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Java各種排序演算法的實作程式碼範例

黄舟
黄舟原創
2017-10-20 09:54:431613瀏覽

這篇文章主要介紹了java實作的各種排序演算法程式碼範例,比較全面,程式碼親測可用,如有不足之處,歡迎留言指出。

折半插入排序

#折半插入排序是直接插入排序的簡單改進。這裡介紹的折半插入,其實就是透過不斷地折半來快速確定第i個元素的
插入位置,這實際上是一種查找演算法:折半查找。 Java的Arrays類別裡的binarySearch()方法,就是折半查找的實現,用
於從指定數組中查找指定元素,前提是該數組已經處於有序狀態。與直接插入排序的效果相同,只是更快了一些,因
為折半插入排序可以更快地確定第i個元素的插入位置

代碼:


#
package interview; 
/** 
 * @author Administrator 
 * 折半插入排序 
 */ 
public class BinaryInsertSort { 
  public static void binaryInsertSort(DataWrap[] data) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    for (int i = 1; i < arrayLength; i++) { 
      DataWrap temp = data[i]; 
      int low = 0; 
      int high = i - 1; 
      while (low <= high) { 
        int mid = (low + high) / 2; 
        if (temp.compareTo(data[mid]) > 0) { 
          low = mid + 1; 
        } else { 
          high = mid - 1; 
        } 
      } 
      for (int j = i; j > low; j--) { 
        data[j] = data[j - 1]; 
      } 
      data[low] = temp; 
      System.out.println(java.util.Arrays.toString(data)); 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "")}; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    binaryInsertSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}

結果:


排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-30, -16, 9, 21*, 23, -49, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 23, 21, 30*, 30]
[-49, -30, -16, 9, 21, 21*, 23, 30*, 30]
[-49, -30, -16, 9, 21, 21*, 23, 30*, 30]
[-49, -30, -16, 9, 21, 21*, 23, 30, 30*]
排序之后:
[-49, -30, -16, 9, 21, 21*, 23, 30, 30*]

冒泡排序

程式碼:


package interview; 
/** 
 * @author Administrator 
 * 冒泡排序 
 */ 
public class BubbleSort { 
  public static void bubbleSort(DataWrap[] data) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    for (int i = 0; i < arrayLength - 1; i++) { 
      boolean flag = false; 
      for (int j = 0; j < arrayLength - 1 - i; j++) { 
        if (data[j].compareTo(data[j + 1]) > 0) { 
          DataWrap temp = data[j + 1]; 
          data[j + 1] = data[j]; 
          data[j] = temp; 
          flag = true; 
        } 
      } 
      System.out.println(java.util.Arrays.toString(data)); 
      if (!flag) 
        break; 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "")}; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    bubbleSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}

執行結果:


排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
[-16, 9, 21*, -30, -49, 21, 23, 30*, 30]
[-16, 9, -30, -49, 21*, 21, 23, 30*, 30]
[-16, -30, -49, 9, 21*, 21, 23, 30*, 30]
[-30, -49, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]


桶式排序




演算法的時間效率:時間效率極高,只要經過兩輪遍歷即可演算法的空間效率:空間開銷較大,需要兩個陣列來完成,算

法的穩定性:穩定

程式碼:


package interview; 
import java.util.Arrays; 
/** 
 * @author Administrator 
 * 桶式排序 
 */ 
public class BucketSort { 
  public static void bucketSort(DataWrap[] data, int min, int max) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    DataWrap[] temp = new DataWrap[arrayLength]; 
    int[] buckets = new int[max - min]; 
    for (int i = 0; i < arrayLength; i++) { 
      buckets[data[i].data - min]++; 
    } 
    System.out.println(Arrays.toString(buckets)); 
    for (int i = 1; i < max - min; i++) { 
      buckets[i] = buckets[i] + buckets[i - 1]; 
    } 
    System.out.println(Arrays.toString(buckets)); 
    System.arraycopy(data, 0, temp, 0, arrayLength); 
    for (int k = arrayLength - 1; k >= 0; k--) { 
      data[--buckets[temp[k].data - min]] = temp[k]; 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(5, ""), 
        new DataWrap(-1, ""), new DataWrap(8, ""), 
        new DataWrap(5, "*"), new DataWrap(7, ""), 
        new DataWrap(3, ""), new DataWrap(-3, ""), 
        new DataWrap(1, ""),new DataWrap(3, "*")}; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    bucketSort(data, -3, 10); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}

結果

排序之前:
[9, 5, -1, 8, 5*, 7, 3, -3, 1, 3*]
开始排序
[1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1]
[1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 8, 9, 10]
排序之后:
[-3, -1, 1, 3, 3*, 5, 5*, 7, 8, 9]

