02-线性结构4 Pop Sequence-优快云博客

本文链接：https://blog.youkuaiyun.com/Johnson_yjs/article/details/106883999

本文介绍了一种算法，用于判断给定的序列是否可能为有限容量栈的弹出序列。通过模拟进栈和出栈的过程，文章详细解释了如何检查一个序列是否符合栈操作的规则，并提供了完整的代码实现。

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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.

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

原题网页：https://pintia.cn/problem-sets/1268384564738605056/problems/1271415149946912771

思路：模拟进栈出栈的动作，以所给需要判断的出栈序列进行循环与栈顶元素进行比较：；< 则break，判断为NO；= 出栈一次，continue； > 持续进栈直到相等，然后判断当前栈的size是否大于栈的允许容量，大于则break否则出栈一次；循环结束后，如果栈为空，则YES，否则NO。

代码如下：

#include <stdio.h>
#include <malloc.h>
#define MaxSize 1000

typedef int ElemType;
typedef struct
{
    ElemType data[MaxSize];
    int top;
} SqStack;

void InitStack(SqStack *&s)
{
    s = (SqStack*)malloc(sizeof(SqStack));
    s->top = -1;
}

bool Push(SqStack *&s, ElemType e)
{
    if (s->top == MaxSize - 1) 
        return false;
    s->top++;
    s->data[s->top] = e;
    return true;
}

bool Pop(SqStack *&s)
{
    if (s->top == -1)
        return  false;
    s->data[s->top] = 0;
    s->top--;
    return true;
}

int main()
{
    int M, N, K;
    scanf("%d %d %d", &M, &N, &K);
    for (int i=0; i<K; i++)
    {
        SqStack *s;
        InitStack(s);
        int num = 0;
        int a[MaxSize] = {0};
        for (int j=0; j<N; j++)
            scanf("%d", &a[j]);
        for (int j=0; j<N; j++)
        {
            if (s->top == -1)
                Push(s, ++num);
            if (s->data[s->top] > a[j])
                break;
            if (s->data[s->top] == a[j])
            {
                Pop(s);
                continue;
            }    
            while(s->data[s->top] < a[j])
                Push(s, ++num);
            if (s->top > M-1)
                break;
            else
                Pop(s);  
        }
        if (s->top == -1)
            printf("YES\n");
        else
            printf("NO\n");
    }
}