/**
* A class that contains several sorting routines,
* implemented as static methods.
* Arrays are rearranged with smallest item first,
* using compares.
* @author Mark Allen Weiss
*/
public final class Sort
{
/**
* Simple insertion sort.
* @param a an array of Comparable items.
*/
public static <AnyType extends Comparable<? super AnyType>> void insertionSort( AnyType [ ] a )
{
for( int p = 1; p < a.length; p++ )
{
AnyType tmp = a[ p ];
int j = p;
for( ; j > 0 && tmp.compareTo( a[ j - 1 ] ) < 0; j-- )
a[ j ] = a[ j - 1 ];
a[ j ] = tmp;
}
}
/**
* Shellsort, using a sequence suggested by Gonnet.
* @param a an array of Comparable items.
*/
public static <AnyType extends Comparable<? super AnyType>> void shellsort( AnyType [ ] a )
{
for( int gap = a.length / 2; gap > 0;
gap = gap == 2 ? 1 : (int) ( gap / 2.2 ) )
for( int i = gap; i < a.length; i++ )
{
AnyType tmp = a[ i ];
int j = i;
for( ; j >= gap && tmp.compareTo( a[ j - gap ] ) < 0; j -= gap )
a[ j ] = a[ j - gap ];
a[ j ] = tmp;
}
}
/**
* Standard heapsort.
* @param a an array of Comparable items.
*/
public static <AnyType extends Comparable<? super AnyType>> void heapsort( AnyType [ ] a )
{
for( int i = a.length / 2 - 1; i >= 0; i-- ) /* buildHeap */
percDown( a, i, a.length );
for( int i = a.length - 1; i > 0; i-- )
{
swapReferences( a, 0, i ); /* deleteMax */
percDown( a, 0, i );
}
}
/**
* Internal method for heapsort.
* @param i the index of an item in the heap.
* @return the index of the left child.
*/
private static int leftChild( int i )
{
return 2 * i + 1;
}
/**
* Internal method for heapsort that is used in
* deleteMax and buildHeap.
* @param a an array of Comparable items.
* @index i the position from which to percolate down.
* @int n the logical size of the binary heap.
*/
private static <AnyType extends Comparable<? super AnyType>> void percDown( AnyType [ ] a, int i, int n )
{
int child;
AnyType tmp;
for( tmp = a[ i ]; leftChild( i ) < n; i = child )
{
child = leftChild( i );
if( child != n - 1 && a[ child ].compareTo( a[ child + 1 ] ) < 0 )
child++;
if( tmp.compareTo( a[ child ] ) < 0 )
a[ i ] = a[ child ];
else
break;
}
a[ i ] = tmp;
}
/**
* Mergesort algorithm.
* @param a an array of Comparable items.
*/
public static <AnyType extends Comparable<? super AnyType>> void mergeSort( AnyType [ ] a )
{
AnyType [ ] tmpArray = (AnyType []) new Comparable[ a.length ];
mergeSort( a, tmpArray, 0, a.length - 1 );
}
/**
* Internal method that makes recursive calls.
* @param a an array of Comparable items.
* @param tmpArray an array to place the merged result.
* @param left the left-most index of the subarray.
* @param right the right-most index of the subarray.
*/
private static <AnyType extends Comparable<? super AnyType>> void mergeSort( AnyType [ ] a, AnyType [ ] 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.
* @param a an array of Comparable items.
* @param tmpArray an array to place the merged result.
* @param leftPos the left-most index of the subarray.
* @param rightPos the index of the start of the second half.
* @param rightEnd the right-most index of the subarray.
*/
private static <AnyType extends Comparable<? super AnyType>> void merge( AnyType [ ] a, AnyType [ ] 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 ].compareTo( a[ rightPos ] ) <= 0 )
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.
* @param a an array of Comparable items.
*/
public static <AnyType extends Comparable<? super AnyType>> void quicksort( AnyType [ ] a )
{
quicksort( a, 0, a.length - 1 );
}
private static final int CUTOFF = 10;
/**
* Method to swap to elements in an array.
* @param a an array of objects.
* @param index1 the index of the first object.