堆排序



package interview; 
/** 
 * @author Administrator 
 * 堆排序 
 */ 
public class HeapSort { 
  public static void heapSort(DataWrap[] data) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    // 循环建堆 
    for (int i = 0; i < arrayLength - 1; i++) { 
      // 建堆 
      builMaxdHeap(data, arrayLength - 1 - i); 
      // 交换堆顶和最后一个元素 
      swap(data, 0, arrayLength - 1 - i); 
      System.out.println(java.util.Arrays.toString(data)); 
    } 
  } 
  // 对data数组从0到lastIndex建大顶堆 
  private static void builMaxdHeap(DataWrap[] data, int lastIndex) { 
    // 从lastIndex处节点(最后一个节点)的父节点开始 
    for (int i = (lastIndex - 1) / 2; i >= 0; i--) { 
      // k保存当前正在判断的节点 
      int k = i; 
      // 如果当前k节点的子节点存在 
      while (k * 2 + 1 <= lastIndex) { 
        // k节点的左子节点的索引 
        int biggerIndex = 2 * k + 1; 
        // 如果biggerIndex小于lastIndex,即biggerIndex +1 
        // 代表k节点的右子节点存在 
        if (biggerIndex < lastIndex) { 
          // 如果右子节点的值较大 
          if (data[biggerIndex].compareTo(data[biggerIndex + 1]) < 0) { 
            // biggerIndex总是记录较大子节点的索引 
            biggerIndex++; 
          } 
        } 
        // 如果k节点的值小于其较大子节点的值 
        if (data[k].compareTo(data[biggerIndex]) < 0) { 
          // 交换它们 
          swap(data, k, biggerIndex); 
          // 将biggerIndex赋给k,开始while循环的下一次循环 
          // 重新保证k节点的值大于其左、右节点的值 
          k = biggerIndex; 
        } else { 
          break; 
        } 
      } 
    } 
  } 
  // 交换data数组中i、j两个索引处的元素 
  private static void swap(DataWrap[] data, int i, int j) { 
    DataWrap temp = data[i]; 
    data[i] = data[j]; 
    data[j] = temp; 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "")}; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    heapSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}

結果:

排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
[-16, 30, 21*, 23, -30, -49, 21, 9, 30*]
[-16, 23, 21*, 9, -30, -49, 21, 30, 30*]
[21, 9, 21*, -16, -30, -49, 23, 30, 30*]
[-49, 9, 21*, -16, -30, 21, 23, 30, 30*]
[-30, 9, -49, -16, 21*, 21, 23, 30, 30*]
[-30, -16, -49, 9, 21*, 21, 23, 30, 30*]
[-49, -30, -16, 9, 21*, 21, 23, 30, 30*]
[-49, -30, -16, 9, 21*, 21, 23, 30, 30*]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30, 30*]

#直接插入排序

##
package interview;
public class InsertSort {
	public static void insertSort(DataWrap[] data){ 
	  System.out.println("开始排序"); 
	  int arrayLength = data.length; 
	  for(int i = 1;i < arrayLength;i++){ 
	    DataWrap temp = data[i]; 
	    if(data[i].compareTo(data[i-1]) < 0){ 
	      int j = i -1; 
	      for(;j >= 0 && data[j].compareTo(temp) > 0;j--){ 
	        data[j +1] = data[j]; 
	      } 
	      data[j + 1] = temp; 
	    } 
	    System.out.println(java.util.Arrays.toString(data)); 
	  } 
	} 
	public static void main(String[] args) { 
	  DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
	      new DataWrap(21, "*"), new DataWrap(23, ""), 
	      new DataWrap(-30, ""), new DataWrap(-49, ""), 
	      new DataWrap(21, ""), new DataWrap(30, "*"), 
	      new DataWrap(30, "")}; 
	  System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
	  insertSort(data); 
	  System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
	} 
}

結果

排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-16, 9, 21*, 23, -30, -49, 21, 30*, 30]
[-30, -16, 9, 21*, 23, -49, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 23, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]

