
        }
    }

    vector<int> sortArray(vector<int>& nums) {
        quickSort(nums, 0, nums.size() - 1);
        return {nums};
    }
};

#ifndef SORT_H
#define SORT_H

/**
 * Several sorting routines.
 * Arrays are rearranged with smallest item first.
 */

#include <vector>
#include <functional>
using namespace std;

/**
 * Simple insertion sort.
 */
template <typename Comparable>
void insertionSort( vector<Comparable> & a )
{
    for( int p = 1; p < a.size( ); ++p )
    {
        Comparable tmp = std::move( a[ p ] );

        int j;
        for( j = p; j > 0 && tmp < a[ j - 1 ]; --j )
            a[ j ] = std::move( a[ j - 1 ] );
        a[ j ] = std::move( tmp );
    }
}


/**
 * Internal insertion sort routine for subarrays
 * that is used by quicksort.
 * a is an array of Comparable items.
 * left is the left-most index of the subarray.
 * right is the right-most index of the subarray.
 */
template <typename Comparable>
void insertionSort( vector<Comparable> & a, int left, int right )
{
    for( int p = left + 1; p <= right; ++p )
    {
        Comparable tmp = std::move( a[ p ] );
        int j;

        for( j = p; j > left && tmp < a[ j - 1 ]; --j )
            a[ j ] = std::move( a[ j - 1 ] );
        a[ j ] = std::move( tmp );
    }
}



/**
 * Shellsort, using Shell's (poor) increments.
 */
template <typename Comparable>
void shellsort( vector<Comparable> & a )
{
    for( int gap = a.size( ) / 2; gap > 0; gap /= 2 )
        for( int i = gap; i < a.size( ); ++i )
        {
            Comparable tmp = std::move( a[ i ] );
            int j = i;

            for( ; j >= gap && tmp < a[ j - gap ]; j -= gap )
                a[ j ] = std::move( a[ j - gap ] );
            a[ j ] = std::move( tmp );
        }
}

/**
 * Standard heapsort.
 */
template <typename Comparable>
void heapsort( vector<Comparable> & a )
{
    for( int i = a.size( ) / 2 - 1; i >= 0; --i )  /* buildHeap */
        percDown( a, i, a.size( ) );
    for( int j = a.size( ) - 1; j > 0; --j )
    {
        std::swap( a[ 0 ], a[ j ] );               /* deleteMax */
        percDown( a, 0, j );
    }
}

/**
 * Internal method for heapsort.
 * i is the index of an item in the heap.
 * Returns the index of the left child.
 */
inline int leftChild( int i )
{
    return 2 * i + 1;
}

/**
 * Internal method for heapsort that is used in
 * deleteMax and buildHeap.
 * i is the position from which to percolate down.
 * n is the logical size of the binary heap.
 */
template <typename Comparable>
void percDown( vector<Comparable> & a, int i, int n )
{
    int child;
    Comparable tmp;

    for( tmp = std::move( a[ i ] ); leftChild( i ) < n; i = child )
    {
        child = leftChild( i );
        if( child != n - 1 && a[ child ] < a[ child + 1 ] )
            ++child;
        if( tmp < a[ child ] )
            a[ i ] = std::move( a[ child ] );
        else
            break;
    }
    a[ i ] = std::move( tmp );
}

/**
 * Internal method that makes recursive calls.
 * a is an array of Comparable items.
 * tmpArray is an array to place the merged result.
 * left is the left-most index of the subarray.
 * right is the right-most index of the subarray.
 */
template <typename Comparable>
void mergeSort( vector<Comparable> & a,
                vector<Comparable> & tmpArray, int left, int right )
{
    if( left < right )
    {
        int center = ( left + right ) / 2;
        mergeSort( a, tmpArray, left, center );
        mergeSort( a, tmpArray, center + 1, right );
        merge( a, tmpArray, left, center + 1, right );
    }
}

/**
 * Mergesort algorithm (driver).
 */
template <typename Comparable>
void mergeSort( vector<Comparable> & a )
{
    vector<Comparable> tmpArray( a.size( ) );

    mergeSort( a, tmpArray, 0, a.size( ) - 1 );
}


/**
 * Internal method that merges two sorted halves of a subarray.
 * a is an array of Comparable items.
 * tmpArray is an array to place the merged result.
 * leftPos is the left-most index of the subarray.
 * rightPos is the index of the start of the second half.
 * rightEnd is the right-most index of the subarray.
 */
template <typename Comparable>
void merge( vector<Comparable> & a, vector<Comparable> & tmpArray,
            int leftPos, int rightPos, int rightEnd )
{
    int leftEnd = rightPos - 1;
    int tmpPos = leftPos;
    int numElements = rightEnd - leftPos + 1;

    // Main loop
    while( leftPos <= leftEnd && rightPos <= rightEnd )
        if( a[ leftPos ] <= a[ rightPos ] )
            tmpArray[ tmpPos++ ] = std::move( a[ leftPos++ ] );
        else
            tmpArray[ tmpPos++ ] = std::move( a[ rightPos++ ] );

    while( leftPos <= leftEnd )    // Copy rest of first half
        tmpArray[ tmpPos++ ] = std::move( a[ leftPos++ ] );

    while( rightPos <= rightEnd )  // Copy rest of right half
        tmpArray[ tmpPos++ ] = std::move( a[ rightPos++ ] );

    // Copy tmpArray back
    for( int i = 0; i < numElements; ++i, --rightEnd )
        a[ rightEnd ] = std::move( tmpArray[ rightEnd ] );
}


