456. 132 Pattern

Problem

Given an array of n integers nums, a 132 pattern is a subsequence of three integers nums[i], nums[j] and nums[k] such that i < j < k and nums[i] < nums[k] < nums[j].

Return true** if there is a 132 pattern in nums, otherwise, return false.**

  Example 1:

Input: nums = [1,2,3,4]
Output: false
Explanation: There is no 132 pattern in the sequence.

Example 2:

Input: nums = [3,1,4,2]
Output: true
Explanation: There is a 132 pattern in the sequence: [1, 4, 2].

Example 3:

Input: nums = [-1,3,2,0]
Output: true
Explanation: There are three 132 patterns in the sequence: [-1, 3, 2], [-1, 3, 0] and [-1, 2, 0].

  Constraints:

• n == nums.length

• 1 <= n <= 2 * 10^5

• -10^9 <= nums[i] <= 10^9

Solution (Java)

class Solution {
    /*
     * It scans only once, this is the power of using correct data structure.
     * It goes from the right to the left.
     * It keeps pushing elements into the stack,
     * but it also keeps poping elements out of the stack as long as the current element is bigger than this number.
     */
    public boolean find132pattern(int[] nums) {
        Deque<Integer> stack = new LinkedList<>();
        int s3 = Integer.MIN_VALUE;
        for (int i = nums.length - 1; i >= 0; i--) {
            if (nums[i] < s3) {
                return true;
            } else {
                while (!stack.isEmpty() && nums[i] > stack.peek()) {
                    s3 = Math.max(s3, stack.pop());
                }
            }
            stack.push(nums[i]);
        }
        return false;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).