Stack-Based Approach to Detect 132 Pattern

[gautamjag7]

Intuition

We are looking for a subsequence in the array that follows the 132 pattern: a sequence where there exists indices i < j < k such that nums[i] < nums[k] < nums[j]. The key is to track the largest '2' in the 132 pattern using a stack.

Approach

1. Traverse the array in reverse (starting from the rightmost element).
2. Use a stack to keep track of potential '3' values in the 132 pattern.
3. Maintain a variable prev to store the most recent valid '2' found in the sequence.
4. For each element nums[i], check if it is less than the current prev ('2'). If yes, we've found a valid 132 pattern.
5. Update prev by popping from the stack, ensuring we always have the largest possible '2'.
6. Push the current element into the stack as a potential '3'.

Complexity

• Time complexity:
  The time complexity is ( O(n) ), where ( n ) is the size of the input array. Each element is pushed and popped from the stack at most once.

• Space complexity:
  The space complexity is ( O(n) ) in the worst case, due to the space used by the stack.

[HarshwardhanPatil07]

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