/**
 * Return median of left, center, and right.
 * Order these and hide the pivot.
 */
template <typename Comparable>
const Comparable & median3( vector<Comparable> & a, int left, int right )
{
    int center = ( left + right ) / 2;
    
    if( a[ center ] < a[ left ] )
        std::swap( a[ left ], a[ center ] );
    if( a[ right ] < a[ left ] )
        std::swap( a[ left ], a[ right ] );
    if( a[ right ] < a[ center ] )
        std::swap( a[ center ], a[ right ] );

        // Place pivot at position right - 1
    std::swap( a[ center ], a[ right - 1 ] );
    return a[ right - 1 ];
}

/**
 * Internal quicksort method that makes recursive calls.
 * Uses median-of-three partitioning and a cutoff of 10.
 * a is an array of Comparable items.
 * left is the left-most index of the subarray.
 * right is the right-most index of the subarray.
 */
template <typename Comparable>
void quicksort( vector<Comparable> & a, int left, int right )
{
    if( left + 10 <= right )
    {
        const Comparable & pivot = median3( a, left, right );

            // Begin partitioning
        int i = left, j = right - 1;
        for( ; ; )
        {
            while( a[ ++i ] < pivot ) { }
            while( pivot < a[ --j ] ) { }
            if( i < j )
                std::swap( a[ i ], a[ j ] );
            else
                break;
        }

        std::swap( a[ i ], a[ right - 1 ] );  // Restore pivot

        quicksort( a, left, i - 1 );     // Sort small elements
        quicksort( a, i + 1, right );    // Sort large elements
    }
    else  // Do an insertion sort on the subarray
        insertionSort( a, left, right );
}

/**
 * Quicksort algorithm (driver).
 */
template <typename Comparable>
void quicksort( vector<Comparable> & a )
{
    quicksort( a, 0, a.size( ) - 1 );
}


/**
 * Internal selection method that makes recursive calls.
 * Uses median-of-three partitioning and a cutoff of 10.
 * Places the kth smallest item in a[k-1].
 * a is an array of Comparable items.
 * left is the left-most index of the subarray.
 * right is the right-most index of the subarray.
 * k is the desired rank (1 is minimum) in the entire array.
 */
template <typename Comparable>
void quickSelect( vector<Comparable> & a, int left, int right, int k )
{
    if( left + 10 <= right )
    {
        const Comparable & pivot = median3( a, left, right );

            // Begin partitioning
        int i = left, j = right - 1;
        for( ; ; )
        {
            while( a[ ++i ] < pivot ) { }
            while( pivot < a[ --j ] ) { }
            if( i < j )
                std::swap( a[ i ], a[ j ] );
            else
                break;
        }

        std::swap( a[ i ], a[ right - 1 ] );  // Restore pivot

            // Recurse; only this part changes
        if( k <= i )
            quickSelect( a, left, i - 1, k );
        else if( k > i + 1 )
            quickSelect( a, i + 1, right, k );
    }
    else  // Do an insertion sort on the subarray
        insertionSort( a, left, right );
}

/**
 * Quick selection algorithm.
 * Places the kth smallest item in a[k-1].
 * a is an array of Comparable items.
 * k is the desired rank (1 is minimum) in the entire array.
 */
template <typename Comparable>
void quickSelect( vector<Comparable> & a, int k )
{
    quickSelect( a, 0, a.size( ) - 1, k );
}


template <typename Comparable>
void SORT( vector<Comparable> & items )
{
    if( items.size( ) > 1 )
    {
        vector<Comparable> smaller;
        vector<Comparable> same;
        vector<Comparable> larger;
        
        auto chosenItem = items[ items.size( ) / 2 ];
        
        for( auto & i : items )
        {
            if( i < chosenItem )
                smaller.push_back( std::move( i ) );
            else if( chosenItem < i )
                larger.push_back( std::move( i ) );
            else
                same.push_back( std::move( i ) );
        }
        
        SORT( smaller );     // Recursive call!
        SORT( larger );      // Recursive call!
        
        std::move( begin( smaller ), end( smaller ), begin( items ) );
        std::move( begin( same ), end( same ), begin( items ) + smaller.size( ) );
        std::move( begin( larger ), end( larger ), end( items ) - larger.size( ) );

/*
        items.clear( );
        items.insert( end( items ), begin( smaller ), end( smaller ) );
        items.insert( end( items ), begin( same ), end( same ) );
        items.insert( end( items ), begin( larger ), end( larger ) );
*/
    }
}

/*
 * This is the more public version of insertion sort.
 * It requires a pair of iterators and a comparison
 * function object.
 */
template <typename RandomIterator, typename Comparator>
void insertionSort( const RandomIterator & begin,
                    const RandomIterator & end,
                    Comparator lessThan )
{
    if( begin == end )
        return;
        
    RandomIterator j;

    for( RandomIterator p = begin+1; p != end; ++p )
    {
        auto tmp = std::move( *p );
        for( j = p; j != begin && lessThan( tmp, *( j-1 ) ); --j )
            *j = std::move( *(j-1) );
        *j = std::move( tmp );
    }
}

/*
 * The two-parameter version calls the three parameter version, using C++11 decltype
 */
template <typename RandomIterator>
void insertionSort( const RandomIterator & begin,
                    const RandomIterator & end )
{
    insertionSort( begin, end, less<decltype(*begin )>{ } );
}



#endif