2.2.5

question:

Give the sequence of subarray sizes in the merges performed by both the top-down and the bottom-up mergesort algorithms, for N = 39.

answer:

//top-down

import edu.princeton.cs.algs4.*;

public class Merge
{
    private static Comparable[] aux;
    
    public static boolean less(Comparable v, Comparable w)
    {
        return v.compareTo(w) < 0;
    }
    
    public static void merge(Comparable[] a, int lo, int mid, int hi)
    {
        int i = lo;
        int j = mid + 1;
        for(int k = lo; k <= hi; k++)
            aux[k] = a[k];
        for(int k = lo; k <= hi; k++)
        {
            if(i > mid)
                a[k] = aux[j++];
            else if(j > hi)
                a[k] = aux[i++];
            else if(less(aux[j], aux[i]))
                a[k] = aux[j++];
            else
                a[k] = aux[i++];
        }
    }
    
    public static void sort(Comparable[] a)
    {
        aux = new Comparable[a.length];
        sort(a, 0, a.length-1);
    }
    
    public static void sort(Comparable[] a, int lo, int hi)
    {
        if(hi<=lo)
            return;
        int mid = lo + (hi - lo)/2;
        sort(a,lo,mid);
        sort(a,mid+1,hi);
        merge(a,lo,mid,hi);
        show(lo,hi);
    }
    
    public static void show(int lo, int hi)
    {
        StdOut.print(hi-lo+1 + " ");
    }
    
    public static void main(String[] args)
    {
        //输入一个N为39的string数组
        //c a s e r t y w a w q c v b n m e t v m e q w r o p k l f g e x v r m n y i u
        String[] a = In.readStrings();
        sort(a);
    }
}

//bottom-up

import edu.princeton.cs.algs4.*;

public class MergeBU
{
    private static Comparable[] aux;
    
    public static boolean less(Comparable v, Comparable w)
    {
        return v.compareTo(w) < 0;
    }
    
    public static void merge(Comparable[] a, int lo, int mid, int hi)
    {
        int i = lo;
        int j = mid + 1;
        for(int k = lo; k <= hi; k++)
            aux[k] = a[k];
        for(int k = lo; k <= hi; k++)
        {
            if(i > mid)
                a[k] = aux[j++];
            else if(j > hi)
                a[k] = aux[i++];
            else if(less(aux[j], aux[i]))
                a[k] = aux[j++];
            else
                a[k] = aux[i++];
        }
    }
    
    public static void sort(Comparable[] a)
    {
        aux = new Comparable[a.length];
        int N = a.length;
        for(int sz = 1; sz < N; sz+=sz)
        {
            for(int j = 0; j < N-sz; j+=2*sz)
            {
                merge(a,j,j+sz-1,Math.min(j+2*sz-1,N-1));
                show(j,Math.min(j+2*sz-1,N-1));
            }
        }
    }
    
    public static void show(int lo, int hi)
    {
        StdOut.print(hi-lo+1 + " ");
    }
    
    public static void main(String[] args)
    {
        //输入一个N为39的string数组
        //c a s e r t y w a w q c v b n m e t v m e q w r o p k l f g e x v r m n y i u
        String[] a = In.readStrings();
        sort(a);
    }
}