Given a sequence of n integers a1, a2, ..., an, a 132 pattern is a subsequence ai, aj, ak such that i<j<k and ai< ak< aj. Design an algorithm that takes a list of n numbers as input and checks whether there is a 132 pattern in the list.
Note:n will be less than 15,000.
Example 1:
1
Input: [1, 2, 3, 4]
2
3
Output: False
4
5
Explanation: There is no 132 pattern in the sequence.
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Example 2:
1
Input: [3, 1, 4, 2]
2
3
Output: True
4
5
6
Explanation: There is a 132 pattern in the sequence: [1, 4, 2].
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Example 3:
1
Input: [-1, 3, 2, 0]
2
3
Output: True
4
5
6
Explanation: There are three 132 patterns in the sequence: [-1, 3, 2], [-1, 3, 0] and [-1, 2, 0].
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2. Implementation
(1) Monotone Stack
思路: 这题只要返回true or false，所以我们从后往前遍历数组，利用单调递减stack寻找第二大的数，一旦遍历的过程中找到一个前面的数小于第二大的数，则我们找到pattern