#歸併排序













##演算法的時間效率:歸併演算法需要遞歸地進行分解、合併,每進行一趟歸併排序,需要merge()方法一次,每次執行

merge()需要比較n次,較差,需要一個與原始序列相同大小的輔助序列。演算法的穩定性:穩定

程式碼:

package interview; 
/** 
 * @author Administrator 
 * 归并排序 
 */ 
public class MergeSort { 
  public static void mergeSort(DataWrap[] data) { 
    // 归并排序 
    sort(data, 0, data.length - 1); 
  } 
  // 将索引从left到right范围的数组元素进行归并排序 
  private static void sort(DataWrap[] data, int left, int right) { 
    if(left < right){ 
      //找出中间索引 
      int center = (left + right)/2; 
      sort(data,left,center); 
      sort(data,center+1,right); 
      //合并 
      merge(data,left,center,right); 
    } 
  } 
  // 将两个数组进行归并,归并前两个数组已经有序,归并后依然有序 
  private static void merge(DataWrap[] data, int left, int center, int right) { 
    DataWrap[] tempArr = new DataWrap[data.length]; 
    int mid = center + 1; 
    int third = left; 
    int temp = left; 
    while (left <= center && mid <= right) { 
      if (data[left].compareTo(data[mid]) <= 0) { 
        tempArr[third++] = data[left++]; 
      } else { 
        tempArr[third++] = data[mid++]; 
      } 
    } 
    while (mid <= right) { 
      tempArr[third++] = data[mid++]; 
    } 
    while (left <= center) { 
      tempArr[third++] = data[left++]; 
    } 
    while (temp <= right) { 
      data[temp] = tempArr[temp++]; 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "") }; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    mergeSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}
結果:

##
排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]

##基數排序


基數排序已經不再是一種常規的排序方法,它更像是一種排序方法的應用,基數排序必須依賴另外的排序方法。

基數排序的整體想法就是將待排資料拆分成多個關鍵字進行排序,也就是說,基數排序的實質就是多關鍵字排序。

多關鍵字排序的想法是將待排資料裡的排序關鍵字拆分成多個排序關鍵字:第1個子關鍵字、第2個子關鍵字、第3個子關鍵字。 。 。然後,根據子關鍵字對待排資料進行排序。在進行多關鍵字排序時有兩種解決方案:最高位元優先法MSD
最低位元優先法LSD


#比較MSD法和LSD法,一般來講,LSD法要比MSD法來得簡單,因為LSD法是從頭到尾進行若干次分配和收集,執行

的次數取決於構成關鍵字值的成分為多少;而MSD法則要處理各序列與子序列的獨立排序問題,就可能複雜一些。


程式碼:

package interview; 
 
import java.util.Arrays; 
 
/** 
 * @author Administrator 
 * 基数排序 
 */ 
public class MultiKeyRadixSort { 
  public static void radixSort(int[] data, int radix, int d) { 
    System.out.println("开始排序:"); 
    int arrayLength = data.length; 
    int[] temp = new int[arrayLength]; 
    int[] buckets = new int[radix]; 
    for (int i = 0, rate = 1; i < d; i++) { 
      // 重置count数组,开始统计第二个关键字 
      Arrays.fill(buckets, 0); 
      // 当data数组的元素复制到temp数组中进行缓存 
      System.arraycopy(data, 0, temp, 0, arrayLength); 
      for (int j = 0; j < arrayLength; j++) { 
        int subKey = (temp[j] / rate) % radix; 
        buckets[subKey]++; 
      } 
      for (int j = 1; j < radix; j++) { 
        buckets[j] = buckets[j] + buckets[j - 1]; 
      } 
      for (int m = arrayLength - 1; m >= 0; m--) { 
        int subKey = (temp[m] / rate) % radix; 
        data[--buckets[subKey]] = temp[m]; 
      } 
      System.out.println("对" + rate + "位上子关键字排序:" 
          + java.util.Arrays.toString(data)); 
      rate *= radix; 
    } 
  } 
 
  public static void main(String[] args) { 
    int[] data = { 1100, 192, 221, 12, 13 }; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    radixSort(data, 10, 4); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}
結果

排序之前:
[1100, 192, 221, 12, 13]
开始排序:
对1位上子关键字排序:[1100, 221, 192, 12, 13]
对10位上子关键字排序:[1100, 12, 13, 221, 192]
对100位上子关键字排序:[12, 13, 1100, 192, 221]
对1000位上子关键字排序:[12, 13, 192, 221, 1100]
排序之后:
[12, 13, 192, 221, 1100]


快速排序


#程式碼:

#

package interview; 
/** 
 * @author Administrator 
 * 快速排序 
 */ 
public class QuickSort { 
  private static void swap(DataWrap[] data, int i, int j) { 
    DataWrap temp = data[i]; 
    data[i] = data[j]; 
    data[j] = temp; 
  } 
  private static void subSort(DataWrap[] data, int start, int end) { 
    if (start < end) { 
      DataWrap base = data[start]; 
      int i = start; 
      int j = end + 1; 
      while (true) { 
        while (i < end && data[++i].compareTo(base) <= 0) 
          ; 
        while (j > start && data[--j].compareTo(base) >= 0) 
          ; 
        if (i < j) { 
          swap(data, i, j); 
        } else { 
          break; 
        } 
      } 
      swap(data, start, j); 
      subSort(data, start, j - 1); 
      subSort(data, j + 1, end); 
    } 
  } 
  public static void quickSort(DataWrap[] data){ 
    subSort(data,0,data.length-1); 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "") }; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    quickSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}
結果

