Data Structures & Algorithms(second：sort)

排序：对一种抽象数据类型按照其自然规律或逻辑规律排序（eg:从小到大，从前到后…)
sort：sorting is the processing of rearranging a sequence of objects so as to put them in a logical order.

There are three reasons to study sorting algorithms :

1: A easy start to start all kinds of other algorithms
2：Exercise a ability to compare with other algorithms
3: Similar techniques in other problems

Seven kinds of sorting algorithms :

algorithm	stable?	in place?	order of running time	extra space	notes
算法	稳定性?	是否在原数组中操作?	时间复杂度	额外空间大小	注意
selection sort	no	yes	N^2	1	none
insertion sort	yes	yes	N~N^2	1	time depends on original order of items
shellsort	no	yes	NlogN or N^(6/5)	1	none
quicksort	no	yes	NlogN	lgN	probabilistic (概率性的)
3-way quicksort	no	yes	N~NlogN	lgN	probabilistic and depends on what kinds of intput source
mergesort	yes	no	NlogN	N	none
heapsort	no	yes	NlogN	1	none

一：selection sort

It is the simplest sorting algorithms .
Its core logic is a for-loop.

core codes :

public static void sort(Comparable[] a) {
		int N=a.length;
		for (int i = 0; i <N; i++) {
			int min =i;
			for(int j=i+1;j<N;j++) {
				if(less(a[j], a[min]))
					min=j;
			}
			exch(a, i,min);
		}
	}

complete codes:

package algorithms_4th_chapter2_1;

import edu.princeton.cs.algs4.In;
/**
 * 2.1
 * O(time)=N^2
 * @author Enzo
 *
 */
public class Selection {
	
	public static void sort(Comparable[] a) {
		int N=a.length;
		for (int i = 0; i <N; i++) {
			int min =i;
			for(int j=i+1;j<N;j++) {
				if(less(a[j], a[min]))
					min=j;
			}
			exch(a, i,min);
		}
	}
	public static boolean less (Comparable v,Comparable w) {
		return  v.compareTo(w)<0;
	}
	public static void exch (Comparable[] a,int i,int j) {
		
		Comparable t=a[i];
		a[i]=a[j];
		a[j]=t;
	}
	public static void show(Comparable [] a) {
		for(int i=0;i<a.length;i++) {
			System.out.print(a[i]+"");
		}
		System.out.println();
	}
	public static boolean is_sorted (Comparable [ ] a) {
		for (int i = 0; i < a.length-1; i++) {
			if(less(a[i+1], a[i]))
				return false;
		}
		return true;
	}
	

	public static void main(String[] args) {
			// TODO Auto-generated method stub
		String[] a =new  In("tiny.txt").readAllStrings();
		sort(a);
		assert is_sorted(a);
		show(a);
		
	}

}

Nodes:
Use Comparable interface

Every loop to find the minimum item in array and decrease 1 of needed to retrieval array items ,also put this min item in a[i].

---

Features:
1: Running time is insensitive to input
2: Data move is minimal

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