* @param index2 the index of the second object.
*/
public static final <AnyType> void swapReferences( AnyType [ ] a, int index1, int index2 )
{
AnyType tmp = a[ index1 ];
a[ index1 ] = a[ index2 ];
a[ index2 ] = tmp;
}
/**
* Internal quicksort method that makes recursive calls.
* Uses median-of-three partitioning and a cutoff of 10.
* @param a an array of Comparable items.
* @param low the left-most index of the subarray.
* @param high the right-most index of the subarray.
*/
private static <AnyType extends Comparable<? super AnyType>> void quicksort( AnyType [ ] a, int low, int high )
{
if( low + CUTOFF > high )
insertionSort( a, low, high );
else
{
// Sort low, middle, high
int middle = ( low + high ) / 2;
if( a[ middle ].compareTo( a[ low ] ) < 0 )
swapReferences( a, low, middle );
if( a[ high ].compareTo( a[ low ] ) < 0 )
swapReferences( a, low, high );
if( a[ high ].compareTo( a[ middle ] ) < 0 )
swapReferences( a, middle, high );
// Place pivot at position high - 1
swapReferences( a, middle, high - 1 );
AnyType pivot = a[ high - 1 ];
// Begin partitioning
int i, j;
for( i = low, j = high - 1; ; )
{
while( a[ ++i ].compareTo( pivot ) < 0 )
;
while( pivot.compareTo( a[ --j ] ) < 0 )
;
if( i >= j )
break;
swapReferences( a, i, j );
}
// Restore pivot
swapReferences( a, i, high - 1 );
quicksort( a, low, i - 1 ); // Sort small elements
quicksort( a, i + 1, high ); // Sort large elements
}
}
/**
* Internal insertion sort routine for subarrays
* that is used by quicksort.
* @param a an array of Comparable items.
* @param low the left-most index of the subarray.
* @param n the number of items to sort.
*/
private static <AnyType extends Comparable<? super AnyType>> void insertionSort( AnyType [ ] a, int low, int high )
{
for( int p = low + 1; p <= high; p++ )
{
AnyType tmp = a[ p ];
int j;
for( j = p; j > low && tmp.compareTo( a[ j - 1 ] ) < 0; j-- )
a[ j ] = a[ j - 1 ];
a[ j ] = tmp;
}
}
/**
* Quick selection algorithm.
* Places the kth smallest item in a[k-1].
* @param a an array of Comparable items.
* @param k the desired rank (1 is minimum) in the entire array.
*/
public static <AnyType extends Comparable<? super AnyType>> void quickSelect( AnyType [ ] a, int k )
{
quickSelect( a, 0, a.length - 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].
* @param a an array of Comparable items.
* @param low the left-most index of the subarray.
* @param high the right-most index of the subarray.
* @param k the desired rank (1 is minimum) in the entire array.
*/
private static <AnyType extends Comparable<? super AnyType>>void quickSelect( AnyType [ ] a, int low, int high, int k )
{
if( low + CUTOFF > high )
insertionSort( a, low, high );
else
{
// Sort low, middle, high
int middle = ( low + high ) / 2;
if( a[ middle ].compareTo( a[ low ] ) < 0 )
swapReferences( a, low, middle );
if( a[ high ].compareTo( a[ low ] ) < 0 )
swapReferences( a, low, high );
if( a[ high ].compareTo( a[ middle ] ) < 0 )
swapReferences( a, middle, high );
// Place pivot at position high - 1
swapReferences( a, middle, high - 1 );
AnyType pivot = a[ high - 1 ];
// Begin partitioning
int i, j;
for( i = low, j = high - 1; ; )
{
while( a[ ++i ].compareTo( pivot ) < 0 )
;
while( pivot.compareTo( a[ --j ] ) < 0 )
;
if( i >= j )
break;
swapReferences( a, i, j );
}
// Restore pivot
swapReferences( a, i, high - 1 );
// Recurse; only this part changes
if( k <= i )
quickSelect( a, low, i - 1, k );
else if( k > i + 1 )
quickSelect( a, i + 1, high, k );
}
}
}