數據結構-歸併排序

時間 2020-04-24

標籤數據結構歸併排序简体版

原文原文鏈接

（1）基本思想：歸併（Merge）排序法是將兩個（或兩個以上）有序表合併成一個新的有序表，即把待排序序列分爲若干個子序列，每一個子序列是有序的。而後再把有序子序列合併爲總體有序序列。歸併排序（MERGE-SORT）是創建在歸併操做上的一種有效的排序算法,該算法是採用分治法（Divide and Conquer）的一個很是典型的應用。將已有序的子序列合併，獲得徹底有序的序列；即先使每一個子序列有序，再使子序列段間有序。若將兩個有序表合併成一個有序表，稱爲二路歸併。java

歸併過程爲：比較a[i]和a[j]的大小，若a[i]≤a[j]，則將第一個有序表中的元素a[i]複製到r[k]中，並令i和k分別加上1；不然將第二個有序表中的元素a[j]複製到r[k]中，並令j和k分別加上1，如此循環下去，直到其中一個有序表取完，而後再將另外一個有序表中剩餘的元素複製到r中從下標k到下標t的單元。歸併排序的算法咱們一般用遞歸實現，先把待排序區間[s,t]以中點二分，接着把左邊子區間排序，再把右邊子區間排序，最後把左區間和右區間用一次歸併操做合併成有序的區間[s,t]。算法

（2）算法描述
數組

歸併操做的工做原理以下：ide

第一步：申請空間，使其大小爲兩個已經排序序列之和，該空間用來存放合併後的序列；spa

第二步：設定兩個指針，最初位置分別爲兩個已經排序序列的起始位置；3d

第三步：比較兩個指針所指向的元素，選擇相對小的元素放入到合併空間，並移動指針到下一位置；指針

重複步驟3直到某一指針超出序列尾，將另外一序列剩下的全部元素直接複製到合併序列尾。orm

（3）代碼以下：htm

package structsmethod;

import java.util.Arrays;  

public class mergingSort { 
	/*
	 * 歸併排序
	 */
	int a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};  
	public  mergingSort(){  
	    sort(a,0,a.length-1);  
	    for(int i=0;i<a.length;i++)  
	        System.out.println(a[i]);  
	}  
	public void sort(int[] data, int left, int right) { 
	    if(left<right){  
	        //找出中間索引  
	        int center=(left+right)/2;  
	        //對左邊數組進行遞歸  
	        sort(data,left,center);  
	        //對右邊數組進行遞歸  
	        sort(data,center+1,right);  
	        //合併  
	        merge(data,left,center,right);  
	          
	    }  
	}  
	public void merge(int[] data, int left, int center, int right) {  
	    int [] tmpArr=new int[data.length];  
	    int mid=center+1;  
	    //third記錄中間數組的索引  
	    int third=left;  
	    int tmp=left;  
	    while(left<=center&&mid<=right){  
	        //從兩個數組中取出最小的放入中間數組  
	        if(data[left]<=data[mid]){  
	            tmpArr[third++]=data[left++];  
	        }else{  
	            tmpArr[third++]=data[mid++];  
	        }  
	    }  
	    //剩餘部分依次放入中間數組  
	    while(mid<=right){  
	        tmpArr[third++]=data[mid++];  
	    }  
	    while(left<=center){  
	        tmpArr[third++]=data[left++];  
	    }  
	    //將中間數組中的內容複製回原數組  
	    while(tmp<=right){  
	        data[tmp]=tmpArr[tmp++];  
	    }  
	    System.out.println(Arrays.toString(data));  
	}  
	public static void main(String[] args) {
		mergingSort ms=new mergingSort();
		ms.sort(ms.a, 0, ms.a.length-1);
	}
}

排序結果以下：
blog

[38, 49, 65, 97, 76, 13, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[38, 49, 65, 97, 13, 76, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[38, 49, 65, 97, 13, 27, 76, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 49, 78, 12, 34, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 5, 64, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 4, 5, 64, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[13, 27, 38, 49, 65, 76, 97, 4, 5, 12, 34, 49, 64, 78, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 62, 99, 54, 98, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 17, 56, 18, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 17, 18, 56, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 23, 34, 15, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 34, 35, 25, 53, 51]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 34, 35, 25, 51, 53]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 25, 34, 35, 51, 53]

[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 15, 17, 18, 23, 25, 34, 35, 51, 53, 54, 56, 62, 98, 99]

[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]

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