动态规划算法据序偶原理求解0/1背包问题(C++实现)
可程序根据序偶原理,应用动态规划算法求解。
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Code
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//说明:本程序有一定代码冗余,若分割为多个函数的形式会使程序简洁明了。
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#include <iostream>
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using namespace std;
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#include <queue>
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#include <stack>
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const int N=5; //物品个数,其中包括(0,0).
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const float W=60; //背包最大载重。
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struct GoodsStruct
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![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
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int ID; //物品编号
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float benefit; //物品效益
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float weight; //物品重量
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int com; //标记最优解中是否含有该物品,有则为1,没有则为0.
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};
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int main()
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![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
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GoodsStruct StructGoods;
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GoodsStruct StructTemp;
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GoodsStruct StructCom;
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GoodsStruct StructCalTemp;
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queue <GoodsStruct> QueueGoods; //存放原始物品信息的队列,用于求解集合,完后全部被弹出。
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queue <GoodsStruct> QueueSourse;//存放原始物品信息的队列,用于回溯过程,作为最后结果。
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queue <GoodsStruct> QueueTemp;
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queue <GoodsStruct> QueuePush;
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queue <GoodsStruct> QueueCom; //两个队列在支配规则下的合并结果队列。
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queue <GoodsStruct> QueueComTemp;//两个队列在支配规则下的合并时的临时变量。
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queue <GoodsStruct> QueueCalTemp;
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stack <queue<GoodsStruct>> StackGoods;
31![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
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/**//*float benefits[N]={0,2,2,1};//测试数据。
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float weights[N]={0,2,3,2};*/
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/**//*float benefits[N]={0,2,3,4};
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float weights[N]={0,1,2,5};*/
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float benefits[N]=
{0,2,5,8,1};
37![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
float weights[N]=
{0,10,15,6,9};
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bool check=false;
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//将物品信息存入队列和堆栈中。
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for (int i=0;i<N;i++)
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{
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StructTemp.ID=i;
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StructTemp.benefit=benefits[i];
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StructTemp.weight=weights[i];
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StructTemp.com=0;
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QueueSourse.push(StructTemp);
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}
49![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
50![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
/**///////////////////////////////////////////////////////////////////////////
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//求解集合
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//(0,0)先入栈。
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QueueGoods=QueueSourse;
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StructGoods=QueueGoods.front();
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QueueGoods.pop();
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QueuePush.push(StructGoods);
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StackGoods.push(QueuePush);
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while (!QueueGoods.empty())
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{
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StructGoods=QueueGoods.front();
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QueueGoods.pop();
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QueueTemp=QueuePush;
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//计算出临时队列的过程,此处使用支配规则。
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while (!QueueTemp.empty())
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{
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StructTemp=QueueTemp.front();
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QueueTemp.pop();
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StructTemp.benefit+=StructGoods.benefit;
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StructTemp.weight+=StructGoods.weight;
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QueueCalTemp=QueuePush;
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if (StructTemp.weight<=W)
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{
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while (!QueueCalTemp.empty())
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{
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StructCalTemp=QueueCalTemp.front();
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QueueCalTemp.pop();
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if (StructTemp.weight>=StructCalTemp.weight && StructTemp.benefit<StructCalTemp.benefit)
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{
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//支配规则把新值StructCom去掉。
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check=false;
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break;
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}
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else
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{
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check=true;
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}
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}
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if (check==true)
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{
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QueueComTemp.push(StructTemp);
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}
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}
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}
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//QueueComTemp与QueuePush通过支配规则进行合并,去掉不可能的解。
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while (!QueuePush.empty())
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{
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StructCom=QueuePush.front();
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QueuePush.pop();
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QueueTemp=QueueComTemp;
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while (!QueueTemp.empty())
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{
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StructTemp=QueueTemp.front();
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QueueTemp.pop();
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if (StructCom.weight>=StructTemp.weight && StructCom.benefit<StructTemp.benefit)
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{
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//支配规则把新值StructCom去掉。
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check=false;
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break;
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}
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else
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{
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check=true;
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}
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}
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if (check==true)
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{
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QueueCom.push(StructCom);
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}
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}
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//将QueueComTemp全部接入QueueCom中,因为QueueComTemp不会被支配掉。
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while (!QueueComTemp.empty())
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{
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StructTemp=QueueComTemp.front();
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QueueComTemp.pop();
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QueueCom.push(StructTemp);
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}
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StackGoods.push(QueueCom);
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QueuePush=QueueCom;
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while (!QueueCom.empty())
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{
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QueueCom.pop();
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}
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}
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/**///////////////////////////////////////////////////////////////////////////
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//求解最终序偶
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QueueTemp=StackGoods.top();
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StructGoods=QueueTemp.back();
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while (!QueueTemp.empty())
143![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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StructTemp=QueueTemp.front();
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QueueTemp.pop();
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if (StructGoods.weight<StructTemp.weight)
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{
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StructGoods=StructTemp;
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}
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}
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cout<<"(P,W)=("<<StructGoods.benefit<<","<<StructGoods.weight<<")"<<endl;
152![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
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/**///////////////////////////////////////////////////////////////////////////
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//回溯
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int count=N-1;
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StackGoods.pop();
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while(!StackGoods.empty())
158![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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QueueTemp=StackGoods.top();
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StackGoods.pop();
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while (!QueueTemp.empty())
162![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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StructTemp=QueueTemp.front();
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QueueTemp.pop();
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if (StructTemp.benefit==StructGoods.benefit && StructTemp.weight==StructGoods.weight)
166![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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check=false;
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for (int i=0;i<N;i++)
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{
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StructCalTemp=QueueSourse.front();
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QueueSourse.pop();
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if (StructCalTemp.ID==count)
173![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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StructCalTemp.com=0;
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}
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QueueSourse.push(StructCalTemp);
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}
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break;
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}
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else
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{
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check=true;
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}
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}
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if (check==true)
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{
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for (int i=0;i<N;i++)
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{
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StructCalTemp=QueueSourse.front();
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QueueSourse.pop();
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if (StructCalTemp.ID==count)
192![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
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StructCalTemp.com=1;
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}
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QueueSourse.push(StructCalTemp);
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}
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StructGoods.benefit-=StructCalTemp.benefit;
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StructGoods.weight-=StructCalTemp.weight;
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}
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count--;
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}
202![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
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QueueSourse.pop();
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while(!QueueSourse.empty())
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{
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StructTemp=QueueSourse.front();
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QueueSourse.pop();
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cout<<"X"<<count+1<<"="<<StructTemp.com<<endl;
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count++;
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}
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return 0;
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}
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