Week 1 # D Rails

Posted 2020-09-29

原题描述：

D - Rails

 

Description

There is a famous railway station in PopPush City. Country there is incredibly hilly. The station was built in last century. Unfortunately, funds were extremely limited that time. It was possible to establish only a surface track. Moreover, it turned out that the station could be only a dead-end one (see picture) and due to lack of available space it could have only one track. 

 

The local tradition is that every train arriving from the direction A continues in the direction B with coaches reorganized in some way. Assume that the train arriving from the direction A has N <= 1000 coaches numbered in increasing order 1, 2, ..., N. The chief for train reorganizations must know whether it is possible to marshal coaches continuing in the direction B so that their order will be a1, a2, ..., aN. Help him and write a program that decides whether it is possible to get the required order of coaches. You can assume that single coaches can be disconnected from the train before they enter the station and that they can move themselves until they are on the track in the direction B. You can also suppose that at any time there can be located as many coaches as necessary in the station. But once a coach has entered the station it cannot return to the track in the direction A and also once it has left the station in the direction B it cannot return back to the station. 

Input

The input consists of blocks of lines. Each block except the last describes one train and possibly more requirements for its reorganization. In the first line of the block there is the integer N described above. In each of the next lines of the block there is a permutation of 1, 2, ..., N. The last line of the block contains just 0. 

The last block consists of just one line containing 0.

Output

The output contains the lines corresponding to the lines with permutations in the input. A line of the output contains Yes if it is possible to marshal the coaches in the order required on the corresponding line of the input. Otherwise it contains No. In addition, there is one empty line after the lines corresponding to one block of the input. There is no line in the output corresponding to the last ``null‘‘ block of the input.

Sample Input

5
1 2 3 4 5
5 4 1 2 3
0
6
6 5 4 3 2 1
0
0

Sample Output

Yes
No

Yes

这个题目用到了栈，为此我还看了下书。不过还是蛮容易的。我就在草稿纸上画了三个方框来表示，一个表示原本的排车顺序就是递增的那种。再一个就是表示出战的顺序。还有一个表示栈。

我们从出战第一个和进站第一个相比较，如果相同就直接过去，如果不同，我们判断一下栈里面又没有，有的话就直接上去继续判断。看下就把进站的车放进去，这样直到进站没有车，如果出站的车还没按顺序出去就说明这种出战方式不存在。直接判断Yes No。

要注意的是案例和出站顺序都是用0来表示的。栈的头文件#include <stack>栈的定义  stack <栈的类型> 栈的名称 栈是先进先出，并且只能取顶端数。我们这里用到了

top()函数：取栈的顶端元素，但不删除。

pop()函数：删除顶端元素。

empty()：如果栈的值为空就返回 1 否则 0 。

push()函数：在顶端加入新元素。

AC代码：

 1 #include <iostream>
 2 #include <stack>
 3 using namespace std;
 4 const int N=1010;
 5 int main()
 6 {
 7     int n;
 8      while(cin>>n&&n)
 9      {
10          int a[n+2],b[n+1],g;
11          while(cin>>b[1])
12          {
13              g=1;
14              if(b[1]==0){cout<<endl;break;}
15              a[1]=1;a[n+1]=0;
16              for(int i=2;i<=n;i++)
17             {
18                 cin>>b[i];
19                 a[i]=i;
20             }
21             stack <int> c;
22             int i=1,j=1;
23             while(j<=n)
24             {
25                 if(a[i]==b[j]) {i++;j++;}
26                 else if(!c.empty()&&b[j]==c.top()) {j++;c.pop();}
27                     else if(i<=n) {c.push(a[i]);i++;}
28                     else {g=0;break;}
29             }
30             if(g==1) cout<<"Yes"<<endl;
31             else cout<<"No"<<endl;
32          }
33      }
34     return 0;
35 }