UVa_514 - Rails

最新推荐文章于 2024-11-10 02:14:24 发布

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本文介绍了一个经典的列车调度问题，通过模拟进出站流程判断给定的车厢序列是否可以通过特定的车站进行合法调度。文章提供了详细的解题思路及实现代码。

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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.

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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 $N \leŸ 1000$ coaches numbered in increasing order $1, 2, \dots, N$ . 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 $a_1. a_2, \dots, a_N$ . 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 file 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 $1, 2, \dots, N$ The last line of the block contains just 0.

The last block consists of just one line containing 0.

Output

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

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

题意：

判定给定序列是否合法，合法Yes,否则No.

解体思路：

1. 实质上是一个判定出栈序列是否合法的问题；

2. 用一数组a保存给定的出栈序列，A标示出栈序列的下标，初始A=1；

一个栈rail保存模拟输入的值，B标示进栈的值，初始B=1；

3. 分几种情况：

（1）当B=a[A] A++; B++; 直接跳过；

（2）栈rail非空且栈顶值等于a[A] rail出栈且A++

（3）上述二种情况不成立，且B<=N,rail入栈

（4）其余，直接break

代码如下：

#include<iostream>
#include<cstdio>
#include<string>
#include<stack>
using namespace std;

const int MAX=1005;
int a[MAX];
int main()
{
    int N,i;
    while(cin>>N&&N!=0)
    {
        while(cin>>a[1]&&a[1]!=0)
        {
            for(i=2;i<=N;i++) cin>>a[i];
            stack<int> rail;
            int A=1;//标示已知的输出序列
            int B=1;//标示输入，从1~N
            while(A<=N)
            {
                if(B==a[A]) {A++;B++;}
                else if(!rail.empty()&&rail.top()==a[A]) { rail.pop(); A++; }
                else if(B<=N) { rail.push(B++);}
                else break;
            }
            if(rail.empty()) cout<<"Yes"<<endl;
            else cout<<"No"<<endl;
        }
        cout<<endl;
    }
	return 0;
}