编程之美——快速找出机器故障问题

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题目：

　　简化后问题：有很多机器id，其中只有一个或两个id被丢失，正常情况下每个id个数为2，请问如何找到丢失的id是几。

java解法一实现：

/**
* 使用异或操作　Ｘ异或X等于０，X异或0等于X，所有元素异或结果就是丢失的元素
* 如果丢失id个数为2，异或结果就是A异或B的结果，然后将数组分成两组，分别找出来。
* @author zhaozh
*
*/
public class MachineErrorID1 {
   private int[] machineIds;//所有机器id列表
   private int[] deleteIdIndexes;//丢失的机器id列表索引
   private int[] lostIds;//丢失的机器id

   public MachineErrorID1(int[] machineIds, int[] deleteIdIndexes){
       this.machineIds = new int[machineIds.length - deleteIdIndexes.length];
       int k = 0;
       for(int i = 0; i < machineIds.length; i++){//初始化丢失id后的机器id列表
           boolean flag = true;
           for (int j = 0; j < deleteIdIndexes.length; j++){
               if(i == deleteIdIndexes[j])
                   flag = false;//被删除
           }
           if(flag){
               this.machineIds[k++] = machineIds[i];
           }
       }
       this.deleteIdIndexes = deleteIdIndexes;
       this.lostIds = new int[deleteIdIndexes.length];
   }

   public void findLostmachineIds(){
       if(deleteIdIndexes.length == 1){
           lostIds[0] = findLostMachineId();
       }else{
           int i_result = findLostMachineId();
           lostIds = findLostMachineId(i_result);
       }
   }

   private int[] findLostMachineId(int i_result){
       if(i_result == 0){
           System.out.println("被删除的两个id是一样的，我找不出来了。");
           return null;
       }else{
           int i_temp = 1;
           while((i_result & i_temp) == 0)
               i_temp = i_temp << 2;
           int[] i_lostIds = new int[2];
           for(int i = 0; i < machineIds.length; i++){
               if((i_temp & machineIds[i]) == 0){
                   i_lostIds[0] = i_lostIds[0] ^ machineIds[i];
               }else if((i_temp & machineIds[i]) != 0){
                   i_lostIds[1] = i_lostIds[1] ^ machineIds[i];
               }
           }
           return i_lostIds;
       }
   }

   private int findLostMachineId(){
       int i_lostId = 0;
       for (int i = 0; i < machineIds.length; i++) {
           i_lostId = i_lostId ^ machineIds[i];
       }
       return i_lostId;
   }

   public void output(){
       if(lostIds != null){
           System.out.println("the lost machine id is :" );
           for(int i = 0; i < lostIds.length; i++){
               System.out.print(" " + lostIds[i]);
           }
       }
   }

   public static void main(String[] args) {
       int[] machineIds = new int[]{1,1,2,2,3,3,4,4,5,5};
       int[] deleteIdIndexes = new int[]{1,9};

       MachineErrorID1 machineErrorId = new MachineErrorID1(machineIds, deleteIdIndexes);
       machineErrorId.findLostmachineIds();
       machineErrorId.output();
   }

}

java解法二实现：

/**
* 原理：末丢失id前的id总和，减去丢失id后的总和，就是丢失的id。
* 如果丢失一下，就可以直接找出来
* 如果丢失的是两个，就要再构造一个方程，如丢失前后，所有id的乘积之差（防止溢出也可以是　所有id的平方和）。由x+y=a,x*y=b求出x,y
* @author zhaozh
*
*/
public class MachineErrorID2 {
   private int[] machineIds;//所有机器id列表
   private int[] deleteIdIndexes;//丢失的机器id列表索引
   private int[] lostIds;//丢失的机器id
   private int sum_ids;//丢失前id的和
   private int mult_ids;//丢失前id的积

   public MachineErrorID2(int[] machineIds, int[] deleteIdIndexes){
       this.machineIds = new int[machineIds.length - deleteIdIndexes.length];
       int k = 0;
       for(int i = 0; i < machineIds.length; i++){//初始化丢失id后的机器id列表
           boolean flag = true;
           for (int j = 0; j < deleteIdIndexes.length; j++){
               if(i == deleteIdIndexes[j])
                   flag = false;//被删除
           }
           if(flag){
               this.machineIds[k++] = machineIds[i];
           }
       }
       for(int i = 0; i < machineIds.length; i++){//计算id的和
           sum_ids += machineIds[i];
       }
       if(deleteIdIndexes.length > 1){//计算id的积
           mult_ids = machineIds[0];
           for(int i = 1; i < machineIds.length; i++){
               mult_ids *= machineIds[i];
           }
       }
       this.deleteIdIndexes = deleteIdIndexes;
       this.lostIds = new int[deleteIdIndexes.length];
   }

   public void findLostmachineIds(){
       if(deleteIdIndexes.length == 1){
           lostIds[0] = sumMachineId();
       }else{
           int i_multi = multiMachineId();
           int i_sum = sumMachineId();
           lostIds[1] = (int) ((i_sum + Math.sqrt(i_sum * i_sum - 4 * i_multi))/2);
           lostIds[0] = i_sum - lostIds[1];
       }
   }

   private int multiMachineId(){
       int i_multids = machineIds[0];
       for(int i = 1; i < machineIds.length; i++){
           i_multids *= machineIds[i];
       }
       return this.mult_ids / i_multids;
   }

   private int sumMachineId(){
       int i_lostId = 0;
       for (int i = 0; i < machineIds.length; i++) {
           i_lostId += machineIds[i];
       }
       return this.sum_ids - i_lostId;
   }

   public void output(){
       if(lostIds != null){
           System.out.println("the lost machine id is :" );
           for(int i = 0; i < lostIds.length; i++){
               System.out.print(" " + lostIds[i]);
           }
       }
   }

   public static void main(String[] args) {
       int[] machineIds = new int[]{1,1,2,2,3,3,4,4,5,5};
       int[] deleteIdIndexes = new int[]{1,9};

       MachineErrorID2 machineErrorId = new MachineErrorID2(machineIds, deleteIdIndexes);
       machineErrorId.findLostmachineIds();
       machineErrorId.output();
   }

}

输出结果：

the lost machine id is :
1 5

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