线性结构 Pop Sequence

Given a stack which can keep M numbers at most. Push N numbers in the order of 1, 2, 3, ..., 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.

输入样例:

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

输出样例:

YES
NO
NO
YES
NO

题解

判断出栈序列是否合法，可以用一个栈来模拟出栈顺序。先判断栈是否为空或栈顶元素是否与序列相等，空或者不相等则按照顺序将元素入栈，直到相等或已全部入栈。入栈时要判断栈满，栈满则不能入栈，序列非法。最后栈应该为空，不为空非法。
如序列3 2 1 7 5 6 4，一开始为3，栈空，按照顺序入栈，1，2，3，然后3出栈，2出栈，1出栈。到7，按照顺序入栈4，5，6，7，7出栈。到5与栈顶元素不同，且元素已全部入栈，栈非空，序列非法。

c代码

#include <stdio.h>
#include <stdlib.h>

int k, n, m;

int main() {
    scanf("%d%d%d", &m, &n, &k);
    int* stack = (int *)malloc(sizeof (int) * (m + 5));
    int* sq = (int *)malloc(sizeof (int) * (n + 5));
    
    while (k--) {
        int top = -1;
        for (int i = 1; i <= n; i++) scanf("%d", &sq[i]);   //读入出栈序列
        
        for (int i = 1, j = 1; i <= n; i++ ) {
            stack[++top] = i;    //按顺序入栈
            if(top >= m)  break;   //栈满，非法
            while(top != -1 && stack[top] == sq[j]) {    //判断栈顶元素是否与序列相同
                top--;   
                j++;
            }
        }
        
        if(top == -1)  puts("YES");
        else  puts("NO");
    }
    
    return 0;
}