NC14326 Rails

NC14326 Rails

题目

题目描述

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.

输入描述

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.

输出描述

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.

示例1

输入

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

输出

Yes
No

Yes

题解

思路

知识点：栈。

这是一道理解栈的特点的题：元素按固定顺序入栈，给定一组结果序列，问是否可能做到。

因为入栈顺序是给定的，只能控制出栈时间。设置一个指针指向结果序列，随后按顺序入栈，每次入栈如果入栈元素和指针指向元素相同，则要立即出栈并将指针后挪一位，直到栈顶不是对应元素或者栈空；如果栈顶元素与指针指向元素不同或者栈空，则要入栈，直到出现相同的元素。

如果序列是不合法的，会发现按如上顺序操作（也是唯一可能的顺序），最后栈是非空的，因为序列中元素某些顺序是无法用栈来得到的。

时间复杂度 \(O(n)\)

空间复杂度 \(O(n)\)

代码

#include <bits/stdc++.h>

using namespace std;

int a[100007];

int main() {
    std::ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    int n;
    while (cin >> n, n) {
        while (cin >> a[1], a[1]) {
            stack<int> s;
            for (int i = 2;i <= n;i++) cin >> a[i];
            for (int i = 1, j = 1;i <= n;i++) {
                s.push(i);
                while (!s.empty() && s.top() == a[j]) s.pop(), j++;
            }
            if (!s.empty()) cout << "No\n";
            else cout << "Yes\n";
        }
        cout << '\n';
    }
    return 0;
}