334. Increasing Triplet Subsequence

Description of Problem

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 * 10^5
-2^31 <= nums[i] <= 2^31 - 1

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

Solution

Code

impl Solution {
    pub fn increasing_triplet(nums: Vec<i32>) -> bool {
        let (mut smaller, mut bigger) = (i32::MAX, i32::MAX);
        for n in nums.into_iter(){
            // keep updating the smaller and bigger
            if n <= smaller {smaller = n;}
            else if n <= bigger {bigger = n;}
            // until we find the biggest
            else {return true;}
        }
        return false;
    }
}

Complexity

n is length of nums

Time Complexity

\( T(n) = O(n) \)

Auxiliary Space

\( S(n) = O(1) \)

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