#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 = a[ p ];

        int j;
        for( j = p; j > 0 && tmp < a[ j - 1 ]; j-- )
            a[ j ] = a[ j - 1 ];
        a[ j ] = 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 = a[ i ];
            int j = i;

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

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

/**
 * 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 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 );
    }
}

/**
 * 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++ ] = a[ leftPos++ ];
        else
            tmpArray[ tmpPos++ ] = a[ rightPos++ ];

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

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

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

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


/**
 * 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 ] )
        swap( a[ left ], a[ center ] );
    if( a[ right ] < a[ left ] )
        swap( a[ left ], a[ right ] );
    if( a[ right ] < a[ center ] )
        swap( a[ center ], a[ right ] );

        // Place pivot at position right - 1
    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 )
    {
        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 )
                swap( a[ i ], a[ j ] );
            else
                break;
        }

        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 );
}

/**
 * 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 = a[ p ];
        int j;

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

/**
 * 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 );
}


/**
 * 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 )
    {
        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 )
                swap( a[ i ], a[ j ] );
            else
                break;
        }

        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 );
}

/**
 * Class that wraps a pointer variable.
 */
template <typename Comparable>
class Pointer
{
  public:
    Pointer( Comparable *rhs = NULL ) : pointee( rhs ) { }

    bool operator<( const Pointer & rhs ) const
        { return *pointee < *rhs.pointee; }

    operator Comparable * ( ) const
        { return pointee; }
  private:
    Comparable *pointee;
};

/**
 * Sort objects -- even large ones --
 * with only N + ln N Comparable moves on average.
 */
template <typename Comparable>
void largeObjectSort( vector<Comparable> & a )
{
    vector<Pointer<Comparable> > p( a.size( ) );
    int i, j, nextj;

    for( i = 0; i < a.size( ); i++ )
        p[ i ] = &a[ i ];

    quicksort( p );

        // Shuffle items in place
    for( i = 0; i < a.size( ); i++ )
        if( p[ i ] != &a[ i ] )
        {
            Comparable tmp = a[ i ];
            for( j = i; p[ j ] != &a[ i ]; j = nextj )
            {
                nextj = p[ j ] - &a[ 0 ];
                a[ j ] = *p[ j ];
                p[ j ] = &a[ j ];
            }
            a[ j ] = tmp;
            p[ j ] = &a[ j ];
        }
}

/*
 * This is the guts of the generic insertion sort routine.
 * It is logically a private routine.
 * It requires a beginning and ending iterator,
 * a comparison function object,
 * and a dummy parameter that is used to establish
 * the type of objects that are in the container.
 */
template <typename RandomIterator, typename Comparator, typename Object>
void insertionSort( const RandomIterator & begin,
                    const RandomIterator & end,
                    Comparator lessThan,
                    const Object & obj )
{
    RandomIterator j;

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

/*
 * This is the more public version of insertion sort.
 * It requires a pair of iterators and a comparison
 * function object. It calls the four parameter version
 * by sending *begin as the additional parameter.
 * The template expansion will allow the routine
 * above to then deduce Object, on the basis of *begin.\
 */
template <typename RandomIterator, typename Comparator>
void insertionSort( const RandomIterator & begin,
                    const RandomIterator & end,
                    Comparator lessThan )
{
    if( begin != end )
        insertionSort( begin, end, lessThan, *begin );
}

/*
 * The two-parameter version logically would call
 * the three parameter version, and send in a
 * default function object. The function object
 * would be less<Object>, but what is Object?
 * We don't know, so we pass *begin to another
 * version of insertionSort to deduce it.
 */
template <typename RandomIterator>
void insertionSort( const RandomIterator & begin,
                    const RandomIterator & end )
{
    if( begin != end )
        insertionSortHelp( begin, end, *begin );
}

/*
 * The three-parameter helper
 * uses Object to construct less<Object>, and
 * calls the three-parameter version of insertionSort.
 */
template <typename RandomIterator, typename Object>
void insertionSortHelp( const RandomIterator & begin,
                        const RandomIterator & end,
                        const Object & obj )
{
    insertionSort( begin, end, less<Object>( ) );
}


#endif