7-3 Pop Sequence (25 分)

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
NO
NO
YES
NO

【解题】

用的python写的题：

序列要同时满足两点才可能弹出：

• 某个数字P_i后面的序列，去除比P_i小的数字之后的序列必须是逆序。（原理见铁路调度问题）
• 因为栈的最大容量是M，所有序列的前N-M-1个数字分别不能大于M,M+1,M+2,...,M+(N-M-1)

import numpy as np
def solution(M,N,L):
    for i in range(N-M):
        if L[i]>M+i:
            return("NO")
    for i in range(N-3,-1,-1):
        tmp_L=np.array(L[i+1:])
        idx=tmp_L<np.repeat(L[i],len(tmp_L))
        tmp_L=list(tmp_L[idx])
        if not sorted(tmp_L,reverse=True)==tmp_L:
            return ("NO")
    return("YES")
if __name__=='__main__':
    M,N,K=tuple(map(int,raw_input().split(" ")))
    for i in range(K):
        L=map(int,raw_input().split(" "))
        print(solution(M,N,L))