Data Structures and Algorithms with Object-Oriented Design Patterns (4)

  Sort Algorithms 

       Insertion Sort

              Straight Insertion Sort   best: O (n)      average: O (n^2)    worse: O (n^2)

                     It is efficient for the almost sorted array

              Binary Insertion Sort     best: O (n log n)     average: O (n^2)    worse: O (n^2)

       Exchange Sort

              Bubble Sort    always: O (n^2)

              Quick Sort      best: O (n log n)     average: O (n log n)      worse: O (n^2)

                     Recursive implementation

                     We can sort the array to be almost sorted using quick sort and then sort it using insertion sort

       Selection Sort

              Straight Selection Sort   always: O (n^2)

              Heap Sort       always: O (n log n) build heap phase: O (n) sort phase: O (n log n)

       Merge Sort

              Two-way Merge Sort     always: O (n log n)

       Distribution Sort

              Distribution Sorting Algorithms rely on the priori knowledge about the universal set from which the data to be sorted are drawn. It does not make use the comparisons to do the sorting.

              Bucket Sort    O (n)

              Radix Sort      O (n)

                     Radix Sort can be used when each element of the universal set can be viewed as a sequence of digits or the cross product of a finite number of finite set.

              Example: Sort the playing cards

       A Lower Bound on Comparison-Based Sorting

              O (n log n)     a binary decision tree with n! leaves and n log n height

 

Code:

Straight Insertion Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;
public class StraightInsertionSorter extends Sorter...{

    public void sort(Comparable[] array)
    ...{
        this.array=array;
        for(int i=0;i<array.length;i++)
        ...{
            for(int j=i;j>0 && array[j-1].isGT(array[j]);j--)
            ...{
                swap(j, j-1);
            }
        }
        return;
    }
    
}

 

Binary Insertion Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;

public class BinaryInsertionSorter extends Sorter...{

    public void sort(Comparable[] array)
    ...{
        this.array=array;
        for(int i=1;i<array.length;i++)
        ...{
            int left=0;
            int right=i;
            Comparable item=array[i];
            while(left<right)
            ...{
                int middle=(left+right)/2;
                if(array[middle].isGT(item))
                ...{
                    right=middle;
                }
                else
                ...{
                    left=middle+1;
                }
            }
            for(int j=i;j>left;j--)
            ...{
                swap(j,j-1);
            }
            for(int j=0;j<array.length;j++)
            ...{
                if(i==j)
                    System.out.print("*");
                System.out.print(array[j].getValue()+" ");
            }
            System.out.println("");
        }
    }
}

 

Bubble Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;
public class BubbleSorter extends Sorter...{

    public void sort(Comparable[] array) ...{
        // TODO Auto-generated method stub
        
        this.array=array;
        int length=array.length;
        for(int i=0;i<length;i++)
        ...{
            for(int j=0;j<length-1-i;j++)
            ...{
                if(array[j].isGT(array[j+1]))
                ...{
                    swap(j,j+1);
                }
            }
        }
    }

}

 

Quick Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;
public class QuickSorter extends Sorter...{

    
    public void sort(Comparable[] array) ...{
        // TODO Auto-generated method stub
        this.array=array;
        sort(0,array.length-1);
    }

    private void sort(int left, int right)
    ...{
        if(left==right)
        ...{
            return;
        }
        int pivot=selectPivot(left, right);
        swap(right, pivot);
        int i=left;
        int j=right-1;
        Comparable item=array[right];
        while(true)
        ...{
            while(i<j && array[i].isLT(item))i++;
            while(i<j && array[j].isGT(item))j--;
            if(i>=j)
                break;
            swap(i++,j--);
        }
        if(array[i].isGT(item))
        ...{
            swap(i, right);
        }
        if(i>left)
        ...{
            sort(left,i-1);
        }
        if(i<right)
        ...{
            sort(i+1,right);
        }
        
    }
    
    private int selectPivot(int left, int right)
    ...{
        return right;
    }
    
}

 

Straight Selection Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;
public class StraightSelectionSorter extends Sorter...{

    public void sort(Comparable[] array) ...{
        // TODO Auto-generated method stub
        this.array=array;
        int length=array.length;
        for(int i=0;i<length;i++)
        ...{
            int min=i;
            for(int j=i+1;j<length;j++)
            ...{
                if(array[j].isLT(array[min]))
                ...{
                    min=j;
                }
            }
            swap(i,min);
        }
    }

}

 

Heap Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;
import com.allenwu.container.Heap;

public class HeapSorter extends Sorter...{

    private Heap heap;

    public void sort(Comparable[] array) ...{
        // TODO Auto-generated method stub
        Heap heap=Heap.buildHeap(array);
        for(int i=0;i<array.length;i++)
        ...{
            array[i]=heap.get();
        }
    }
    
    
}

//==================Heap===================
package com.allenwu.container;
import com.allenwu.Comparable;
public class Heap ...{

    private Comparable[] items=null;
    private int maxSize=16;
    private int size=0;
    private Heap()
    ...{
        
    }
    
    public Comparable get()
    ...{
        Comparable min=items[0];
        items[0]=items[size-1];
        size--;
        modify(0);
        return min;
    }
    
    public static Heap buildHeap(Comparable[] items)
    ...{
        Heap heap=new Heap();
        heap.items=(Comparable[])items.clone();
        heap.maxSize=items.length;
        heap.size=items.length;
        for(int i=heap.size/2;i>=0;i--)
        ...{
            heap.modify(i);
        }
        return heap;
    }
    
    public static Heap buildHeap()
    ...{
        Heap heap=new Heap();
        heap.items=new Comparable[heap.maxSize];
        return heap;
    }
    
    
    private void swap(int i, int j)
    ...{
        Comparable temp=items[i];
        items[i]=items[j];
        items[j]=temp;
    }
    
    private void modify(int i)
    ...{

        int max=i;
        if(2*i<size && items[2*i].isLT(items[max]))
        ...{
            max=2*i;
        }
        if(2*i+1<size && items[2*i+1].isLT(items[max]))
        ...{
            max=2*i+1;
        }
        if(max!=i)
        ...{
            swap(i,max);
            modify(max);
        }
    }
    
    public void insert(Comparable item)
    ...{
        if(items.length>=maxSize)
        ...{
            maxSize*=2;
            Comparable[] tmpItems=new Comparable[maxSize];
            for(int i=0;i<items.length;i++)
            ...{
                tmpItems[i]=items[i];
            }
            items=tmpItems;
        }        
    }
    
    
}

 Merge Sort

package com.allenwu.sorter;

import com.allenwu.Comparable;

public class MergeSorter extends Sorter...{

    public void sort(Comparable[] array) ...{
        // TODO Auto-generated method stub
        this.array=array;
        sort(0, array.length-1);
    }
    
    private void sort(int left, int right)
    ...{
        if(left<right)
        ...{
            int middle=(left+right)/2;
            sort(left, middle);
            sort(middle+1, right);
            merge(left, middle, right);
        }
    }
    
    private void merge(int left, int middle, int right)
    ...{
        int i=left;
        int j=0;
        int k=middle+1;
        Comparable[] tmp=new Comparable[right-left+1];
        while(i<=middle && k<=right)
        ...{
            if(array[i].isLT(array[k]))
            ...{
                tmp[j++]=array[i++];
            }
            else
            ...{
                tmp[j++]=array[k++];
            }
        }
        while(i<=middle)
        ...{
            tmp[j++]=array[i++];
        }
        for(i=0;i<j;i++)
        ...{
            array[left+i]=tmp[i];
        }
    }

    
}