#1051. Pop Sequence【栈 + 模拟】

原题链接

Problem Description：

Given a stack which can keep $M$ numbers at most. Push $N$ numbers in the order of $1,2,3,\dots ,N$ and pop randomly. You are supposed to tell if a given sequence of numbers is a possible pop sequence of the stack. For example, if $M$ is 5 and $N$ is 7, we can obtain 1, 2, 3, 4, 5, 6, 7 from the stack, but not 3, 2, 1, 7, 5, 6, 4.

Input Specification:

Each input file contains one test case. For each case, the first line contains 3 numbers (all no more than 1000): $M$ (the maximum capacity of the stack), $N$ (the length of push sequence), and $K$ (the number of pop sequences to be checked). Then $K$ lines follow, each contains a pop sequence of $N$ numbers. All the numbers in a line are separated by a space.

Output Specification:

For each pop sequence, print in one line “YES” if it is indeed a possible pop sequence of the stack, or “NO” if not.

Sample Input:

5 7 5
1 2 3 4 5 6 7
3 2 1 7 5 6 4
7 6 5 4 3 2 1
5 6 4 3 7 2 1
1 7 6 5 4 3 2

Sample Output:

YES
NO
NO
YES
NO

Problem Analysis:

本题是一个栈模拟题，给定 $k$ 组弹出序列，对于每一组弹出序列，我们模拟栈压入弹出的过程进行判断即可。时间复杂度为 $O(n^2)$

Code

#include <iostream>
#include <algorithm>
#include <stack>

using namespace std;

const int N = 1010;

int n, m, k;
int a[N];

bool check()
{
    
    
    stack<int> stk;
    for (int i = 1, j = 0; i <= n; i ++ )
    {
    
    
        stk.push(i);
        if (stk.size() > m) return false;
        
        while (stk.size() && stk.top() == a[j])
        {
    
    
            stk.pop();
            j ++ ;
        }
    }
    return stk.empty();
}

int main()
{
    
    
    cin >> m >> n >> k;
    while (k -- )
    {
    
    
        for (int i = 0; i < n; i ++ ) scanf("%d", &a[i]);
        if (check()) puts("YES");
        else puts("NO");
    }

    return 0;
}