132 Pattern
Tags: leetcode, dsa, theabbie
Published: 2022-06-11 18:00:42

Given an array of `n` integers `nums`, a **132 pattern** is a subsequence of three integers `nums[i]`, `nums[j]` and `nums[k]` such that `i < j < k` and `nums[i] < nums[k] < nums[j]`.

Return `true` _if there is a **132 pattern** in_ `nums`_, otherwise, return_ `false`_._

**Example 1:**

**Input:** nums = \[1,2,3,4\]
**Output:** false
**Explanation:** There is no 132 pattern in the sequence.

**Example 2:**

**Input:** nums = \[3,1,4,2\]
**Output:** true
**Explanation:** There is a 132 pattern in the sequence: \[1, 4, 2\].

**Example 3:**

**Input:** nums = \[-1,3,2,0\]
**Output:** true
**Explanation:** There are three 132 patterns in the sequence: \[-1, 3, 2\], \[-1, 3, 0\] and \[-1, 2, 0\].

**Constraints:**

*   `n == nums.length`
*   `1 <= n <= 2 * 105`
*   `-109 <= nums[i] <= 109`

**SOLUTION:**

    class Solution:
        def find132pattern(self, nums: List[int]) -> bool:
            n = len(nums)
            if n < 3:
                return False
            stack = []
            k = -1
            for i in range(n - 1, -1, -1):
                if k > -1 and nums[k] > nums[i]:
                    return True
                while len(stack) > 0 and nums[i] > nums[stack[-1]]:
                    k = stack.pop()
                stack.append(i)
            return False
    
    # class Solution:
    #     def makeSeg(self, arr, i, j):
    #         seg = self.seg
    #         if (i, j) in seg:
    #             return seg[(i, j)]
    #         if i == j:
    #             seg[(i, j)] = arr[i]
    #             return arr[i]
    #         mid = (i + j) // 2
    #         curr = max(self.makeSeg(arr, i, mid), self.makeSeg(arr, mid + 1, j))
    #         seg[(i, j)] = curr
    #         return curr
        
    #     def getMax(self, arr, i, j, ni, nj):
    #         seg = self.seg
    #         if ni >= i and nj <= j:
    #             return seg[(ni, nj)]
    #         if (ni < i and nj < i) or (ni > j and nj > j):
    #             return float('-inf')
    #         mid = (ni + nj) // 2
    #         return max(self.getMax(arr, i, j, ni, mid), self.getMax(arr, i, j, mid + 1, nj))
        
    #     def find132pattern(self, nums: List[int]) -> bool:
    #         n = len(nums)
    #         self.seg = {}
    #         self.makeSeg(nums, 0, n - 1)
    #         for i in range(n):
    #             for j in range(i + 2, n):
    #                 if nums[j] > nums[i] and self.getMax(nums, i, j, 0, n - 1) > nums[j]:
    #                     return True
    #         return False
    
    # class Solution:
    #     def find132pattern(self, nums: List[int]) -> bool:
    #         n = len(nums)
    #         next_lowest = [n for i in range(n)]
    #         stack = []
    #         for i in range(n):
    #             while len(stack) > 0 and nums[i] < nums[stack[-1]]:
    #                 curr = stack.pop()
    #                 next_lowest[curr] = i
    #                 for j in range(curr):
    #                     if nums[j] < nums[i]:
    #                         return True
    #             stack.append(i)
    #         return False
    
    # class Solution:
    #     def find132pattern(self, nums: List[int]) -> bool:
    #         currMin = float('inf')
    #         currMax = float('-inf')
    #         for num in nums:
    #             currMin = min(currMin, num)
    #             currMax = max(currMax, num)
    #             if num > currMin and num < currMax:
    #                 return True
    #         return False