# 456. 132 Pattern

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:

Input: [1, 2, 3, 4]

Output: False

Explanation: There is no 132 pattern in the sequence.

Example 2:

Input: [3, 1, 4, 2]

Output: True

Explanation: There is a 132 pattern in the sequence: [1, 4, 2].

Example 3:

Input: [-1, 3, 2, 0]

Output: True

Explanation: There are three 132 patterns in the sequence: [-1, 3, 2], [-1, 3, 0] and [-1, 2, 0].

class Solution {
public:
bool find132pattern(vector<int>& nums) {
int n = nums.size(), mn = INT_MAX;
for (int j = 0; j < n; ++j) {
mn = min(mn, nums[j]);
if (mn == nums[j]) continue;
for (int k = n - 1; k > j; --k) {
if (mn < nums[k] && nums[j] > nums[k]) return true;
}
}
return false;
}
};

class Solution {
public:
bool find132pattern(vector<int>& nums) {int n = nums.size(), i = 0, j = 0, k = 0;
while (i < n) {
while (i < n - 1 && nums[i] >= nums[i + 1]) ++i;
j = i + 1;
while (j < n - 1 && nums[j] <= nums[j + 1]) ++j;
k = j + 1;
while (k < n) {
if (nums[k] > nums[i] && nums[k] < nums[j]) return true;
++k;
}
i = j + 1;
}
return false;
}
};

class Solution {
public:
bool find132pattern(vector<int>& nums) {
int third = INT_MIN;
stack<int> st;
for (int i = nums.size() - 1; i >= 0; --i) {
if (nums[i] < third) return true;
while (!st.empty() && nums[i] > st.top()) {
third = st.top(); st.pop();
}
st.push(nums[i]);
}
return false;
}
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/456

https://leetcode.com/problems/132-pattern/

https://leetcode.com/problems/132-pattern/discuss/94135/c_ac

https://leetcode.com/problems/132-pattern/discuss/94133/Simple-java-accepted-well-explained-O(n2)-solution

https://leetcode.com/problems/132-pattern/discuss/94071/single-pass-c-on-space-and-time-solution-8-lines-with-detailed-explanation

https://leetcode.com/problems/132-pattern/discuss/94089/Java-solutions-from-O(n3)-to-O(n)-for-%22132%22-pattern-(updated-with-one-pass-slution)

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