排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21, 21*, 23, 30*, 30]

######直接選擇排序####################################################### ##
package interview; 
/** 
 * @author Administrator 
 * 直接选择排序 
 */ 
public class SelectSort { 
  public static void selectSort(DataWrap[] data) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    for (int i = 0; i < arrayLength - 1; i++) { 
      for (int j = i + 1; j < arrayLength; j++) { 
        if (data[i].compareTo(data[j]) > 0) { 
          DataWrap temp = data[i]; 
          data[i] = data[j]; 
          data[j] = temp; 
        } 
      } 
      System.out.println(java.util.Arrays.toString(data)); 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = { new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "") }; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    selectSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}
#########
排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
[-49, 9, 21*, 23, -16, -30, 21, 30*, 30]
[-49, -30, 21*, 23, 9, -16, 21, 30*, 30]
[-49, -30, -16, 23, 21*, 9, 21, 30*, 30]
[-49, -30, -16, 9, 23, 21*, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 23, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
############Hyall排序###################################### ##########
package interview; 
/** 
 * @author Administrator 
 * Shell排序 
 */ 
public class ShellSort { 
  public static void ShellSort(DataWrap[] data) { 
    System.out.println("开始排序"); 
    int arrayLength = data.length; 
    int h = 1; 
    /** 
     * 将数组分割成若干个子序列 
     */ 
    while (h <= arrayLength / 3) { 
      h = h * 3 + 1; 
      System.out.println("h的结果:" + h); 
    } 
    while (h > 0) { 
      System.out.println("===h的值:" + h + "==="); 
      /** 
       * 将分成的若干子序列进行直接插入排序 
       */ 
      for (int i = h; i < arrayLength; i++) { 
        DataWrap temp = data[i]; 
        if (data[i].compareTo(data[i - h]) < 0) { 
          int j = i - h; 
          for (; j >= 0 && data[j].compareTo(temp) > 0; j -= h) { 
            data[j + h] = data[j]; 
          } 
          data[j + h] = temp; 
        } 
        System.out.println(java.util.Arrays.toString(data)); 
      } 
      h = (h - 1) / 3; 
    } 
  } 
  public static void main(String[] args) { 
    DataWrap[] data = {  
        new DataWrap(9, ""), new DataWrap(-16, ""), 
        new DataWrap(21, "*"), new DataWrap(23, ""), 
        new DataWrap(-30, ""), new DataWrap(-49, ""), 
        new DataWrap(21, ""), new DataWrap(30, "*"), 
        new DataWrap(30, "")}; 
    System.out.println("排序之前:\n" + java.util.Arrays.toString(data)); 
    ShellSort(data); 
    System.out.println("排序之后:\n" + java.util.Arrays.toString(data)); 
  } 
}
###結果:############
排序之前:
[9, -16, 21*, 23, -30, -49, 21, 30*, 30]
开始排序
h的结果:4
===h的值:4===
[-30, -16, 21*, 23, 9, -49, 21, 30*, 30]
[-30, -49, 21*, 23, 9, -16, 21, 30*, 30]
[-30, -49, 21*, 23, 9, -16, 21, 30*, 30]
[-30, -49, 21*, 23, 9, -16, 21, 30*, 30]
[-30, -49, 21*, 23, 9, -16, 21, 30*, 30]
===h的值:1===
[-49, -30, 21*, 23, 9, -16, 21, 30*, 30]
[-49, -30, 21*, 23, 9, -16, 21, 30*, 30]
[-49, -30, 21*, 23, 9, -16, 21, 30*, 30]
[-49, -30, 9, 21*, 23, -16, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 23, 21, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
排序之后:
[-49, -30, -16, 9, 21*, 21, 23, 30*, 30]
############所需的工具類別:### ##################
package interview;
public class DataWrap implements Comparable<DataWrap>{  
	 int data;  
	 String flag;  
	 public DataWrap(int data, String flag) {  
	   this.data = data;  
	   this.flag = flag;  
	 }  
	 public String toString(){  
	   return data + flag;  
	 }  
	 @Override  
	 public int compareTo(DataWrap dw) {  
	   return this.data > dw.data ?  
	       1 : (this.data == dw.data ? 0 : -1);  
	 }  
	}

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