# Find Increasing Triplet Sub-sequence

Objective: Given an integer array A[1..n], find an instance of i,j,k where 0 < i < j < k <= n and A[i] < A[j] < A[k].

Example :

```int arrA[] = { 10, 9, 4, 3, 2, 1, 7, 3, 1, 11, 2, 6, 9 };
Output :
Increasing triplets are

1, 7, 11
1, 2, 6
1, 3, 9

likewise you can find more triplets.
```

Approach:

Naive Solution : Brute-Force O(n^2) – Use two for loops and try every triplet till you find the increasing triplet.

Better Solution : O(n)

• Cre­ate 2 Aux­i­lary Arrays say Lmin[] and Rmax[] of the same size as main array
• Put Lmin[0]=0 and Rmax[Rmax.length-1] =Rmax.length-1
• Tra­verse the main array and fill the Lmin array with the index posi­tion which has the min­i­mum value so far
• Tra­verse the main array back­words and fill the Rmax array with the index posi­tion which has the max­imun value so far.
• Now Traverse the main array and check for the element with the following condition and print it.

arrA[Lmin[i]] < arrA[i] && arrA[Rmax[i]] > arrA[i]

Code:

Output:

`Triplet 1 7 11`

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