18. Increasing Triplet Subsequence.cpp

/*
Increasing Triplet Subsequence
==============================

Given an integer array nums, return true if there exists a triple of indices (i, j, k) such that i < j < k and nums[i] < nums[j] < nums[k]. If no such indices exists, return false.

Example 1:
Input: nums = [1,2,3,4,5]
Output: true
Explanation: Any triplet where i < j < k is valid.

Example 2:
Input: nums = [5,4,3,2,1]
Output: false
Explanation: No triplet exists.

Example 3:
Input: nums = [2,1,5,0,4,6]
Output: true
Explanation: The triplet (3, 4, 5) is valid because nums[3] == 0 < nums[4] == 4 < nums[5] == 6.

Constraints:
1 <= nums.length <= 105
-231 <= nums[i] <= 231 - 1

Follow up: Could you implement a solution that runs in O(n) time complexity and O(1) space complexity?
*/

class Solution
{
public:
  bool increasingTriplet(vector<int> &nums)
  {
    int n = nums.size();
    vector<int> mi(n, 0), ma(n, 0);

    int curr = INT_MAX;
    for (int i = 0; i < n; ++i)
    {
      curr = min(curr, nums[i]);
      mi[i] = curr;
    }

    curr = INT_MIN;
    for (int i = n - 1; i >= 0; --i)
    {
      curr = max(curr, nums[i]);
      ma[i] = curr;
    }

    for (int i = 0; i < n; ++i)
    {
      if (mi[i] < nums[i] && nums[i] < ma[i])
        return true;
    }

    return false;
  }
};