/*
Leetcode 75

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 <= 5 * 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?
*/

package increasingtriplets

import "math"

func IncreasingTriplet(nums []int) bool {
	for i := 0; i < len(nums); i++ {
		for j := i + 1; j < len(nums); j++ {
			for k := j + 1; k < len(nums); k++ {
				if nums[i] < nums[j] && nums[j] < nums[k] {
					return true
				}
			}
		}
	}
	return false
}

func IncreasingTripletOptimal(nums []int) bool {
	first, second := math.MaxInt64, math.MaxInt64
	for _, num := range nums {
		if num <= first {
			first = num
		} else if num <= second {
			second = num
		} else {
			return true
		}
	}
	return false
}
